Chapter 8

The Answers

Chapter 1

  1. A well written sample essay that will score well on the GMAT exam is shown below:

    The speaker, perhaps in an attempt to make an argument that battles persistent and unfair stereotypes about young people who enjoy playing role playing games, makes a leap in logic that leads to a flawed argument. Her premises are flawed, and thus, her conclusion (that more people should play role playing games) is unsupported.

    To begin with, let’s consider the premises of the argument. The speaker states one stereotype about RPG players that is undoubtedly persistent and unfair, the idea that they are “nerds without social skills.” But in order to refute this idea, she provides a statistic from a survey that states that young adults who play RPGs value social skills and courtesy more than those who were surveyed 10 years ago. There are two essential flaws in the premise of that argument.

    First, the speaker fails to recognize that the survey she is using asked the same group — young people who play RPG’s — ten years apart. Suggesting that RPGs are the reason the young people value social skills and courtesy now fails to recognize that, according to the survey, 10 years ago, young people who play RPGs did not value social skills and courtesy. It’s clear that what has changed cannot be the playing of RPGs, which the group that is being surveyed does as a precondition of being part of the group.

    The second essential flaw is that the speaker fails to connect the results of the survey, which indicate that young people who play RPGs “value” social skills and courtesy, with her interpretation, which is that the evidence suggests that role playing games “are actually promoting social interaction and friendship.” The logic is stretched too far. One can value something without promoting it. It’s also worth noting that “promoting” an ideal and “practicing” an ideal are not the same thing. By conflating these three distinct ideas, the speaker weakens her already flawed argument. It would be better if she stated that those who value a quality will often seek to practice it themselves.

    Additionally, whether or not RPG players value, promote, or practice social skills and courtesy, this is a strange premise to support the idea that more people should play RPGs. There are many more qualities about RPGs that might make them alluring to new players, and these qualities have nothing to do with whether their co-players are courteous or good have social skills, or whether their own social skills will be improved by playing RPGs. These include an interest in the created narrative and the enjoyment in feeling like one is immersed in a fantastical world.

    It’s admirable of this speaker to try to eradicate a tired cliché about young people who participate in role-playing games. The statistic that she provides, however, is not well used in making this argument. Instead of her current flawed logic, the speaker might point out that the change in valuing “social skills and courtesy” over the last 10 years among RPG players shows that they have become increasingly aware of their false reputation and wish to show that they do not fit the stereotype. The idea that they “value” these qualities most likely goes hand in hand with practicing them themselves, and thus welcome new players. The speaker might also suggest other, more compelling reasons for new players to try RPGs. It’s likely that the speaker would do better to find a different statistic or anecdotal proof to make her case. As the argument stands now, it is too flawed to carry much weight.

    This essay would likely score a 6 (out of 6) on the GMAT. It fulfills the prompt by considering and explaining the questionable assumptions that underline the speaker’s principal argument, and showing how or why those assumptions are likely misinterpretations. The essay is well organized and moves smoothly, with plenty of transitions between ideas. The writer also proposes alternative evidence that could help the speaker strengthen her argument. Finally, the tone throughout is notably even. The writer of this essay praises the speaker’s assumed good will and is gentle in rebuking her flawed ideas.

  2. A well written sample essay that will score well on the GMAT exam is shown below:

    Most of us have faced a so-called “hard sell,” when a salesperson reaches too far and acts too aggressively in a desperate attempt to secure our business. Unfortunately, that’s what’s happened with the Stipesville Business Directory’s mailing as shown in the prompt. The advertisement uses faulty logic to make a flawed argument that may ultimately turn potential advertisers away from the Directory, instead of increasing sales.

    The premise is wrong from the first line, which states that “one of the best ways to reach new customers is also one of the cheapest.” This line of thinking is doesn’t make much sense, as no facts or figures are provided to show that the Business Directory is an inexpensive choice compared to other means of alerting potential customers about one’s business. It also assumes that local business owners value “cheapness,” which may not be true.

    The ad continues to make a flawed argument with the statement that “local business owners” who bought ads in the Directory in past years will testify that doing so is “one of the best” ways to reach new customers. This argument has no meat to it since no testimonials from local business owners are included. It’s possible that the Directory is more helpful for businesses like repair shops, which rely on serving customers faced with emergencies, than businesses like hair salons, which rely on repeat customers and word of mouth. But that argument is not considered here.

    Perhaps the most glaring error in the ad is the assumption presented in the listing of “three of our town’s top doctors, two of our top-five caterers, and several of our top dog groomers” who bought ads last year. There’s no means provided of understanding what “top” means here: Are these businesses the top in a local newspaper’s customer satisfaction survey or the top in money earned or some other means of measuring their success? And by what means is their success, however it is measured, tied to their participation in the business Directory? This information is not explained and thus equates participation in the Stipesville Business Directory with success as a business in a way that is not at all clear.

    Additionally, this flawed logic continues with an anecdote about an unnamed hairdresser who apparently attributes her 5% drop in business to not purchasing an ad in the Stipesville Business Directory. This is flimsy evidence, and without knowing more about the hairdresser, we cannot be sure that the drop in her business is related to her failure to place an ad in the Directory. Her business might be located in an area of Stipesville where construction has taken place over several months, causing a decrease in visitors. Or she might have taken a vacation of a month or more, during which time her business would obviously see a decrease in earnings.

    The shoddiness of the arguments presented ends up making the Stipesville Business Directory seem like an organization that’s overaggressive and abrasive, which is unfortunate. The inclusion of more detailed testimonials from satisfied local business owners who bought ads would provide more convincing, if anecdotal, evidence. The Directory’s compilers might also try to accrue more convincing figures, perhaps by surveying local businesses before and after they’ve placed ads. This sort of information, presented coherently, would ultimately be much more convincing to local business who are on the fence about placing an ad in the Stipesville Business Directory.

    This essay would likely score a 6 (out of 6) on the GMAT. It fulfills the prompt by considering and explaining the questionable assumptions that underline the speaker’s principal argument, and showing how or why those assumptions are unconvincing in a piece of writing that seeks, above all, to convince. The essay is well organized and moves smoothly, using transitions between ideas well, working down the advertisement in a way that makes natural sense. The writer also proposes alternative ways that the ad could be written to make it more convincing. While the tone of this essay borders on being too harsh, the case made here is very convincing.

  3. A well written sample essay that will score well on the GMAT exam is shown below:

    Imagine telling a group of high school seniors that their prom, senior trip, senior work day, and the school musical have been cancelled. Why? They need to focus on raising their test scores on a standardized test that in no way benefits them, but only helps the school from which they will soon graduate — the very school that just cancelled all their senior activities. If the school board member quoted in the argument gets his way, that’s exactly what will happen.

    The argument he makes is not just cruel but deeply flawed. To begin with, he does not prove his opening premise, that the students at Richmeade Senior High School (RSHS) are scoring poorly on their standardized test. He fails to point out that the only standardized test given in June is an exit test for graduating high school seniors, and that RSHS has never required students to sit for it unlike Richmeade Prep. It’s also possible that, as is typical for a private school, Richmeade Prep has a smaller class than Richmeade Senior High School.

    It would be most practical to simply make taking the test mandatory for all graduating RSHS seniors. That would significantly improve the scores. But instead of suggesting that, the school board member presents another flawed argument. He points out that Richmeade Prep School doesn’t offer any extracurricular or special activities during the month before the test is given and suggests that RSHS try the same thing. He mentions but fails to grasp the important fact that Richmeade Prep School gives the test in May, after they may have had a two-week break for spring break and/or spring holidays, which is typical for American high schools. Thus, the students are only required to focus on the test for two weeks instead of a month.

    But more importantly, there is faulty logic at work here. The elimination of extracurricular and special activities does not automatically lead to an uptick in students’ studying for their standardized tests. Indeed, even if students react without the rancor suggested in the first paragraph, there’s no reason to think that they’ll spend more time in test preparation. The standardized tests do not benefit the students taking them, even if their scores are very high.

    There are ideas that might do better to increase students’ desire to both sit for and do well on the tests. A program might be presented which demonstrates to students how high scores on the test would benefit the younger students in the school, for example. Or the RSHS might move the testing forward to the same timeframe as Richmeade Prep, and thus make the senior activities a reward for doing well on it. A discount on Senior Prom tickets might be given to any senior who takes the test. Finally, simply requiring that students at Richmeade Senior High School take the test, the way that Richmeade Prep does, will go a long way toward solving the problem.

    No matter what other ideas are tried, it’s clear that the connection between Richmeade Prep’s test scores and the RSHS is tangential at best. There are financial reasons for a school to want to do well on a standardized test, so it may be worthwhile to develop a new plan. But this will require far greater research, and a better understanding of logical cause and effect, to avoid the disaster suggested in the opening paragraph.

    This essay would likely score a 6 (out of 6) on the GMAT. It fulfills the prompt by considering and explaining the questionable assumptions that underline the speaker’s principal argument. The writer unpacks the lengthy series of false assumptions that the speaker has made in a well-organized way. It transitions clearly from one idea to the next. The writer validates the concern the speaker has but shows alternative ways for the concern to be addressed. Finally, the writer opens with a gripping idea that should propel readers to continue.

  4. A well written sample essay that will score well on the GMAT exam is shown below:

    The article in a conventional cosmetic industry newsletter makes one case for why a customer might not need to buy organic makeup products. The author of this article is writing on behalf of the conventional cosmetics industry and clearly wants to undercut the growing movement towards buying organic cosmetics. However, the argument presented here is not convincing and might even drive more business into organic cosmetics!

    The author relies on selected facts from a study of the chemical class Zbt, mentioning that chemical class Zbt has never been shown to cause scarring on human test subjects. While this fact may be true, using it reveals that it has been shown to cause scarring in animal studies. This begs the question as to whether any studies have been done on human subjects at all! Clearly, this is poor logic. In a situation in which a conventional cosmetic industry employee is trying to convince a potential customer to buy their product using this fact, many potential customers would not be convinced. They might ask not only if tests were ever done on human subjects, but whether the scarring on animals was so severe that tests on humans were not allowed. Even if customers don’t ask, the idea that chemical class Zbt causes scarring in animal studies will remain a vivid picture in their minds. That’s not going to improve sales.

    It would be better for the conventional cosmetic industry employee to use nearly any other argument than the one presented here, which ends up begging too many questions that are not answered. A better argument is briefly alluded to at the end of the column, when it is mentioned that “searching out organic cosmetics” is a “hassle.” Pursuing this line of thought would be more convincing because many consumers would respond well to the idea that they are too busy to specially search out certain items that are not widely available. In addition, you can build a case around the expense of organic cosmetics, which are often twice or even three times as expensive as conventional cosmetics. Organic makeup can be both difficult to find and expensive to purchase, and reminding customers of these facts will not beg any questions about the likelihood of scarring. This argument is not well-reasoned, but another, better, argument is available.

    This essay would likely score a 6 (out of 6) on the GMAT. While it is shorter than other example essays, it fulfills the prompt by considering and explaining the questionable assumptions that underline the speaker’s principal argument, and showing how the argument would be picked apart by the very people it hopes to convince. In a tone that is fair-minded, the author also suggests several alternative arguments that could be made to amplify the stance of the article while rejecting the argument made at this time.

  5. A well written sample essay that will score well on the GMAT exam is shown below:

    In his zeal to cut costs and increase profits, the bank executive quoted here employs dubious logic. Let’s take a look at how his arguments fall apart.

    To begin, consider the comparison he makes between the profits of today’s six locations versus the profits of a single location. The executive says — without any statistical proof — that the main location was once more profitable than the combined profit from the six locations that North Bank offers today. He then attributes the loss in profitability to having six locations, without ever quite explaining what he means. It’s not clear if he feels that six locations are more expensive to operate, or if customer usage has somehow declined, or how, exactly, the increase in locations means a decrease in profits. It’s counter-intuitive — although not impossible — that a bank with one location would do less business than a bank with six. More explanation is needed.

    It’s also worth noting that the executive doesn’t give a timeframe for when the single bank was more profitable. With more information, the story could be clearer. It’s possible, for example, that he refers to a time when North Bank not only had but one location, but was also the only bank in town. A monopoly on the town’s business would surely increase profits. Logically, the bank cannot be expected to meet the same profit margin today that it could many years ago when that was so.

    While there is more to say about the first premise, let’s move on to the second premise. The executive claims that customers will enjoy the “nostalgic feel” of having to use one North Bank location for their business. This does not match up with any easily seen trends in banking, in which more and more people prefer to use ATMs and online banking instead of traveling several miles to do their banking in person. But even if the case could be made that, for some reason, North Bank’s customers are not following the trends, proof is needed but not provided. Believing the logic here requires the acceptance of a premise that is unproven and goes against common observation.

    Perhaps there is a logical case to be made for reducing North Bank to one location. The executive could, for example, provide evidence that shows five branches bring in less money that they spend in salary and building costs. But that is not the argument he makes here, and thus, this argument must be rejected as illogical and unconvincing.

    This essay would likely score a 6 (out of 6) on the GMAT. The writer does a good job of exposing the two assumptions the executive made in his comments and showing why they are not logically sound. The writer also makes good use of transitions and moves logically and clearly from one point to the next, closing by making a suggestion of what a more convincing case would be before soundly rejecting this case.

Chapter 2

6.1. A. Yes

6.2. B. No

6.3. B. No

For 6.1, sort by Kind of Business. Under Column 4, the combined sales of the six kinds of businesses in March 2016 was

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Under Column 2, the combined sales of the six kinds of businesses in March 2017 was

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The percent change is

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Note: The symbol “images” means “approximately equal to.” Therefore, the answer is Yes.

For 6.2, sort by Inventories March 2017. The business with the highest March 2017 inventory is motor vehicle and parts dealers. Re-sort by Inventories/Sales Ratios March 2017. The business with the highest March 2017 Inventories/Sales Ratio is clothing stores. Therefore, the answer is No.

For 6.3, sort by Kind of Business. Under Column 8, the inventories/sales ratio for general merchandise stores for March 2017 is 1.43, indicating that this business has more than one month’s worth of merchandise on hand. Therefore, the answer is No.

7.1. B. Greater than or equal to median

7.2. A. Less than median

7.3. A. Less than median

For 7.1, sort by Stock. Under Column 4, the volume quote for Company B is 2,315. Re-sort by Volume. The median for the 20 companies is halfway between 2,290 and 2,315. Thus, the volume quote for Company B is greater than or equal to the median.

For 7.2, sort by Stock. Under Column 7, the close quote for Company G is 39.65. Re-sort by Close. The median for the 20 companies is halfway between 55.27 and 56.45. Thus, the close quote for Company G is less than the median.

For 7.3, sort by Stock. Under Column 8, the net change quote for Company L is 0.23. Re-sort by Net Change. The median for the 20 companies is halfway between 0.32 and 0.67. Thus, the net change quote for Company L is less than the median.

8.1. A. Yes

8.2. A. Yes

8.3. B. No

For 8.1, sort by the average number of daily sales in January. The median is 144. Re-sort by the average number of daily sales in March. The median is 140. The median in January is greater. Therefore, the answer is Yes.

For 8.2, sort by the Total Sales Amount, Feb. Store A is the store with the highest total sales in February. Re-sort by the average number of daily sales in February. Store A is the store with the highest average number of daily sales in February. Therefore, the answer is Yes.

For 8.3, sort by Total Sales Amount, Feb. Count the number of stores for which the total sales amount in February exceeds the total sales amount in March. Only 7 of the 15 stores reported February total sales amounts that exceed March’s total sales amounts. Therefore, the answer is No.

9.1. D. 250

9.2. C. 200

Let x = the rate of increase for company X, and y = the rate of increase for company Y. Given that the number of components in inventory for the two companies will be equal in 20 months, set up an equation and solve for x in terms of y.

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This result tells you that company X’s rate is 50 greater than company Y’s rate. The only selections in the table where company X’s rate is 50 greater than company Y’s is 250 and 200, respectively.

10.1. B. two

10.2. D. four

For 10.1, according to condition (b), if item 1 is selected, then two cases are possible. Case I. Suppose item 1 and item 3 are selected. Given that item 4 is not selected, then, according to condition (c), item 2 must be selected. Neither condition (a), (d), nor (e) requires that additional items must be selected. Thus, if item 1 and item 3 are selected, a total of three items must be selected. Case II. Suppose item 1 and item 4 are selected. Then none of conditions (a) through (e) requires that additional items must be selected. Thus, if item 1 and item 4 are selected, a total of two items must be selected. Therefore, the minimum number of items that must be selected if item 1 is selected is two.

For 10.2, if item 5 is selected, then only two cases that satisfy all conditions are possible. Case I. Item 5, item 1, item 3, and item 2 are selected. This combination does not violate any of the conditions (a) through (e). Item 4 cannot be selected because of condition (b), and item 6 cannot be selected because of condition (e). Thus, if item 5, item 1, item 3, and item 2 are selected, then the maximum possible number of items that can be selected is four. Case II. Item 5, item 6, item 4, and item 2 are selected. This combination does not violate any of the conditions (a) through (e). Item 3 cannot be selected because of condition (d), and item 1 cannot be selected because of condition (e). Note that item 4 and item 2 can both be selected. Condition (c) applies only if item 4 is not selected. Thus, if item 5, item 6, item 4, and item 2 are selected, the maximum possible number of items that can be selected is four. Therefore, the maximum possible number of items that can be selected if item 5 is selected is four.

11.1. D. $120.00

11.2. C. $117.50

For 11.1, Ace Company’s chain discounts of 20% and 5% are equivalent to the single discount rate of

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For 11.2, Deuce Company’s chain discounts of 15% and 10% are equivalent to the single discount rate of

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12.1. E. Anyone who likes swimming likes the ocean

12.2. A. Anyone who likes the ocean likes swimming

For 12.1, the correct choice is the statement for which Aziz and Presley are both committed to believing is true. Aziz’s second statement that “anyone who does not like the ocean, does not like swimming” is logically equivalent to “anyone who likes swimming likes the ocean.” Presley’s second statement that “liking the ocean is a necessary condition for liking swimming” is also logically equivalent to “anyone who likes swimming likes the ocean.” Thus, they both agree on statement E.

For 12.2, the correct choice is the statement for which one of the two people, Aziz or Pressley, is committed to believing is true, and the other person is committed to believing is false. Aziz’s first statement that “Anyone who does not like swimming must not like the ocean either” is logically equivalent to “Anyone who likes the ocean likes swimming.” Thus, Aziz believes statement A is true. Pressley’s first statement, “That’s not true. I do not like swimming, but I do like the ocean” refutes statement A and gives a counterexample. Thus, Aziz and Pressley disagree on statement A.

Statements B, C, and D are all logically equivalent to “anyone who likes the ocean does not like swimming,” which Pressley does not express a committed opinion on.

13.1. C. images

13.2. E. images

For 13.1, the finance charge is the difference between the sum of payments and the amount borrowed, which is images.

For 13.2, the finance charge per $100 borrowed is images

14.1. D. 22

14.2. A. 11

Solve images for X in terms of Y.

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Thus, the value of X is twice the value of Y. The only values in the table that satisfy this relationship are X equal to 22 and Y equal to 11.

15.1. D. 36

15.2. B. 18

Let x equal the time (in hours) it will take machine X, working alone, to finish the job, and let images equal the time (in hours) it will take machine Y, working alone, to finish the job. The portion of the job that machine X can complete in one hour is images and the portion of the job that machine Y can complete in one hour is images. The portion of the job that the two machines, working together, can complete in one hour is images. Thus, images. Solve this equation for x and 2x:

images

Therefore, the time for machine X, working alone, is 18 hours, and the time for machine Y, working alone, is 36 hours.

16.1. B. negative

16.2. B. 140,000

For 16.1, the line of best fit indicates that weekly fuel consumption and weekly average hourly temperature tend to move in a linear pattern, with higher fuel consumption being associated with lower temperatures, and conversely. Therefore, the relationship between weekly fuel consumption and weekly average hourly temperature is best described as negative.

For 16.2, using (39, 10.0) and (46, 9.0), an estimate of the slope of the line of best fit is images. Therefore, when the weekly average hourly temperature increases by 1 degree, the mean (average) weekly fuel consumption decreases (because the slope is negative) by images.

17.1. B. 2

17.2. C. 300

For 17.1, percentages for question 2 are plotted on the vertical axis. Vertically, the center of disk A is at 20%, and the center of disk B is at 40%, which is twice as much.

For 17.2, given that the diameter of disk D is twice the diameter of disk A, then the area of disk D is 4 times the area of disk A. Let a% = the percentage of customers who would recommend restaurant A to their friends. Then the percentage of customers who would recommend restaurant D to their friends is 4a%, which equals images. Therefore, the percentage of customers who would recommend restaurant D to their friends is 300% greater than the percentage of customers who would recommend restaurant A to their friends.

18.1. C. images

18.2. B. images

For 18.1, The diagram shows there are four ways for exactly one of the two marbles drawn to be red: BR, which has probability images; GR, which has probability images; RB, which has probability images; and RG, which has probability images. Therefore, the probability that exactly one of the two marbles drawn is red is images.

For 18.2, The diagram shows there are three ways for both marbles to be the same color: BB, which has probability images; GG, which has probability images; and RR, which has probability images. Therefore, the probability that both marbles drawn will be the same color is images.

19.1. B. less than

19.2. D. 72.75

For 19.1, the histogram shows an imbalance created by the one low score between 25.5 and 40.5. The result of this imbalance is that the mean of the scores will be influenced by this low score, but the median will not. As a result, the mean of the 20 exam scores is less than the median of the 20 exam scores.

For 19.2, because of the grouping of the scores into intervals, the exact scores are not shown in the histogram. However, from the question information, you know that each score is a multiple of 5. Thus, the possible scores between 25.5 and 40.5 are 30, 35, and 40; between 55.5 and 70.5 are 60, 65, and 70; between 70.5 and 85.5 are 75, 80, and 85; and between 85.5 and 100.5 are 90, 95, and 100. There were no scores between 40.5 and 55.5, meaning there were no scores of 45, 50, or 55. The least possible mean score corresponds to the case where each student scored the minimum score in the interval in which the score falls. That is, 1 score of 30, 5 scores of 60, 9 scores of 75, and 5 scores of 90. Therefore, the least possible value for the mean (arithmetic average) score on the exam is

images

20.1. B images

20.2. A images

For 20.1, the diagram shows that 130 of the seniors have a home computer. Out of this 130, 40 have Wi-Fi access. Therefore, the probability that the person selected has Wi-Fi access at home, given that the person has a home computer is images.

For 20.2, out of the 160 senior citizen, 30 have Wi-Fi access, but no computer at home. Therefore, the probability that the person selected has Wi-Fi access, but no computer at home is images.

21.1. A. positive

21.2. C. 66

For 21.1, the graph shows that median annual earnings increase as educational attainment increases. This pattern is consistent from left to right across the table. Therefore, the relationship between educational attainment and median annual earnings in 2014 is best described as positive.

For 21.2, the median annual earnings in 2014 of those whose highest educational attainment was a bachelor’s degree were close to 66 percent higher than the median annual earnings in 2014 of those whose highest educational attainment was high school completion. This is true because

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22.1. B. No

22.2. B. No

22.3. A. Yes

For 22.1, the statement is not supported by the information provided. Chen provided guidance; and, given she is Allmedia’s CFO, she likely expects the incentive program to yield a net profit. However, there is no information indicating that this outcome is of primary importance to her. Therefore, the correct answer is No.

For 22.2, Talley has concerns about the incentive program, but having these concerns does not necessarily mean that he thinks the program should be discontinued. He might just want modifications to be made to the program. Therefore, the correct answer is No.

For 22.3, from Talley’s concern in his memo to Chen about the incentive program possibly leading some clients to buy advertising they don’t need, you can reasonably conclude that Talley is uncomfortable with WXXX being involved with clients in that way. Therefore, the correct answer is Yes.

23.1. A. Yes

23.2. A. Yes

23.3. B. No

For 23.1, according to Talley’s memo to Chen, the radio station needed $17,000 in additional monies from each incentive program participant to break even. According to Table 1, there were 12 program participants. To break even, a total of images in additional monies was needed from these clients. The table shows that the station obtained a total of $202,000 in additional monies from these 12 clients, resulting in a deficit of images. Therefore, the statement is true, and the correct answer is Yes.

For 23.2, Talley’s memo states the radio station needed $17,000 in additional monies from each incentive program participant to break even. Table 1 shows that only four of the 10 current clients met that minimum. Therefore, the statement is true, and the correct answer is Yes.

For 23.3, the median amount of additional advertising purchased by current clients participating in the incentive program was $14,500, not $16,000. Therefore, the statement is false, and the correct answer is No.

24. E. From a business standpoint, offering incentives to advertisers builds solid client relationships.

Eliminate choices (A), (C), and (D) because each of these statements would indicate an unfavorable attitude toward continuing the program. Between choices (B) and (E), choice (E) would indicate more directly that Chen is in favor of continuing the program.

25.1. A. Yes

25.2. B. No

25.3. A. Yes

For 25.1, the statement is inferable because the superintendent begins his memo with an enthusiastic statement about the campaign. Therefore, the correct answer is Yes.

For 25.2, the superintendent’s memo states that a board of trustee member will serve on the campaign committee, but there is no indication that the board member will serve as chairperson. Therefore, the correct answer is No.

For 25.3, the superintendent’s memo states that the committee has already obtained federal and state authorization for the campaign. This information implies that the DW Campaign is in compliance with federal and state policies. Therefore, the correct answer is Yes.

26.1. A. Yes

26.2. A. Yes

26.3. A. Yes

For 26.1, the model shows funding as an input. This information assumes that funding for the campaign can be secured. Therefore, the statement is a reasonable assumption, and the correct answer is Yes.

For 26.2, the model shows the logical connections that flow from inputs to outputs to outcomes. The outcomes include short-, intermediate-, and long-term behavior outcomes related to students. This information assumes that students can and will be motivated to change. Therefore, the statement is a reasonable assumption and the correct answer is Yes.

For 26.3, the model shows that local celebrities/athletes will be enlisted to promote the campaign. This information assumes that local celebrities/athletes can be recruited to do that. Therefore, the statement is a reasonable assumption, and the correct answer is Yes.

27. D. 53,000

As reported in the superintendent’s memo (according to the dental hygienist’s presentation), nationally, 63 percent of youth consume at least one sugar-sweetened beverage daily. The superintendent’s memo gives the number of students in the district as 84,000. If these students follow the national trend, then images students consume at least one sugar-sweetened beverage on a given day. This number is closest to Choice (D).

Chapter 3

  1. D. 329

    Substitute 165 for C in the equation, and then solve the equation for F:

    images

  2. B. 0.27

    Let N = the total number of members in the university orchestra. The probability of randomly selecting a senior band member equals the number of senior band members in the orchestra divided by N. Choose a convenient value for N. Given that you are working with percentages, let N = 100. Then the number of senior orchestra member is 60%(100) = 0.6(100) = 60. Of that number, 45% are band members, so there are 45%(60) = 0.45(100) = 27 senior band members in the orchestra. Therefore, the probability of randomly selecting a senior band member is images.

  3. B. images

    Square the expression, and then simplify the result:

    images

  4. C. 45

    This is a combination counting question. You can answer the question by finding the combination of 10 items (teams) taken 2 at a time. Using the combination formula, you have

    images

    Thus, there are 45 games in the season. (Note: 10! (read “n factorial”) is the product of all positive integers descending down from 10 to 1.)

  5. B. 134

    Illustrate the problem with a Venn diagram to answer the question. Use three overlapping circles, one for each course. Fill in the diagram using the information in the question. Start with intersections. None of the students are enrolled in both mathematics and psychology, so put 0s in the intersection of mathematics and psychology. It follows that none of the 12 students enrolled in both mathematics and English are enrolled in psychology. Those 12 students are represented in the region corresponding to mathematics and English only. Similarly, none of the 22 students enrolled in psychology and English are enrolled in mathematics. Those 12 students are represented in the region corresponding to psychology and English only. With the numbers in the intersections completed, you can determine that images students are enrolled in mathematics only; images students are enrolled in psychology only; and images students are enrolled in English only.

    image

    © John Wiley & Sons, Inc.

    Therefore, according to the diagram, images students are enrolled in at least one of these courses.

  6. A. 7

    Recall that n! (read “n factorial”) is the product of all positive integers descending down from n to 1. Given that n! is divisible by 840, then it must be divisible by the factors in the prime factorization of 840. The prime factorization of 840 is images. Therefore, n! must have factors of 2, 3, 4, 5, and 7. The least positive value of n such that n! contains these factors is 7 (because images).

  7. D. 34

    images. Thus, any number ≤ 15 is a factor of 15! Eliminate Choice (A) because 14 is a factor of 15! Eliminate Choice B because 22 is a factor of 15! (given that images). Eliminate Choice (C) because 19 is a prime number. Choice (D) is not a prime number and images is not a factor of 15! Thus, 34 is the least integer that satisfies the requirements given in the question. You do not have to check Choice (E) because images.

  8. C. 4

    Using your knowledge that the factorial of a positive integer k is the product of all positive integers descending down from k to 1, simplify the equation. Next, check the answer choices to find a value for n that makes the simplified equation true.

    images

    Tip: The answer choices are listed in ascending order, so start by checking Choice (C). If Choice (C) is incorrect, you possibly can eliminate other answer choices using logical reasoning based on the result obtained with Choice (C). Check Choice (C): images. Thus, n = 4 makes the equation true.

  9. E. 20

    Let t = the time (in hours) it would take Melora, working alone, to paint the room. The portion of the room Melora, working alone, can paint in one hour is images. The portion of the room Kyra and Sage, working together, can paint in one hour is images. The portion of the room the three of them, working together, can paint in one hour is images. Therefore, images. Solve the equation:

    images

    Melora would take 20 hours, working alone, to paint the room.

  10. A. 10π

    An angle inscribed in a semicircle is a right angle. Thus, triangle PQR is a right triangle with legs of lengths 16 and 12. The length, PR, of the hypotenuse is images. Thus, the diameter of the semicircle is 20. The length of the arc PQR is half the circumference of the circle that contains the semicircle. This length is images.

  11. D. images

    The sum, S, of all 20 numbers divided by 20 equals A; that is, images. Hence, images. Similarly, the sum of the 10 numbers whose average is 16 equals (10)(16) = 160. Therefore, the sum of the remaining 10 numbers is images. The average of these 10 numbers is images.

  12. C. $1,200

    Let x = the amount (in dollars) allocated for utilities, 3x = the amount (in dollars) allocated for food, and 5x = the amount (in dollars) allocated for home mortgage payment. Solve the equation for x, and then determine 3x, the amount allocated for food.

    images

    The amount allocated for food is $1,200.

  13. A. images

    Illustrate the problem with a Venn diagram to answer the question. Use two overlapping circles, labeled C for cat ownership and D for dog ownership. Fill in the diagram using the information in the question. Start with the intersection. There are b students in the intersection. It follows that images students are cat only owners and imagesstudents are dog only owners.

    image

    © John Wiley & Sons, Inc.

    Therefore, according to the diagram, the number of students who own neither a cat nor a dog is

    images

  14. E. 21

    The second plant grew 6 inches plus 250% of 6 inches, which is

    images

  15. B. II only

    Because 15! is the product all positive integers descending down from 15 to 1, 13 (II) is a factor of 15! Also, 13 is a factor of 13. Hence, 13 is a common factor of 15! and 13, so it is a factor of the sum images. Thus, the correct answer choice must include II. Eliminate Choice (A). If you assume 11 (I) is a factor of images, then given that 11 is also a factor of 15!, it would follow that 11 is a factor of images. But 11 is not a factor of 13 which implies that your assumption is false, meaning 11 is not a factor of images. In a similar manner, you can show that 15 (III) also is not a factor of images. Eliminate choices (C), (D), and (E), leaving Choice (B), II only, as the correct answer choice.

  16. E. 12

    Simplify the expression using scientific notation and the rules for exponents.

    images

    Thus, the product images is an integer. Given that 125 is an integer, then images must be an integer as well. Thus, images. Therefore, the least possible value of images is 0, which implies that the least possible value of p is 12.

  17. E. 2.5

    The slopes of two perpendicular lines, neither of which is a vertical line, are negative reciprocals of each other. Find the slope of the given line by writing its equation in slope-intercept form. Next, determine the negative reciprocal of the slope obtained.

    images

    The slope of the given line is images. The negative reciprocal of this slope is images.

  18. D. 9,515

    Let N = the attendance on the final day of the festival. Solve the equation:

    images

    The attendance on the final day was 9,515.

  19. D. 3.6

    Let t = the time (in hours) it would take if both inlet pipes are opened simultaneously. The portion of the cistern’s capacity that the first inlet pipe can fill in one hour is images. The portion of the cistern’s capacity that the second inlet pipe can fill in one hour is images. If both pipes are opened simultaneously, the portion of the cistern’s capacity they can fill in one hour is images. Therefore, images. Solve the equation:

    images

    It will take 3.6 hours to fill the tank.

  20. C. 90

    Let N = the number of marbles in the box. The fraction of N that are yellow is

    images

    Therefore, images, which implies images.

  21. A. 60

    Let W = the garden’s width (in feet) and images the garden’s length (in feet). The formula for the perimeter of a rectangle is images, where L is the rectangle’s length and W is its width. Substitute into the formula and solve for W, and then find 2W, the garden’s length.

    images

    The garden’s length is 60 feet.

  22. B. images

    Solve the equation:

    images

  23. D. I and II only

    The expression in I is rational because images, which is rational. The correct answer must contain I, so eliminate choices (B), (C), and (E). The expression in II is rational because images, which is rational. The correct answer must contain II. Eliminate Choice (A). Therefore, I and II only is the correct answer. Just to verify, the expression in III is not rational because it is the product of a rational number, 46, and an irrational number, images.

  24. B. images

    Using the distributive property, images. Substitute images to obtain images.

  25. D. 50

    Let N = the minimum number of seeds that should be planted. According to the question information, images. Solve the equation:

    images

  26. D. 4,000

    Let A = the size (in acres) of the original field. Then imagesthe size (in acres) of the cleared land. The percent of the cleared land planted in gooseberry plants is images. Therefore, images. Solve the equation:

    images

    The size of the original field is 4,000 acres.

  27. C. images

    Simplify the expression:

    images

  28. A. 8:1

    Let n = the number of triangles; then 2n = the number of circles; and images = the number of squares. The ratio of the number of squares to the number of triangles is images or 8:1.

  29. D. 360

    Let x = the number of students who like only one of the juices, y = the number of students who like exactly two of the juices, and z = the number of students who like exactly three of the juices. Then images because all of the participants like at least one of these juices. From the question information images, which implies that images. Now, let O = the number of students who like orange juice, A = the number of students who like apple juice, and G = the number of students who like grape juice. From the question information:

    images
    images
    images

    The sum of O, A, and G will count x exactly one time, y exactly two times, and z exactly three times. Thus,

    images

    Solve images and images simultaneously. Solving images for z yields images. Substituting this result into images yields

    images

    Therefore, 360 survey participants like only one of the juices.

  30. D. images

    For each equation, set each factor equal to 0 and solve for x. For the first equation images implies images and images implies images. For the second equation images implies images and images implies images. Therefore, the simultaneous solution is images.

  31. A. 15

    Let N = the number of nonfiction books last year and F = the number of fiction books last year. Then images and images. Solve these two equations simultaneously. Solving images for F yields images. Substituting this result into images yields

    images

    The number of nonfiction books last year was 15.

  32. C. images

    Find images and simplify.

    images
    images

  33. D. 30

    First find the prime factorization of 5,880 using a systematic approach similar to the one shown here:

    images

    To be a perfect square, the prime factors of images must have even exponents. Therefore, k must contain at least one factor each of 2, 3, and 5. Hence, the least value of k is images.

  34. D. images

    Consecutive interior angles of a rhombus are supplementary, so the measure of images. The diagonals of a rhombus are perpendicular bisectors of each other and bisect the angles of the rhombus. Construct the diagonals of the rhombus. Label the intersection E. Thus, triangle AED below is a images right triangle, with hypotenuse images and legs images and images.

    image

    © John Wiley & Sons, Inc.

    Given that the diagonals bisect each other, the length of images is twice the length of images, and the length of images is twice the length of images. Hence, the ratio of the length of images to the length of images is the same as the ratio of the length of images to the length of images. The lengths of the sides of a images right triangle are in the ratio images. Therefore, the ratio of the length of images to images equals the ratio of the length of images to images equals images, which is images in simplified form.

  35. C. Four

    If images the square of a prime number, then images. For each of the first five prime numbers (2, 3, 5, 7, and 11), compute 5 times its square to obtain the following values:

    images

    Only four of these values (20, 45, 125, and 245) lie between 15 and 250; and, thus, are possible values of n. Therefore, there are four possible values of n for which images is the square of a prime number.

  36. B. 0.032

    The probability of guessing correctly is images. Then the probability of guessing incorrectly is images. Each guess is independent of the next, so the probability that the player’s turn ends after three guesses is the product of the probability of guessing correctly twice followed by guessing incorrectly once. This product is images.

  37. D. 60%

    Let images = the probability that team A wins the tournament and images = the probability that team B wins the tournament. Then according to the question information, images and images. Given that there is only one tournament winner, the event that team A wins the tournament and the event that team B wins are mutually exclusive, meaning they cannot occur at the same time. Therefore, the probability that team A or team B wins the tournament equals images.

  38. B. 9

    Determine the number of factors of 3 that are contained in 21!. As shown below, 21! is the product of all positive integers descending down from 21 to 1.

    images

    In this product, images has 1 factor of 3, images has 2 factors of 3, images has 1 factor of 3, images has one factor of 3, images has 2 factors of 3, images has 1 factor of 3, and images has 1 factor of 3. None of the other factors in 21! has a factor of 3. Thus, the total number of factors of 3 in 21! is images. Therefore, the greatest integer p for which images is a factor of 21! is 9.

  39. E. 27

    Square both sides of the equation and then determine x.

    images

  40. D. 270

    According to the figure, triangles ABC and DEC are right triangles, segments images and images are parallel (because they are both perpendicular to the same line), and the measure of images is images. The measure of images is images (because images and images are corresponding angles of parallel lines). Thus, images. Also, images (because the measure of an exterior angle of a triangle equals the sum of the measures of the nonadjacent interior angles). Therefore, images.

  41. A. images

    Each of the three circles is divided into k equal parts, so each part is images of a circle. The fourth circle is divided into images equal parts, so each part is images of a circle. The child colored one of the k parts in each of the three circles, and one of the images parts in the fourth circle. Thus, the total fraction of a whole circle that the child colored is

    images

  42. B. 36

    In a 5-digit number there are five place values to fill. If there were no restrictions on the placement of the two 3s, the number of ways to select two locations for the two 3s from the five place value slots is the combination of 5 things taken 2 at a time. This number is

    images.

    However, you must remove from this number, the number of ways for the two 3s to be adjacent to each other. There are four ways for the two 3s to be adjacent to each other as illustrated here with ? marks taking the place of the other three digits: 33???, ?33??, ??33?, and ???33. Therefore, the number of ways to select the location for the two 3s is the number of ways to select two of the five place value locations minus the four ways in which the two selected locations would be adjacent. This number is images. Now, for each of these 6 ways, there are images ways to arrange the other three digits. This is true because there are 3 ways to select the first digit; and, for each of these ways, there are 2 ways to select the next digit; and, for each of these ways, there is just 1 way to select the last digit. Therefore, there are images ways to arrange the given digits into a 5-digit number so that the two occurrences of the digit 3 are separated by at least one other digit.

  43. D. 32

    Let L be the length of the patio (in feet), then images. Solve the equation:

    images

    The length is closest to 32.

  44. C. 16%

    The curve is symmetric about M, so 50% of the scores are above M (and 50% are below). Again, due to symmetry about M, images of the scores are between M and images. Therefore, images of the scores are greater than images.

  45. D. 50

    For the estimated time, images; and for the actual time, images. Solve these two equations simultaneously. Solving images for T yields images. Substituting this result into images yields

    images

    Reject images because the rate cannot be negative. Therefore, the painter’s regular rate is $50 per hour. Note: In this problem, you are permitted to divide and multiply both sides of an equation by R because the question information implies that images.

  46. B. 7

    Because images, rewrite the given equality as images, which simplifies to images. It follows that p is the least integer such that images or, equivalently, images, which is 7.

  47. B. 11

    From the question information, images and images. Hence,

    images

    Given that x and y are positive integers, then images is an integer, which implies that 11 must be a factor of images. None of the other answer choices must be a factor of images.

  48. D. 0.05

    Use your knowledge of square roots to simplify the expression.

    images

  49. C. 19

    Use logical reasoning to determine the solution. The difference (in years) between the mother’s age and the son’s age is images. Therefore, when the son is 28 years old, the mother will be images years old. The son is 9 years old, so in 19 years (because images), he will be 28 years old and his mother will be 56 years old, twice his age.

  50. E. 60

    Lupita’s schedule (in days) is 12, 24, 36, 48, 60, and so on. Vin’s schedule (in days) is 15, 30, 45, 60, and so on. The number of days until the next time both will swim at that same gym is 60, which is the least common multiple of 12 and 15.

  51. A. images

    Combine the two fractions algebraically by using a common denominator of images.

    images

  52. E. images

    Use your knowledge of exponents and algebraic manipulation to simplify the expression.

    images

  53. B. images

    Use your knowledge of exponents and algebraic manipulation to simplify the expression.

    images

  54. D. I and III only

    Because m and n are positive integers, their sum, images, is a positive integer. Given that m is three times n, let images. Then images. This result implies that images is divisible by 4. A number is divisible by 4 if and only if its last two digits form a number that is divisible by 4. Of the Roman choices given, only 314 (II) fails the test for divisibility by 4 (because the last two digits of 314 are 14, which is not divisible). Therefore, images could be 216 (I) or 1,048 (III) only.

  55. C. 900

    From the figure, ΔABC is a right triangle. To find the area of a right triangle, you find images the product of the lengths of the two legs. To find the area of ΔABC, First, determine CA, the length of leg images. Next, determine BC, the length of leg images. Then find the area of ΔABC by calculating images. First, find CA by adding the lengths of the two segments, images and images: images. Next, to find BC, observe that right triangles ABC and ADE are similar triangles because they have the acute angle A in common. Using properties of similar triangles,

    images

    Thus, the area of ΔABC is images.

  56. C. 20

    The pole, the wire, and the ground form a right triangle. The wire is the hypotenuse of a right triangle that has legs of lengths 16 and 12, in feet. Use the Pythagorean theorem to find the length of the hypotenuse, denoted by c.

    images

    (Note: –20 is also a solution, but it is rejected because length is positive.)

    The length of the wire is 20 feet.

  57. E. 20,000

    Divide images by images.

    images

    The number of grams of sugar in solution Y is 20,000 times the number of grams of sugar in solution X.

  58. E. 840

    The number of different arrangements to seat four spectators in four of seven empty stadium seats that are all in the same row is the number of ways to select the four seats times the number of different arrangements of four spectators in four seats. First, consider selection of four of the seven empty stadium seats. Because different orderings of the seat selection does not produce different arrangements, the number of ways to select four of seven seats is the combination of 7 items taken 4 at a time, which is

    images

    Next, consider the arrangement of the four spectators in the four seats. Because different orderings of the spectators results in different arrangements, the number of different arrangements to seat the four spectators in four seats is images. This is true because there are 4 ways to seat someone in the first seat. And for each of these ways, there are 3 ways to seat a person in the second seat, and so on. Therefore, The number of different arrangements to seat four spectators in four of seven empty stadium seats in the same row is images.

  59. E. images

    This question asks you to find a conditional probability; that is, you are to find the probability when you already know that the student is a seventh grader. Thus, when computing the probability, the number of possible students under consideration is no longer 300, but is reduced to the total number of seventh graders, which is 100. According to the table, 55 of the 100 seventh graders own a cell phone. Therefore, the probability a randomly selected student owns a cell phone given that the student is a seventh grader equals images.

  60. B. 15%

    Fill in the missing probabilities.

    image

    © John Wiley & Sons, Inc.

    With probability tree diagrams, you multiply along the branches to determine the probability of the outcome at the end of the branch. Therefore, the probability that the concert takes place given that it rains is images.

  61. D. images

    There are six slots to be filled, so to speak, on the license plate. There are 26 possible choices for each of the two letters, and there are 10 possible choices for each of the four digits, which means the total number of possible license plate alphanumeric codes is images.

  62. E. 5.4

    To find the rate of gallons per day, change 15 hours to days, and then divide images gallons by the result.

    images
    images

    The motor’s fuel consumption rate is 5.4 gallons per day.

  63. C. Five

    The integers in set M are 4, 8, 12, 16, 20, 24, 28, and so on. The integers in set N are 8, 18, 28, 38, 48, 58, 68, 78, 88, and 98. Of the integers in set N, 8, 28, 48, 68, and 88 are multiples of 4 and therefore these integers are in set M as well. Therefore, sets M and N have five numbers in common.

  64. D. 161

    Let m and n be the two positive integers in the list of six integers whose values are unknown and, without loss of generality, let images. Given that 68 is the mean of the six integers, images. Solve this equation for images:

    images

    Because m and n are positive integers, the least that n can be is 1. Therefore, the greatest that m can be is 161.

  65. A. 114

    Of the 75 students who are enrolled in a science course, 34 are not enrolled in a sociology course. It follows that images students are enrolled in both a science course and a sociology course. Of the 52 students who are enrolled in a sociology course, images students are enrolled in a sociology course only. Sketch a Venn diagram to illustrate the information.

    image

    © John Wiley & Sons, Inc.

    The entire rectangle represents the 200 students. The region that is outside the two intersecting circles represents the students who are enrolled in neither a science course nor a sociology course. From the diagram, this number is

    images.

  66. D. images

    The perimeter of images. From the information given, images. Now, determine PQ and QR to find the perimeter. The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments into which it separates the hypotenuse. Let x = the altitude’s length. Then images. Substitute images and images, and then solve for x.

    images

    (Note: The number –8 is also a solution, but it is rejected because length is positive.). Use the Pythagorean theorem to solve for PQ and QR.

    images

    and

    images

    Therefore, the perimeter of images.

  67. D. images

    Let F = the number of female students enrolled a year ago and M = the number of male students enrolled a year ago. Then the enrollment a year ago is images and the number of students currently enrolled =

    images

    The number of female students currently enrolled = images and the number of male students currently enrolled = images. It follows that images, which implies that images, or equivalently, images.

    This result tells you that a year ago, there were twice as many female students as male students at the private school. Pick convenient values for M and F that satisfy this relationship. For example, let images and images. With these hypothetical values, the total enrollment a year ago is 300. Therefore, the fraction of the current enrollment at the private school that is female students is images.

  68. A. I only

    images implies that images, which is equivalent to images. Check for Roman choices that satisfy this double inequality. Check I: images and images, so 500 satisfies the double inequality. The correct answer contains I, so eliminate choices (C) and (E).

    Check II: images, so 600 does not satisfy the double inequality. Reject II, and eliminate Choice (B). Check III: images so 700 does not satisfy the double inequality. Reject III, and eliminate Choice (D). Thus, Choice (A), I only, is the correct answer. (Note: Eliminating fractions at the outset simplifies the calculations for this problem.)

  69. A. images

    Simplify the equation. Then determine n.

    images

    This result implies that images.

  70. D. 47

    For the recursive formula given, you will need to find images and images before you can find images. Using the formula, images;images; and images.

  71. D. 52

    For each vehicle, divide 1,200 miles by its average miles per gallon of gasoline performance. Then find the difference in the amount of gasoline used. The truck averages 12 miles per gallon of gasoline, so for 1,200 miles, it will use images. The car averages 25 miles per gallon of gasoline, so for 1,200 miles, it will use images. The difference is images.

  72. D. I and II only

    Statement I is true because images implies images, which implies images. Given that images, then images or, equivalently, images. The correct answer choice must include I. Eliminate choices (B), (C), and (E). Statement II is true because images implies images. Given that images, then images. The correct answer choice must include II. Eliminate Choice (A). Therefore, Choice (D), I and II only, is the correct answer. You do not have to check statement III, but it is not necessarily true. If, for example, images, and images, images.

  73. B. images

    The number of integers from 101 to 500 is images. Of these 400 integers, the number that have a hundreds digit of 3 is images. Therefore, the probability that a randomly selected integer from a list of consecutive integers from 101 to 500 will have a hundreds digit of 3 is images.

  74. D. 14.25

    The average weight, kilograms, of the 20 boxes is

    images.

  75. C. 112

    Let 2x = the number of pennies in the collection, 3x = the number of nickels, 5x = the number of dimes, and 6x = the number of quarters. Thus, the total number of coins in the collection is images. You know the number of coins of one of the denomination is 30, so check each denomination in turn to determine the possible values for 16x. If images, then images and images, so Choice (E) is a possible value for 16x. If images, then images and images, so Choice (D) is a possible value for 16x. If images, then images and images, so Choice (B) is a possible value for 16x. If images, then images and images, so choice (A) is a possible value for 16x. Therefore, Choice (C) cannot be the total number of coins in the collection.

  76. A. 25%

    The price reduction is images. This amount represents a percent reduction of images.

  77. C. III only

    Substitute the values of x and y from each given ordered pair to determine whether the values satisfy the equation for every possible value of m. The ordered pair in I yields images, which is true for only one value of m : images. Reject I, and eliminate choices (A), (D), and (E). The ordered pair in II yields images, which is true for only one value of m:images. Reject II, and eliminate Choice (B). Thus, Choice (C), III only, is the correct answer. You do not have to check it, but the ordered pair yields images, which is always true regardless of the value of m.

  78. C. 26

    If K is neither the least nor the greatest of the six numbers, then the range of the six numbers would be images, which is not consistent with the question information that the range is 24. It follows that K is either the least of the six numbers or the greatest of the six numbers. If K is the least of the six numbers then images, which implies that images. If K is the greatest of the six numbers then images, which implies that images. Hence, the two possible values for K are 30 and 4, from which you have 30 is 26 greater than 4.

  79. C. III only

    The equation images implies images. Given that b is positive, this result implies that images (because otherwise, b would be 0 or negative). Substitute images into images to obtain images. Now check the Roman choices. For I, images implies images. This result contradicts images. Reject I, and eliminate choices (A) and (D). For II, images implies images. This result contradicts images. Reject II, and eliminate choices (B) and (E). Therefore, Choice (C), III only, is the correct answer, so move on to the next question. However, to verify, images implies images and images.

  80. A. 4 to 5

    The desired ratio is images. From the question information you have three proportions: images, images, and images. From the first proportion, images. From the second proportion, images. From the third proportion, images. Thus, images, which implies images. Therefore, the ratio of A to C is 4 to 5.

  81. D. 10

    Let H = the number of hardcover books purchased and P = the number of paperback books purchased. Then, images. You have one equation and two variables, so without additional information, finding specific values for H and P is problematic. However, the question scenario implies that H and P are both positive integers. Keeping this additional information in mind, solve the equation for P.

    images

    Knowing that P has to be a positive integer implies that images is positive and that it is divisible by 5. For images to be positive H could be 1, 2, 3, 4, 5, 6, or 7. For each of these values, the corresponding values for images are 7, 6, 5, 4, 3, 2, and 1, respectively. Of these values, only 5, which corresponds to images, is divisible by 5. Thus, images and images. Therefore, the customer purchased a total of images books.

  82. E. images

    The formula for the area of a circle is images, where r is the circle’s radius. The value of images is the square of the distance between the center images and the point images, which lies on the circle. Use the formula for the distance between two points in the xy-plane:

    images

    Therefore, images.

  83. B. images

    Given that the total votes cast by seniors was 40%V, then the total votes cast by juniors was 60%V. The candidate received 10% of the total votes cast by juniors. Thus, the candidate received images votes cast by juniors. Therefore, the candidate received images votes in the election.

  84. C. 30

    The ratio of red to white quinoa is images. Let 3x = the amount (in ounces) of red quinoa in the 110-ounce mixture and 8x = the amount (in ounces) of white quinoa in the mixture. Then, images. Solve this equation for x, and then find 3x, the amount of red quinoa in the mixture.

    images

    The chef puts 30 ounces of red quinoa in the 110-ounce mixture.

  85. C. Four

    Determine the prime factorization of 3,080 using a systematic approach similar to the one shown here.

    images

    Therefore, 3,080 has four distinct prime factors: 2, 5, 7, and 11.

  86. B. images

    For an odd number of data values, the median is the middle number when the values are put in ascending order as are the consecutive integers in this problem. Furthermore images of the data values are below the median and images are above the median. Because K is an odd number, 240 is the middle value in the list of numbers and there are images consecutive integers above 240. Therefore, the greatest integer in the list is images.

  87. C. 81

    Express images as images. Substitute images into this expression and simplify.

    images

  88. D. images

    Let 6x = the length of the box, 4x = the width of the box, and 5x = the height of the box. Then images. Solve images for x and then find 5x, the height of the box:

    images

  89. C. images

    Use logical reasoning to determine the solution. Sofi has half as many game cards as her brother, so her brother has 2S game cards. She has three times as many game cards as her sister, so her sister has images game cards. Therefore, the three siblings have a total of images game cards.

  90. A. 7

    The mean of N numbers is their sum divided by N. Let S = the sum of the list of K numbers. Then images = the sum of the list of images numbers. From the question information, you can write two equations: images and images. Solve these two equations simultaneously. Solving images for S yields images. Substituting this result into images yields

    images

  91. B. images

    Given that images, then images, images, images, images, and so on. You have the pattern images, and so on. Thus, in general, images. Using this formula, images. From the previous calculations, images. Therefore, images, which shows images is images times greater than images.

  92. E. II and III only

    Check the Roman choices. For I, images implies images, which implies images. Thus, images cannot be less than 1. Reject I, and eliminate (A) and (D). For II, images implies images, which implies images. Thus, images. The correct answer must include II. Eliminate Choice (C). For III, images implies images. The correct answer must include III. Eliminate Choice (B), leaving Choice (E), II and III only, as the correct answer.

  93. A. 0

    The six positive numbers are in ascending order, so the median is the average of the middle pair of numbers, which is

    images

    The mean is the sum of the numbers divided by 6, which is

    images

    The mean and the median both equal images, so the difference is 0.

  94. B. 15

    Let x = the amount (in milliliters) of the 1% sulfuric acid solution that must be added. Then images = the amount (in milliliters) in the final 5% sulfuric acid solution. Make a table to organize the information given.

    When?

    Percent sulfuric acid strength

    Amount (in milliliters)

    Amount of sulfuric acid (in milliliters)

    Before

    1%

    x

    1%x

    6%

    60

    6%(60)

    After

    5%

    x + 60

    5%(x + 60)

    Using the table, write an equation based on the following fact: The amount of sulfuric acid before mixing equals the amount of sulfuric acid after mixing.

    images

    The amount of the 1% sulfuric acid solution to be added is 15 milliliters.

  95. B. 3.5

    Use logical reasoning to determine the solution. The combined distance that the two vehicles must travel is 455 miles. They will cover that distance at a combined speed of images. Therefore, the time it will the two vehicles to be 455 miles apart is images.

  96. A. 0

    Follow the order of operations and simplify the expression:

    images

  97. D. II and III only

    Factor images completely and then simplify the factors.

    images

    Therefore, of the choices given, only 3 (II) and 7 (III) are prime factors of images.

    Note: The prime numbers 29 and 641 are also prime factors of images, but that information is not needed to correctly answer the question.

  98. E. 14

    Let W = the width (in feet) of the rectangle and L = 2W + 4 = the length (in feet) of the rectangle. Given the area (in images) of the rectangle is 70, solve the following equation for W, and then determine 2W + 4, which is the length of the rectangle.

    images

    (Note: The number images is rejected because length is positive.) The length of the rectangle is 14 feet.

  99. C. III only

    First determine the values of images. images, images, and images. Thus, images. Therefore, only the double inequality in III is true, so the correct answer is Choice (C), III only.

  100. A. 188

    Let L = the amount of money (in dollars) that Loyce has initially and T = the amount of money (in dollars) Tiara has initially. Then according to the question information, images and images. Solve these two equations simultaneously. Solving images for T yields images. Substituting this result into images yields

    images

    Loyce has $188 initially.

  101. E. 5,832

    First, determine the volume of one 3-inch cube. Next, multiply the result by 216, the number of cubes, to determine the volume of the crate. The volume, in cubic inches, of a 3-in cube is images. Therefore, the volume, in cubic inches, of the crate is images.

  102. A. 15

    Let M = the number of months of membership at which Merida and Jude will have paid the same amount. Solve the following equation.

    images

    After 15 months of membership, Merida and Jude will have paid the same total amount.

  103. E. 0.8

    The median of the 20 times shown in the dot plot is the average of the middle pair of times, which, in minutes, is images. The mean of the 20 times is their sum divided by 20, which, in minutes, is

    images

    The difference, in minutes, between the median and the mean is images.

  104. D. images

    Use logical reasoning to determine the solution. There are images integers in the sequence. The sequence starts and ends with an even integer, so the number of even integers in the sequence is 1 more than the number of odd integers. Subtracting 1 from 41 leaves 40 integers, of which 20 (half) are even and 20 (half) are odd. Thus, there are images even integers. Therefore, the probability that the randomly selected integer is even is images.

  105. D. images

    The outcome of the drawing from one bag has no effect on the outcome of the drawing from the other bag, so the drawings from the two bags are independent. For either bag, let B represent the outcome “the chip drawn is blue,” G represent the outcome “the chip drawn is gold,” and R represent the outcome “the chip drawn is red.”

    Bag 1 contains 24 chips. For this bag, images, images, and images.

    Bag 2 contains 12 chips. For this bag, images, images, and images.

    Make a tree diagram to illustrate the situation.

    image

    © John Wiley & Sons, Inc.

    With probability tree diagrams, you multiply along a branch to determine the probability of the outcome at the end of the branch. Thereafter, if the probability of two or more end outcomes is desired, their probabilities are added to obtain a total probability.

    According to the tree diagram, there are four end outcomes for which neither chip is gold: BB, which has probability images; BR, which has probability images; RB, which has probability images; and RR, which has probability images. Therefore, the probability neither chip is gold is

    images

  106. E. 36

    The greatest length, in feet, for each side of the square plots is the greatest common factor of 18 and 30. Because images and images, the greatest common factor of 18 and 30 is images. Therefore, the greatest area, in square feet, for each of the square plots is images.

  107. E. 8

    Determine the answer by identifying a pattern in the units digits of images, for n, a positive integer. If the units digit of an integer m is 2, then the units digits of images, in the order given, have a 4-digit repeating pattern of 2, 4, 8, 6, 2, 4, 8, 6, and so on. Thus, if n is a nonzero multiple of 4, the units digit of images is 6. Also, for some images, if n has the form images, the units digit of images is 2; if n has the form images, the units digit of images is 4; and if n has the form images, the units digit of images is 8. In this question, images, which has the form images. Thus, the units digit of images is 8.

  108. A. 51 to 31

    First, find the total amount of fruit juice. Next, find the total amount of water and cinnamon sugar. Then, find the ratio of the total amount of fruit juice to the total amount of water and cinnamon sugar. The total amount, in cups, of fruit juice is images. The total amount, in cups, of water and cinnamon sugar is images. Therefore, the ratio of the total amount of fruit juice to the total amount of water and cinnamon sugar is images or, equivalently, 51 to 31.

  109. B. images

    Express images, in terms of p, and then simplify. images implies imagesand images implies images. Therefore, images.

  110. C. 20

    The formula for the perimeter of a rectangle is images, where L is the rectangle’s length and W is its width. Substitute into the formula and solve the equation that follows for x. Next, determine images and images, the rectangle’s dimensions, in feet. Then determine its area, in square feet.

    images

    The rectangle has dimensions 5 feet by 4 feet. Its area, in square feet, is images.

  111. D. 13% profit

    Given that $144 is 20% greater than the initial cost of a microwave oven, it follows that the initial cost for each microwave oven was images. The total revenue is the amount obtained from the sale of images microwave ovens at $144 each plus the amount from the refund of images for each of the 5 microwaves that were returned. This total revenue is images. The total initial cost of the 50 microwave ovens was images. The difference between total revenue and cost is images, which is a profit because it’s positive. The profit as a percent of the total initial cost is images.

  112. B. Two
    images

    Therefore, the decimal representation of images has two nonzero digits.

  113. C. images

    Initially, the box contains 3 defective remote controls and 9 non-defective remote controls. The probability that the first remote control selected is non-defective is images. Thereafter, the box contains 3 defective and 8 non-defective remote controls, so the probability that the second remote control selected is non-defective is images. Therefore, the probability that neither of the first two remote controls tested is defective is images.

  114. D. $230

    Let A = Richard’s average gratuity per day for the last four of the past 10 workdays. Then his total gratuities in dollars for those four days is images. His total gratuities for the previous 6 days was images. Given that his average gratuity for the 10 workdays is $200, solve the following equation:

    images

    Richard’s average gratuity per day for the last four of the past 10 workdays is $230.

  115. C. images

    Use rules of exponents to determine the solution.

    images

  116. B. 1

    Rewrite the expression using the product rule for exponents.

    images. The product images has a units digit of 1 (because images). Thus, every power of images has a units digit of 1. Therefore, the units digit of images is 1, which implies the units digit of images is 1 as well.

  117. B. $22.50

    First, determine the cost of the meal before the gratuity was added. Next, divide the result by 20. Let C = the cost of the meal before the gratuity was added. Solve the following equation:

    images

    Thus, the cost of the meal before the gratuity was added is $450. Therefore, the average price of the meal per person not including the gratuity or sales tax is images.

  118. E. 200

    First, in the given expression, rewrite 80 in prime factored form. Next, apply the exponent 50 to the factored form. You have images. Thus, images is the highest power of 2 that is a factor of images. Therefore, images.

  119. B. images

    Let r = the radius of the circle. A radius from the center of circle to a tangent of the circle is perpendicular to the tangent. Thus, the circle’s center is located at images. Using the distance formula, solve the following equation:

    images

    Therefore, the circle’s radius is images.

  120. C. 14,400

    In going from point A to point E, there are 4 different ways to go from A to B, 2 different ways to go from B to C, 6 different ways to go from C to D, and 5 different ways to go from D to E. In returning from point E to point A, because the player cannot retrace a previous path taken, there are 4 different ways to go from E to D, 5 different ways to go from D to C, 1 way to go from C to B, and 3 different ways to go from B to A. Therefore, there are images different ways for the player to move from point A to point E and back without retracing a previous path taken.

  121. C. $7,000

    To calculate the per capita expenditure, divide $9.8 billion by 1.4 million.

    images

    The government’s per capita expenditure is $7,000.

  122. A. images

    From your knowledge of solving inequalities, you know the open circles at –3 and 4 mean that –3 and 4 are not included in the solution set. Thus, the inequality symbol in the answer must be either < or >, so eliminate choices (C) and (D).

    Test a number from the interval shown in the graph in each of the inequalities given in choices (A), (B), and (E). For convenience and ease of calculation, select 0 as your test number. For Choice (A) when x = 0, images, which is true. Thus, images is the correct answer.

    You have determined the correct answer, so there is no need to check the remaining answer choices. However, you can easily see that x = 0 does not satisfy the inequalities in choices (B) and (E) because images and images, respectively.

  123. D. 20%

    Given that both sales totals are expressed in millions, the percent increase from the previous year to the current year is

    images

  124. D. 53%

    Given that you’re working with percentages, for convenience and ease of calculation, assume the number of attendees at the party was 100. Then images attendees were friends of the bride and images attendees were friends of the bridegroom. Use logical reasoning to determine the solution. Because images, which is greater than 100 (the total number of attendees), logically, you can conclude that the excess images attendees were friends of both the bride and bridegroom. Thus, images attendees were friends of the bride, but not friends of the bridegroom. This number represents images of the attendees.

  125. E. 25

    Solve the following equation for images. Then multiply the result by 15.

    images

    Therefore, images.

  126. C. 6.25%

    Given that Amiel lost images pound each week for 30 weeks, he lost a total of images during this period. This amount represents images of Amiel’s original weight.

  127. D. 8,000

    Evaluate the quantity:

    images

  128. D. 6

    Solve the two equations. For the first equation,

    images

    For the second equation,

    images

    Given that images, images and images. Therefore, the product of m and n is images.

  129. D. 15

    Solve the given equation for x and then determine 3x.

    images

  130. E. 12NCP

    Each crate has images boxes, each of which yields P cents profit. The total profit, in cents, for each case is images. Therefore, the total profit, in cents, for N crates is images.

  131. C. 55%

    Given that you’re working with percentages, for convenience and ease of calculation, assume the total distance for the round trip is 100 miles. Upon arrival at City B, the motorist has driven images. It follows that the drive back to City A is also 50 miles. At the service station, the motorist has completed images of the trip from City B to City A. Thus, at that point, the motorist has completed images, which is images of the round trip.

  132. D. 5

    Given that the graph is symmetric about the vertical line at x =3, x values that are the same horizontal distance from 3 will have the same y values on the graph. From the graph, observe that 1 is 2 units to the left of 3, and 5 is 2 units to the right of 3. Therefore, the y value when x = 5 is the same as the y value when x = 1, which is 5.

  133. E. $247.50

    Compute the difference. images

    Therefore, the difference is $247.50.

  134. B. 200

    Let M = the number of 25-cent coins in the jar. Then images = the number of 10-cent coins in the jar. In dollars, the face value of each 25-cent coin is $0.25, and the face value of each 10-cent coin is $0.10. Given that the total face value of the coins is $94, solve the following equation:

    images

    Therefore, there are 200 25-cent coins in the jar.

  135. B. 22

    The mean of the four integers is their sum divided by 4. Solve the following equation:

    images

  136. D. $18,000

    Let 3x = the amount, in dollars, the youngest grandchild received, 4x = the amount, in dollars, the middle grandchild received, and 6x = the amount, in dollars, the oldest grandchild received. Solve the following equation for x, and then determine 3x, the amount, in dollars, that the youngest grandchild received.

    images

    Therefore, the youngest grandchild received $18,000.

  137. B. 800

    Let M = the school’s previous enrollment. Solve the following equation:

    images

    There were 800 students enrolled the previous year.

  138. B. images

    Each year the value of the investment increases by a factor of 1.02 images over the previous year. Let P = the amount of the initial investment. At the end of the first year, the value of the investment is images. At the end of the second year, the value of the investment is images. At the end of the third year, the value of the investment is images. Solve the following equation for P:

    images

    In terms of S, the amount of the initial investment is images.

  139. D. 20%

    The royalty percentage to number of copies ratio for the first 10,000 copies is

    images

    The royalty percentage to number of copies ratio for the next 15,000 copies is

    images

    The percent decrease in the ratios is

    images

    Therefore, the ratio of the royalty percentage to number of copies decreases by 20% from the first 10,000 copies to the next 15,000 copies.

  140. C. 96%

    Translating the statements into algebraic symbolism yields images and images. It follows that images.

  141. A. images

    Finn drove images at 30 miles per hour. It follows that Finn drove images miles at 60 miles per hour. Use the formula, images, where D is the distance traveled at a constant rate of speed, R, for a given time T, to determine the time for each portion of the trip.

    The time, in hours, it took Finn to drive X miles at 30 miles per hour is images, and the time, in hours, it took Finn to drive images miles at 60 miles per hour is images. Therefore, the total time, in hours, for the trip equals

    images

  142. B. 1,275K

    The sum of the first 50 multiples of K equals

    images

    Thus, the sum is the product of K and the sum of the 50 consecutive integers from 1 to 50. The formula for the sum of the N consecutive integers from 1 to N is images. Therefore, the sum of the first 50 multiples of K equals images.

  143. A. 21

    Together, the girls have less than P colored markers, so images, which implies that images. Given that each girl has at least one colored marker, images and images, which implies, images. Hence, images. Therefore, P = 21 because the situation in the question implies P is a positive integer.

  144. B. images

    Because the pens are randomly drawn from the box, each draw is independent of the other draws. After three non-defective pens have been drawn, there are only seven pens left in the box, one of which is defective. Therefore, the probability that the next pen drawn is defective is images.

  145. B. II only

    The expression in I is not factorable over the real numbers, so images is not a factor of this expression. Reject I, and eliminate choices (A) and (D). The expression in II can be factored as images, so images is a factor of this expression. The correct answer must include II. Eliminate Choice (C). Expanding the expression in III yields images, which does not contain images as a factor. Reject III, and eliminate Choice (E). Therefore, Choice (B), II only, is the correct answer.

  146. B. –2

    Solve the two equations simultaneously using the elimination method. To eliminate m, multiply the second equation by images, and add the result to the first equation. Then solve for n.

    images

  147. C. III only

    The mean of the first three major exams is images. Let F = the student’s score on the fourth major exam. Check the Roman choices using the following expression: images. Check I: images, which is less than 90.0. Thus, reject I, and eliminate choices (A) and (E). Check II: images, which is less than 90.0. Thus, reject II and eliminate choices (B) and (D). Therefore, the correct answer is Choice (C), III only. You do not have to check III, but to verify, images, which is greater than 90.0.

  148. D. 150

    The angles that measure images and imagesare angles formed when parallel lines are cut by a transversal. The angle that measures images and the angle above line n and adjacent to the angle that measures images are congruent because they are alternate interior angles of parallel lines. Thus, the angles that measure images and images are supplementary angles. Recall that the sum of supplementary angles is images. Thus, images. It is given that images, so images. Solve this equation for y, and then determine 5y, the value of x.

    images

    Therefore, the value of x is 150.

  149. B. 125

    Let P = the population of horned lizards in the park. The proportion of tagged lizards in the second group should equal the proportion of tagged lizards in the whole population, P. Set up a proportion and solve for P.

    images

    The best estimate of the horned lizard population in the park is 125.

  150. C. images

    According to the graph, 45 students chose 5 or higher as a response (because 30 chose 5, 5 chose 6, and 10 chose 7) and 30 students chose 3 or lower as a response (because 10 chose 3, 15 chose 2, and 5 chose 1). Therefore, the ratio of the number of students who chose 5 or higher to the number of students who chose 3 or lower is images.

  151. B. 11

    Use logical reasoning to determine the solution. Because images, which is greater than 76 (the total number of customers), you can conclude that the excess images is the number of customers who bought both a washer and a dryer.

  152. A. images

    Plug the units into the lift formula and simplify as you would for variable quantities.

    images

    Given that images has no units, the lift of an airplane has units of images.

  153. E. I, II, and III

    The sum of the lengths of any two sides of a triangle must be greater than the third side. It follows that given two sides of lengths 14 and 31, the length of the third side must be greater than imagesand less than images; that is, images. Select Choice (E) (I, II, and III) because each satisfies the double inequality.

  154. A. images

    The probability of 50 appearing on the up face at least once in three tosses of the number cube is 1 minus the probability of no 50 appearing in three tosses. The probability that 50 appears on the up face in one toss of the number cube is images. Thus, the probability of no 50 in one toss of the number cube is images. The probability of no 50 in three tosses is images. Therefore, the probability of at least one 50 in three tosses of the number cube is images.

  155. C. 4

    The equation imagesis equivalent to images. The rate of change for this equation is 4. Therefore, for every 1-unit increase in x, there is a 4-unit increase in y.

  156. C. $1,365

    The armoire’s original price was 70% of $1,500, which is images. The armoire’s selling price was 130% of $1,050, which is images.

  157. D. 11

    Given that k is an integer, then images and images are integers as well. Because n is a factor of both images and images, then images and images for positive integers a and b. Hence, as shown here, n is a factor of images, which implies, by substitution, that n is a factor of images. The only factors of 11 are 1 and 11. Given that n is prime, it follows that n equals 11.

  158. D. 9

    Expand the right side of the equation, and then set corresponding coefficients equal to each other to determine c.

    images

    Thus, images, which implies images; and images. Therefore, images.

  159. A. images

    The prism is composed of 36 cubes: three images layers of 12 cubes each. After the prism is submerged in paint, the 24 cubes that make up the top and bottom layers will have paint on them. In the middle layer, 10 cubes will have paint on them: the 3 cubes on each of the two ends of the middle layer and the 2 cubes in the center on each side of the middle layer. Hence, images cubes will have paint on them. Thus, only images cubes will have no paint on them. Therefore, the fraction of small cubes that will not have any paint on them is images.

  160. B. images

    The probability that the token is red or black, denoted images, is the probability that the token is red, denoted images, plus the probability that the token is black, denoted images. First, determine the number of red or black tokens in the bag. Then calculate the necessary probabilities. Let G = the number of green tokens, 2G = the number of red tokens, images = the number of black tokens, and images = the number of white tokens. Solve the following equation for G and then determine 2G and images:

    images

    Thus, the number of red tokens is 10 and the number of black tokens is 11. Therefore, the probability that the token drawn is red or black is images

  161. B. 4

    Rewrite images as images, which implies that images. Substitute values for p to determine the least one that makes this inequality true: images. Therefore, images is the least positive integer that satisfies the inequality.

  162. E. 16

    You can list the factors of 1,000 (1, 2, 4, 5, etc.), or you can use the following theorem: If the prime factorization of a positive integer n is images, where each imagesis a distinct positive prime number and images is its corresponding exponent, then the number of positive factors of n is the product images. The prime factorization of 1,000 is images. Therefore, 1,000 has images positive factors.

  163. D. 612

    Given that the units digit is images times the hundreds digit, then the hundreds digit can be only 3, 6, or 9. Thus, the units digit can be only 1, 2, or 3. The units digit is twice the tens digit, so the units digit must be even. Thus, the units digit is 2, which makes the tens digit 1. Therefore, the number is 612.

  164. E. 8

    Perform the indicated operations:

    images

  165. E. 18

    The possible remainders for division by a positive integer D are images. Given that 9 is the remainder when w is divided by x, then images. Similarly, given that 7 is the remainder when z is divided by y, then images. Therefore, the least value of images is images.

  166. D. images

    The ratio of AB to CD is

    images

  167. A. images

    Simplify the expression:

    images

  168. E. 15

    Let t = the time (in hours) it will take to fill the tank if both valves are open. The portion of the tank that is being filled per hour when both valves are open is images. The portion of the tank that the input valve is filling per hour is images. The portion of the tank that the output valve is emptying per hours is images. Thus, because the valves are working counter to each other, the net portion that is being filled per hour when both valves are open is images. Thus, images, which implies images. Therefore, the time to fill the tank to capacity if both valves are open is 15 hours.

  169. B. 0.2

    The probability that the house next door will be sold if the model home is sold first is a conditional probability. If M is the event that the model home will be sold and N is the event that the house next door will be sold, then the probability that the house next door will be sold if the model home is sold first is

    images.

    Looking at this formula, you are given images, but you are not given images, which is the probability that both houses will be sold, regardless which is sold first. Using the formula for the probability that two events occur at the same time and the question information, you have

    images

    Note: images is the probability that at least one of the two houses will be sold, which is given as 0.8 in the question information.

    Therefore

    images

  170. C. 8

    The angle bisector of an angle of a triangle divides the opposite side in the ratio of the two sides that form the angle bisected, with each of these sides corresponding to the segment to which it is adjacent. Thus, solve images:

    images

  171. E. I, II, and III

    images implies images. Make an organized table in which each column contains two factors whose product is 196 in the first two rows and their sum in the third row.

    factor

    1

    2

    4

    7

    14

    factor

    196

    98

    49

    28

    14

    sum

    197

    100

    53

    35

    28

    The possible sums for two-factor combinations are 197 (not a choice), 100 (III), 53 (II), 35 (I), and 28 (not a choice). Therefore, Choice (E) (I, II, and III) is the correct answer.

  172. A. 400

    Show the possible products in a table.

    Spinner 1

    10

    20

    30

    40

    Spinner 2

    10

    100

    200

    300

    400

    20

    200

    400

    600

    800

    30

    300

    600

    900

    1,200

    40

    400

    800

    1,200

    1,600

    The table shows that the product 400 occurs three times, which is more often than the occurrence of any other product. Therefore, the product most likely to occur is 400.

  173. D. II and III only

    The square root symbol images always returns the principal square root, which is nonnegative, so the solution set of images (I) is 2. Thus, the correct answer does not contain I. Eliminate choices (A) and (E). The solution set of images is images. The correct answer contains II. Eliminate Choice (C). The solution set of images contains images. Eliminate Choice (B). Therefore, the correct answer is Choice (D), II and III only.

  174. C. images

    The number of patrons who chose nonfiction genres is images, and the number who chose fiction genres is images. Therefore, the ratio of the number of patrons who chose nonfiction genres to the number who chose fiction genres is images.

  175. C. 420

    First determine T, the time, in hours, that it will take for the two machines working simultaneously to produce 1,050 components. The portion of the 1,050 components that Machine A can produce per hour is images, and the portion of the 1,050 components that Machine B can produce per hour is images. Thus, the number of components the two machines together can produce per hour is

    images

    Thus,

    images

    Therefore, at the end of 3 hours, because Machine B produces 140 components per hour, Machine B has produced images components.

  176. A. images

    The perimeter of triangle SQT is images. Make a sketch. Extend images to images. Label the point of intersection K.

    image

    © John Wiley & Sons, Inc.

    Given that images and imagesare parallel, images is perpendicular to images (because a line perpendicular to one of two parallel lines is perpendicular to the other one as well). Angle KQS is a 45° angle because its measure is images. Given that images and images are parallel and images, images is a 30° angle (because alternate interior angles of parallel lines are congruent). Find KQ and KS, the lengths of the legs of the 45°-45°-90° right triangle SKQ, which has hypotenuse of length 50. The length of the sides of a 45°-45°-90° right triangle are in the ratio images. Hence,

    images.

    Use KQ to find both QT, which is the length of the hypotenuse of the 30°-60°-90° right triangle TKQ; and KT, which is the length of the side opposite the 60° angle. The lengths of the sides of a 30°-60°-90° right triangle are in the ratio images. So images and images. Use KT and KS to find ST, which isimages. Therefore, the perimeter of triangle SQT is

    images

  177. B. 1

    Absolute value is always nonnegative, so images. Thus, the least possible value for images is 0. This equation has solution images. Given that x is an integer, the integer value of x for which images is least is the integer that is closest to images. Therefore, x is 6, which yields images.

  178. C. I and II only

    Do not assume that Carson went in a straight line in one direction. Let D = Carson’s distance, in miles, from the family RV. Make a sketch. Show the RV and ranger station as 6 miles apart. Construct a circle at the ranger station with radius 8 miles.

    image

    © John Wiley & Sons, Inc.

    From the sketch, you can determine that images. Select I and II because each falls in this interval. Eliminate III because it is too far. Therefore, the correct answer is Choice (C), I and II only.

  179. A. images

    The probability that Rory will not get a job offer is images. Therefore, the probability that Katie and Ace will get job offers, but not Rory is images.

  180. C. 12

    The three constraint inequalities define a region in the xy-plane that represents their intersections. The region’s boundary equations are images, images, and images. The maximum value of P will occur at one of the intersections of these three linear equations. To find the maximum value of P, systematically pair the three equations and solve for their intersections. Solving images and images by substitution yields

    images

    Thus, the intersection of images and images is images. Solving images and images by substitution yields

    images

    Thus, the intersection of images and images is images. Solving images and images by elimination yields

    images

    Thus, the intersection of images and images is images. Substitute the intersection points into images to find the maximum. For images, images. For images, images. For images, images. Therefore, subject to the given constraints, the maximum value of P is 12, which occurs at images.

  181. B. images decrease

    If b increases by 50% of its value to images, then a must decrease to images, which is images, so that the product images remains constant. Thus, if b increases by 50% of its value, then a should decrease by images of its value to keep the equation a true statement.

  182. B. 128

    The area of square ABCD is images. Right angle DAB is an inscribed angle. Thus, the degree measure of arc DB is 180° (because the degree measure of an inscribed angle is half the degree measure of its intercepted arc), so imagesis a diameter of the circle. Let D = the length of the diameter, images. Then, images, which implies images. It follows that 16 is the length of the hypotenuse of right triangle DAB, which has congruent legs of length s. Use the Pythagorean theorem to determine images, the area of the square.

    images

    The square’s area is 128.

  183. A. I only

    images is undefined when images because the denominator images equals zero when images. Simplified, images, whose graph is defined for all real numbers except images. Thus, its graph, which, otherwise, would be the graph of the line images does not contain the point images. The graph of images passes through the point images but it does not intersect images because images is excluded from the domain of the latter function. Hence, images and images have zero points of intersection. Therefore, Choice (A), I only, is the correct answer.

  184. B. 20%

    Let x = the number of coins at A, 2x = the number of coins at B, 3x = the number of coins at C, 4x = the number of coins at D, and 5x = the number of coins at E. The minimum number of coins needed to win is 50% of the combined number of coins in locations A, B, and C (because these locations have the fewest number of coins). This minimum number is images. The total number of coins is. images. Therefore, the minimum percent to win is images.

  185. E. 720

    For any two positive integers, their product equals their greatest common factor times their least common multiple. Therefore, the product of p and q = images.

  186. D. 16

    Use logical reasoning to determine the solution. The machines are identical, so if two machines can complete the job in 40 hours, then it should take twice as long for one machine to complete the same job. So one machine can complete the job in 80 hours. If five such machines do the job together, they should take images as long as it takes for one machine. Therefore, five machines can complete the same job in images.

  187. D. 24

    The greatest number of packets that the teacher can make is the greatest common factor of 72 and 48, which is 24. In each of the 24 packets there will be 5 pens: 3 black pens and 2 red pens. No pens will be left over because images.

  188. C. Two

    The equation imagesis undefined when its denominator equals zero. Set the denominator equal to zero and solve for x.

    images

    Therefore, there are two values of x for which images is undefined.

  189. E. 5 to 17

    Half of the 400 multiples of 5 are odd, and half are even. All of the multiples of 4 are even including images that are multiples of 5. Thus, the total number of odd numbers is 200 and the total number of distinct even numbers is images. The ratio of odd to even is images or 5 to 17.

  190. C. 3 to 1

    Write and simplify the ratio:

    images

    Therefore, the ratio is 3 to 1.

  191. D. I and III only

    Factoring the expression on the right side yields images. Thus, y is zero when x is a, b, c, or d; and y is negative when it has one or three negative factors. Make a sign chart showing where y has positive and negative values.

    images

    images

    images

    images

    images

    images

    -

    +

    +

    +

    +

    images

    -

    -

    +

    +

    +

    images

    -

    -

    -

    +

    +

    images

    -

    -

    -

    -

    +

    y

    +

    -

    +

    -

    +

    The chart shows that when x lies to the left of a value that makes a factor zero, that factor is negative, and when x lies to the right of the value, that factor is positive. According to the sign chart, y is negative in the interval images(I) because it has three negative factors in that interval; y is positive in the interval images (II) because it has two negative factors in that interval; and y is negative in the interval images (III) because it has one negative factor in that interval. Therefore, the correct answer is Choice (D), I and III only.

  192. E. images

    Let A = the amount (by weight) of the 25% brown rice mixture (Mixture A) in the blend; let B = amount (by weight) of the 40% brown rice mixture (Mixture B) in the blend; and images = the amount (by weight) of the 30% brown rice blend. Make a table to organize the information given.

    When?

    Percent brown rice

    Amount (by weight)

    Amount of brown rice (by weight)

    Before

    25%

    A

    25%A

    40%

    B

    40%B

    After

    30%

    images

    30%(A + B)

    Using the table, write an equation based on the following fact: The amount of brown rice before mixing equals the amount of brown rice after mixing.

    images

    Therefore, the percent by weight of mixture A in the blend is

    images

  193. B. images

    Simplify the expression:

    images

    This result is equivalent to images.

  194. D. images

    Solve the equation for x.

    images

  195. A. –2

    Let x = the tens digit and y = the units digit of the original number. Solve the following equation for images:

    images

  196. E. 1:15 p.m.

    Use logical reasoning to determine the solution. After images hours (= 1 hour and 30 minutes), the van has traveled

    images

    Thus, when the car starts out at 9:30 a.m. the van is 75 miles ahead. The car is traveling 20 miles per hour faster than the van (because images). To overtake the van, the car will have to make up the 75-mile difference at an average speed, relative to the van, of 20 miles per hour. Thus, the time, in hours, for the car to overtake the van is images hours, which is 3 hours and 45 minutes. Therefore, the car will overtake the van at 9:30 a.m. plus 3 hours and 45 minutes, which is 1:15 p.m.

  197. B. 12

    Given that point O is the origin, point A is located on the positive y-axis, and point B is located on the positive x-axis, triangle AOB is a right triangle with legs of lengths a and 8 and area of 48. Solve the following equation for a:

    images

  198. B. 144

    There are 8 ways to select the first digit; 2 ways to select the second digit, and 9 ways to select the third digit. Therefore, there are images different possible codes.

  199. C. 14

    N is an odd integer because the remainder is 1 when N is divided by 2. Given the remainder is 4 when N is divided by 5, N has the form images where images. The expression images generates the integers 4, 9, 14, 19, 24, 29, etc. These integers show a pattern of ending in 4 or 9. Then, because N is odd, its units digit must be 9. Because the remainder is 2 when N is divided by 3, N cannot equal 9 or any other multiple of 3. Thus, N must have at least two digits. Two-digit candidates for N are 19, 29, 49, 59, 79 and 89. Of these, only 59 has remainder 2 when divided by 3 and remainder 3 when divided by 4. Thus, the least possible value of N is 59. And the sum of its digits is 14.

  200. E. Five

    The least possible product will be negative. Therefore, it must contain an odd number of negative factors. The least negative product possible is images, which can be obtained in five ways using the expression images, where p is 1, 3, 5, 7, or 9. For example, when p is 3, images

  201. B. 49

    Let p, q r, M, x, y, and G be the seven integers, listed from least to greatest. From the question information, imagesand images. The greatest value of G will occur when p has a maximum value, which will occur only if images. Thus, from least to greatest, the integers are p, p, p, 42, x, y, and images. The integers x, y, and G are listed on the right of the median 42. Thus, G will have it maximum value when x and y have their least possible values, which, in this case, is images. Then, from least to greatest, the integers are p, p, p, 42, 42, 42, and images. Solve the following equation for p, then determine images:

    images

    Therefore, the maximum possible value for the greatest of the seven integers is 49.

  202. A. $6.25

    Mani’s total savings, in dollars, for the six months is

    images

    Solve the following equation for S, and then determine images, the amount saved the sixth month:

    images

    Therefore, Mani saves $6.25 in the sixth month.

  203. B. 22

    Let F = the number of pages Rose read on the first day. Solve the following equation:

    images

    Rose read 22 pages on the first day.

  204. D. II and III only

    First, determine values of x that satisfy images.

    images

    Given that x is an integer, only images satisfy the inequality. Substitute each of these values into images and evaluate. For images,

    images

    Thus, the correct answer must include II. Eliminate Choice (A). For images, by inspection, images. Thus, the correct answer must include III. There are no other possible values for x, so Choice (D), II and III only, is the correct answer.

  205. D. 12

    The integers a and b are even because each contains at least one factor of 2. Thus, there exists integers m and n such that images and images. Then by substitution,

    images

    Thus, 12 is the greatest even number that must be a factor of K.

  206. C. images

    First, determine the initial number of bus riders. images bus riders in the school district. Next, determine how many bus riders transferred. images. The number of students remaining in the school district is images. The number of bus riders remaining in the school district is images, which represents images of the students remaining in the school district.

  207. D. I and II only

    The lowest score the student can make is images. The highest score the student can make is images. Thus, images. Any score in this range is possible. Eliminate III because it is too high. Therefore, Choice (D), I and II only, is the correct answer.

  208. B. 10

    First simplify Z:

    images

    Then images.

  209. E. 130

    images (because vertical angles of intersecting lines are congruent); and images (because corresponding angles of parallel lines are congruent). Solve the following equation for x, then determine either images or images:

    images

  210. E. 16

    When a positive integer is divided by 8, the possible remainders are 0, 1, 2, 3, 4, 5, 6, and 7. Thus, any nonnegative integer has the form images. Given that N is not divisible by 2 or 4, then N has the form images. Therefore, the sum of the possible remainders when N is divided by 8 is images.

  211. C. 102%

    Because you’re working with percentages, you can pick a convenient value for the original price of the jacket. Let $100 = the jacket’s original price. Then the 15%-off sale price is images. After the sale, this sale price is increased to images. Therefore, the final price of the jacket is images of its original price.

  212. D. images

    Solve for x:

    images

  213. D. 80

    Triangle PQR is isosceles (because images). The angle at R measures 50° (because base angles of an isosceles triangle are congruent). The sum of the measures of the interior angles of a triangle is 180°. Therefore, images.

  214. E. 6 to 1

    For convenience, suppose initially the solution weighs 100 grams. The percent water by weight in the initial solution is images.Then it would contain 10 grams (= 10% of 100) of salt and 90 grams (= 90% of 100) of water. After evaporation, the amount of salt, in grams, is still 10. This now represents 40% of the evaporated solution by weight. Write the following percent equation and solve for S, the new weight, in grams, of the solution (after evaporation):

    images

    Subtract the weight of the salt to obtain the final weight, in grams, of water in the evaporated solution. images. Therefore, the ratio of the initial weight to the final weight of water in the solution is images, which is 6 to 1.

  215. C. 13

    Use the “3-D” Pythagorean theorem to determine the answer. Therefore, the length of the space diagonal is images.

  216. D. images

    Equilateral triangles are equiangular, so each angle is 60°. The altitude of an equilateral triangle bisects the angle at the vertex from which it is drawn, and it bisects the side to which it is drawn. Let 2x = the length of a side of the equilateral triangle. Make a sketch to illustrate the situation.

    image

    © John Wiley & Sons, Inc.

    The altitude shown is the leg opposite the 60° angle in a 30°-60°-90° right triangle. The sides of a right triangle are in the ratio images. Solve the following proportion for x, then determine 2x:

    images

    Therefore, the area of the triangle is images

  217. E. 16

    In a circle, a radius that is perpendicular to a chord bisects the chord. Let x = one-half the length of the chord. Then 2x = the length of the chord. Make a sketch, filling in the question information.

    image

    © John Wiley & Sons, Inc.

    Using the Pythagorean theorem, solve for x, then determine 2x, the chord’s length:

    images

    Therefore, the length, in centimeters, of the chord is 16.

  218. B. 80%

    Because you’re working with percentages, you can pick a convenient value for the price of season tickets last year. Let $100 = the price of season tickets last year. Then the price of season tickets this year is images. Therefore, last year’s price represents the following percent of this year’s price:

    images

  219. C. 70

    Consecutive angles of a parallelogram are supplementary (that is, their sum is 180°). Write an equation and solve for x. Then determine images and images:

    images

    Therefore, the measure, in degrees, of the smaller angle is 70.

  220. D. 23

    Find all the positive integers that leave a remainder of 2 when you divide 17 by the integer. Test positive integers less than 17 by mentally dividing and checking whether the remainder is 2. Only when 17 is divided by 3, 5, or 15, is the remainder 2 each time. Therefore, the sum of all possible values of K is 23.

  221. A. 3,600

    To determine the number of different meal combinations, find the product of the number of options for each selection. This product is images. Therefore, there are 3,600 different meal combinations.

  222. C. 0.64

    The probability that Jayma will receive an acceptance letter from at least one of the two universities, denoted images, is the probability she will receive an acceptance letter from university A, denoted images, plus the probability she will receive an acceptance letter from university B, denoted images, minus the probability she will receive an acceptance letter from both universities, denoted images. This probability is

    images

  223. B. 24

    The people are not assigned to particular seats but are arranged relative to one another only. Two arrangements are considered different only when the positions of the people are different relative to each other. Thus, given that the chairs are identical, the five different ways the first person can be seated are indistinguishable. It follows that the number of different seating arrangements equals the number of ways to fill the other four chairs once the first person’s position is fixed somewhere around the circular pattern. Therefore, there are 4 ways to seat the second person, 3 ways to seat the third person, 2 ways to seat the fourth person, and 1 way to seat the fifth person, for a total of images different seating arrangements.

  224. D. images

    Write the radicals using fractional exponents, then multiply the exponents and simplify:

    images

  225. A. One

    Solve the inequality:

    images

    The only integer that satisfies this double inequality is the integer 1. Therefore, the answer is one.

  226. B. images

    Simplify the expression using the rules of exponents:

    images

  227. D. 1

    To solve the equation, use the technique of squaring both sides of the equation, as necessary, to eliminate radicals.

    images

  228. C. images

    Observe that the numbers 4, 8, and 128 are powers of 2. Substitute powers of 2 into the given equation and let images to obtain images. Simplifying this equation yields images, which implies images. Solve this equation for x:

    images

  229. B. 5

    When two chords intersect within a circle, the products of their segments are equal. Chords images and images intersect at point E. Thus, solve the following equation for x:

    images

  230. A. images

    For convenience, let 15 (a common denominator for 3 and 5), be the number of student surveyed. Then the number of participants who answered “Strongly Agree” to both questions is images. Thus, images did not answer “Strongly Agree” to both questions. Therefore, the portion of the survey participants who did not answer “Strongly Agree” to both questions is images.

  231. D. I and III only

    The situation in the question implies that B and J are positive integers. According to the question, images, then images. Thus, J is an integer only if images is divisible by 3. Because images, which is divisible by 3, the correct answer must include I. Eliminate choices (B) and (C). Because images, which is not divisible by 3, eliminate Choice (E). Because images, which is divisible by 3, the correct answer must include III. Therefore, the correct answer is Choice (D), I and III only.

  232. D. 61

    Start with the angles for which you can find the measure by using the given information. The sum of the degree measures of the interior angles of a triangle is 180°, so images, which implies images. Then, images (because these angles form a straight angle) implies images. Therefore, images, which implies images.

  233. C. 16

    The possible remainders when an integer is divided by 7 are 0, 1, 2, 3, 4, 5, and 6; and the possible remainders when an integer is divided by 11 are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Therefore, the greatest value for images is images.

  234. B. images

    First, substitute images into the equation and solve for k:

    images

    Next, substitute images into the equation and solve for x:

    images

Chapter 4

  1. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From the question information images and images because both are positive integers. From (1) images, which, because images, implies images (and so implies images), yielding an answer of Yes to the question posed. Thus, (1) is sufficient.

    According to (2) images, so it’s possible for images (if say x = 1 and y = 75) or for images (if say x = 4 and y = 80). So (2) is not sufficient to give a definite Yes or No answer to the question posed. Therefore, statement (1) alone is sufficient.

  2. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From the question information, the total time for the trip is 4 hours images. And the total distance traveled images. Thus, the average speed, call it s, in terms of x and y, is images. Using (1), substitute images into images to obtain

    images

    You have two variables, s and y, and only one equation images, so (1) is not sufficient.

    Using (2), gives images, so (2) is sufficient. Therefore, statement (2) alone is sufficient.

  3. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1) you can conclude that x and y have the same sign because their product is positive, but without additional information you cannot determine whether images. Thus, (1) is not sufficient.

    From (2) you can conclude that y and z have opposite signs because their product is negative, but without additional information, you cannot determine whether images.

    Taking (1) and (2) together, if y is positive, then x is also positive, and z is negative, so images. If y is negative, then x is also negative, and z is positive, so images. Therefore, in either case, you can answer Yes to the question posed. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  4. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), if n is a prime number, then the answer to the question is No, because there are no prime number factors k such that images. However, if n is not a prime number (for example, if images), the prime number factor k could be 3 or 5, so then the answer to the question is Yes. You have no way of knowing whether n is prime or not, so (1) is not sufficient.

    Using (2), 10! is the product of all positive integers descending down from 10 to 1. Then n is one of the nine integers from images to images. Note that any prime number images is a factor of 10! Thus, 2 is a factor of images, images, images, images, and images; 3 is a factor of images and images; 5 is a factor of images; and 7 is a factor of images. Thus, for each integer n from images to images, there is a prime number factor k of n. So the answer to the question posed is Yes. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  5. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let P = the selling price, in dollars, of one tee shirt. From (1), the amount expected to be denoted is 1,000P, which you cannot determine because P is unknown. Thus, (1) is not sufficient.

    From (2), the expected amount plus an additional 500P is $30,000. Thus, the expected amount to be denoted is images, which you cannot determine because P is unknown. Thus, (2) is not sufficient.

    Taking (1) and (2) together gives images, from which you can determine P: and, thereafter, compute 1,000P, the amount the organization expected to denote. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  6. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1) you have the length of the shelf, but without additional information, you cannot give a definite Yes or No answer to the question posed.

    From (2), you can determine that the greatest length that is needed to accommodate the 25 books is images, but without additional information, you cannot give a definite Yes or No answer to the question posed.

    Taking (1) and (2) together, if the average thickness of the books is, for instance, exactly images inches, then the answer to the question posed is No (because images, which is greater than 36). However, if the average thickness is say 1 inch, then the answer is Yes (because images, which is less than 36 inches). Therefore, statements (1) and (2) together are not sufficient.

  7. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let D = the current number of Josephine’s dolls. From (1), images, which implies images. Thus, D cannot be less than 12, but without further information you cannot determine an exact value of D. Thus, (1) is not sufficient.

    From (2), images, which implies images. Thus, D can be any number from 1 to 12, but without further information, you cannot determine an exact value of D.

    Taking (1) and (2) together gives images, which implies that images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  8. D. Each statement ALONE is sufficient.

    If you multiply (or divide) both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol. From (1) images implies images. Thus, images because the cube root of a negative number is negative. So the answer to the question posed is Yes. Thus, (1) is sufficient.

    From (2), images implies images, which yields an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  9. D. Each statement ALONE is sufficient.

    Let P = the number of pepper plants in the garden. Using the question information and (1) gives the proportion images, which you can solve for P. Thus, (1) is sufficient.

    Using the question information and (2) gives the proportion images, which you can solve for P. Therefore, each statement alone is sufficient.

  10. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let A = the number of avocados sold today, and P = the number of pineapples sold today. From (1), images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of A. For example, if images, then images. But if images, then images. Thus, (1) is not sufficient.

    From (2), images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of A. For example, if images, then images. But if images, then images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, yields a system of two equations, images and images, with two variables, A and P. The system has a unique solution because images. Thus, you can determine a unique value of A. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  11. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let R = the number of red chips. From (1), the total number of chips is 48, and the number of black chips is 16. But additional information is needed to determine the number of red chips.

    From (2), the number of green chips is half the number of total chips, but additional information is needed to determine the number of red chips.

    Taking (1) and (2) together, images, which you can solve for R. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  12. D. Each statement ALONE is sufficient.

    From (1), images implies images, which implies images. Thus, (1) is sufficient.

    From (2), images implies images, which implies images. Note that (1) and (2) give the same result because images. Therefore, each statement alone is sufficient.

  13. D. Each statement ALONE is sufficient.

    From (1), images, from which you can solve for B; and, thereafter, determine images.

    From (2), images, from which you can solve for B; and, thereafter, determine images. Therefore, each statement alone is sufficient.

  14. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images implies images (because base angles of an isosceles triangle are congruent). However, without additional information, you cannot determine the value of x or z. Thus, (1) is not sufficient.

    From (2), because the measure of an exterior angle of a triangle equals the sum of the measures of the nonadjacent interior angles, images, which you can solve for z. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  15. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    The formula for the slope m of a line is images, where images and images are two points on the line. This formula indicates that two points are needed to find a line’s slope. From (1), you have one point on line p, but another point on line p is needed to determine the slope and whether it is negative.

    From (2), you have one point on line q, but another point on line q is needed to determine the slope and whether it is negative.

    Taking (1) and (2) together yields no additional useful information. Therefore, statements (1) and (2) together are not sufficient.

  16. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Let B = the number of students enrolled at Sunshine Elementary School who ride the ride the bus to school. From (1), images of the students enrolled at Sunshine Elementary School do not walk to school. However, not all of the non-walkers are necessarily bus riders. Some students may get to school by other means of transportation. Thus, (1) is not sufficient to determine a definite Yes or No answer to the question posed.

    Using (2), if X is the number of students enrolled at Sunshine Elementary School who do not ride the bus to school, then images. Thus, the percent of the students enrolled at Sunshine Elementary School who ride the bus to school is

    images

    So you have a response of Yes to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  17. D. Each statement ALONE is sufficient.

    Recall that images, images, and images images. From (1), if images is even, then 5k is even. Given that 5 does not contain a factor of 2, it follows that k is an even integer, yielding an answer of Yes to the question posed.

    From (2), if images is odd, then images is even. Given that square roots of even numbers are even, it follows that k is an even integer, yielding an answer of Yes to the question posed. Therefore, each statement alone is sufficient.

  18. D. Each statement ALONE is sufficient.

    Let P = Hollis’s current gross hourly pay in dollars, and images = Hollis’s gross hourly pay after an increase of $2 per hour. From (1), the increase in Hollis’s gross hourly pay is images of her current gross hourly pay. Thus, images, which implies images and images = $20. The number of hours Hollis could work each week and earn the same gross weekly pay is

    images

    This result is 4 hours fewer than 40 hours. Thus, (1) is sufficient.

    From (2), images and images = $20. This information is the same as that obtained from statement (1) and will yield the same result. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  19. D. Each statement ALONE is sufficient.

    From (1), images implies images, yielding an answer of Yes to the question posed. Thus, (1) is sufficient. Note that images implies none of the factors a, b, or c is 0.

    From (2), images implies images, which implies images and images, yielding an answer of Yes to the question posed. Note that images implies none of the factors a, b, or c is 0. Therefore, each statement alone is sufficient.

  20. D. Each statement ALONE is sufficient.

    Given that images, then images will equal M, the least common multiple of images and images, only if the greatest common factor of images and images is 1. Thus, by inspection, (1) is sufficient to determine the answer to the question posed.

    To use (2), express images as images. Given D is a factor of images, then because D is a factor of images, D must also be a factor of –1. The factors of –1 are 1 and –1. It follows that D is 1 because it is the greatest common factor of images and images. Thus, (2) is sufficient to determine the answer to the question posed. Therefore, each statement alone is sufficient.

  21. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    To use (1), express images as

    images

    Then, because images, images. Thus, (1) is sufficient.

    From (2), images implies images. Substituting into images yields images. The value of this expression varies depending on the value of b. For example, images if images and images if images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  22. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), given that the units digit of 2K is 6, it follows that the units digit of K is 3 or 8. But without additional information, you cannot determine a single value for the units digit. Thus, (1) is not sufficient.

    From (2), given that the hundreds digit of 100K is 8, then the units digit of K is 8 because the hundreds digit of 100K is always equal to the units digit of K. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  23. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images implies images. Without knowing n, you cannot determine whether this expression is an integer. For example, if images, then images, which is an integer. But if images, images, which is not an integer. Thus, (1) is not sufficient.

    From (2), because n is positive,images implies

    images

    This result is an integer, yielding an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  24. D. Each statement ALONE is sufficient.

    The decimal equivalent of images is approximately 0.429. From (1) images implies images because images. Thus, (1) is sufficient to answer the question posed.

    From (2), images implies images. So images because images. Thus, (2) is sufficient to answer the question posed. Therefore, each statement alone is sufficient.

  25. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Using (1), let S = the amount, in dollars, of the sales clerk’s total weekly sales last week. Then the sales clerk earned images as commission on last week’s total sales. Without knowing S, you cannot determine the amount of the sales clerk’s commission. Thus, (1) is not sufficient.

    Using (2), you can determine neither the amount of last week’s total sales nor the commission rate, both of which are needed to determine the sales clerk’s commission. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you have the commission rate, but not the amount of last week’s total sales, which is needed to determine the sales clerk’s commission. Therefore, statements (1) and (2) together are not sufficient.

  26. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Let B = the price of one banana and N = the price of one navel orange. Then Chiaki paid images. From (1), images, but without additional information, you cannot determine images. Thus, (1) is not sufficient.

    From (2), images. Dividing both sides of this equation by 3 yields images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  27. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    The area of the triangle is images.

    From (1), images implies images. Substituting into images yields images. The value of this expression varies. For example, images gives images; and images gives images. Thus, (1) is not sufficient.

    From (2), images because the Pythagorean theorem applies to the sides of the triangle. Substituting into images yields images. The value of this expression varies depending on the value of a.

    Taken (1) and (2) together, you can substitute images into images and obtain the area. Thus, (2) is sufficient. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  28. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images implies images. Thus, (1) is sufficient.

    From (2), images implies images, which varies depending on the value of y. For example, images gives images; and images gives images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  29. D. Each statement ALONE is sufficient.

    From the question information, given that the mean of the eight numbers is 60, then the sum of the eight numbers is images. From (1), if none of the eight numbers is less than 60, then suppose n of the numbers are greater than 60 and images of the numbers equal 60. For the n numbers that are greater than 60, let images = the positive difference between the first number and 60, images = the positive difference between the second number and 60, and so on to images = the positive difference between the nth number and 60. Let p = the sum of the n images differences. where images. Then the sum of the eight numbers is

    images

    This result indicates that the sum of the eight numbers is greater than 480, which contradicts the fact the sum of the eight numbers equals 480. Thus, n must be 0, which implies each of the eight numbers equals 60. Thus, (1) is sufficient.

    From (2), if none of the eight numbers is greater than 60, then suppose k of the numbers are less than 60 and images of the numbers equal 60. For the k numbers that are less than 60, let images = the positive difference between 60 and the first number, images = the positive difference between 60 and the second number, and so on to images = the positive difference between 60 and the kth number. Let d = the sum of the k images differences, where images. Then the sum of the eight numbers is

    images

    This result indicates that the sum of the eight numbers is less than 480, which contradicts the fact the sum of the eight numbers equals 480. Thus, k must be 0, which implies each of the eight numbers equals 60. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  30. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Given that you’re working with percentages, for convenience, let 100 = the number of members in the organization who are over 40. Statement (1) leads to inexact results. For example, if 50 of the 100 members are female and 50 are male, then images is the number of female members who are over 40 and have college degrees; and images is the number of male members who are over 40 and have college degrees. These results indicate that images of the organization members who are over 40 have college degrees. So in this case, the answer to the question posed is Yes. However, if, for example, 25 of the 100 members are female and 75 are male, then images is the number of female members who are over 40 and have college degrees; and images is the number of male members who are over 40 and have college degrees. These results indicate that images of the organization members who are over 40 have college degrees. So in this case, the answer to the question posed is No. Thus, (1) is not sufficient.

    Statement (2) is not sufficient because it provides no information about the members who are over 40. Taking (1) and (2) together provides no additional useful information. You cannot assume that 55% of the membership over 40 is female. Therefore, statements (1) and (2) together are not sufficient.

  31. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Statement (1) gives inexact results. For example, images and images satisfyimages because images. Substituting these values into images yields images, which is false, meaning the answer to the question posed is No. However, images and images also satisfy images because images. Substituting these values into images yields images, which is true, meaning the answer to the question posed is Yes. Thus, (1) is not sufficient.

    Statement (2) also gives inexact results. You can use images and images, which satisfy images, to obtain a No answer to the question posed. Or images and images, which also satisfy images, to obtain a Yes answer. Thus, (2) is not sufficient.

    Taking (1) and (2) together gives inexact results as well because, for example, both the pair images and images and the pair images and images satisfy the conditions in both (1) and (2) but lead to opposite results. Therefore, statements (1) and (2) together are not sufficient.

  32. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), N could be 9, 18, 27, 36, 45, and so on. images is an integer for 9, 18, and 36 but is not an integer for any other multiple of N. Thus, (1) is not sufficient.

    From (2), N could be could be any of the consecutive integers from 10 to 26. images is an integer for 12 and 18 but is not an integer for any of the other possible values of N. Thus, (2) is not sufficient.

    Taking (1) and (2) together, only images satisfies all conditions given, and it yields an answer of Yes to the question posed. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  33. D. Each statement ALONE is sufficient.

    Given that x and y are both positive, images is equivalent to images, which will be true only if images. From (1) images implies images. This result indicates that images yielding an answer of No to the question posed. Thus, (1) is sufficient.

    From (2) images implies images, which yields an answer of No to the question posed. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  34. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    The ratio of images to images is images. From (1), images implies images. Thus (1) is sufficient.

    From (2), images implies images. The value of this expression varies depending on the value of y. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  35. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Consider the Venn diagram below, where C is the number of seniors enrolled in AP calculus only, S is the number of seniors enrolled in AP statistics only, and x is the number of seniors enrolled in both AP calculus and AP statistics.

    image

    © John Wiley & Sons, Inc.

    From (1), you have images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of x. Thus, (1) is not sufficient.

    From (2), you have images, which implies images, but additional information is needed to determine an exact value of x. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you have images, which implies images and images. More than one value of x makes this equation true. For example, if images, images, images and images. But if images, images, images and images. Therefore, statements (1) and (2) together are not sufficient.

  36. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Let P = Micah’s take-home pay last month. From (1) Micah saved $300 and paid images for rent. This information tells you that images, but additional information is needed to determine an exact value of P. Thus, (1) is not sufficient.

    From (2), you have

    images

    From this equation, you can determine an exact value of P. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  37. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From the figure, images. From (1), images, which is one equation with two unknowns, so without additional information you cannot determine an exact value of x. Thus, (1) is not sufficient.

    From (2), you can determine only that images because the hypotenuse of a right triangle is longer than either leg. But additional information is needed to determine an exact value of x. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you can determine that images, from which you can determine d; and, thereafter, images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  38. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let F = the first term of the sequence and L = the last term of the sequence. Given that 2 is the common difference between terms, the number of terms in the arithmetic sequence is images. From (1), images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of N. Thus, (1) is not sufficient.

    From (2), images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of N. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  39. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Let x = the amount (in cups) of flaxseed in the mixture and 4x = the amount (in cups) of cornmeal in the mixture. Then 5x = the total amount (in cups) in the mixture. From (1), images, which you can solve for x, the amount, in cups, of flaxseed in the mixture. Thus, (1) is sufficient.

    From (2) you can determine that 5x = the total amount (in cups) in the mixture, which you already knew. So additional information is needed to determine x. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  40. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    The fifth term of a geometric sequence is given by images, where images is the first term of the geometric sequence, and r is the common ratio between a term and the term preceding it. From (1), images. This result implies that images. Without knowing r, you cannot determine an exact value of images. For example, if images (which implies images), then images. But if images (which implies images), then images. Thus, (1) is not sufficient.

    From (2), images. This result implies that images. Without knowing r, you cannot determine an exact value of images. For example, if images (which implies images), then images. But if images (which implies images), then images. Thus, (2) is not sufficient.

    Taking (1) and (2) together yields images, which implies images. Thus, r is 6 or images. If r is 6, then images. If r is images, then images. Therefore, statements (1) and (2) together are not sufficient.

  41. D. Each statement ALONE is sufficient.

    From (1), images. Thus, (1) is sufficient.

    From (2), images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  42. D. Each statement ALONE is sufficient.

    Let P = the initial value (purchase price) of the certificate of deposit (CD). The value of the investment increases by 2% (=0.02) each year. Thus, the value of the CD at the end of the fifth year is images and the interest earned at the end of the fifth year is images. From (1), images, from which you can determine P; and, thereafter, images. Thus, (1) is sufficient.

    From (2), images, from which you can determine P; and, thereafter, images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  43. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Using the quadratic formula, the two roots of images are images and images. Adding the roots yields images. Hence, the sum of the roots of images equals images. From (1) images implies images, so the sum of the roots is positive. Thus, (1) is sufficient to answer the question posed.

    From (2), images implies that the product of the two roots is negative, indicating that the two roots have opposite signs. However, without additional information, you cannot determine whether the sum is positive. For instance, the sum of the roots of images, which has roots 3 and –5, is –2. This result yields an answer of No to the question posed. But the sum of the roots of images, which has roots 5 and –3 is 2. This result yields an answer of Yes to the question posed. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  44. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), the rate, in gallons per minute, that the inlet pipe is pumping water into the cistern is

    images

    But without knowing the rate at which water is being pumped out of the cistern, the rate at which the amount of water in the cistern is increasing cannot be determined.

    From (2), the rate, in gallons per minute, that the outlet pipe is pumping water out of the cistern is

    images

    But without knowing the rate at which water is being pumped into the cistern, the rate at which the amount of water in the cistern is increasing cannot be determined.

    Taking (1) and (2) together, the rate at which water in the cistern is increasing is

    images

    Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  45. D. Each statement ALONE is sufficient.

    Let B = the number of black cars, and W = the number of white cars. From the question information, images. The ratio of the number of black cars to the number of white cars in the fleet is images. From (1), images, which implies images, which you can solve for W; and, thereafter, determine images. Thus, (1) is sufficient.

    From (2), images, which implies images, from which it follows that images. Solve this equation simultaneously with the equation images to obtain exact values for B and W; and, thereafter, determine images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  46. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), images, which implies images equals images. Without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), images, which implies images equals images. Without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) yields inexact results because images and images, so images can equal images or images. Therefore, statements (1) and (2) together are not sufficient.

  47. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    The percent increase in the sale price is

    images

    From (1), you cannot determine the amount of the increase in the sale price. Thus, (1) is not sufficient.

    From (2), The percent increase in the sale price is images, which you can compute. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  48. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), images implies images, where x is a prime number and q is a positive integer. If images and images, then images is not a multiple of 36. But if images and images, then images is a multiple of 36. Thus, (1) is not sufficient to determine a definite Yes or No answer to the question posed.

    From (2), images implies images, where p and y are positive integers. If images and images, then images is not a multiple of 36. But if images and images, then images is a multiple of 36. Thus, (2) is not sufficient to determine a definite Yes or No answer to the question posed.

    Taking (1) and (2) together yields images, where x is a prime number and y is a positive integer. If images and images, then images is a multiple of 36; but if images and images, then images is not a multiple of 36. Therefore, statements (1) and (2) together are not sufficient to answer the question posed.

  49. D. Each statement ALONE is sufficient.

    From (1), the remainder when images is divided by 3 is the same as the remainder when the sum of its digits is divided by 3. Hence, the remainder when images is divided by 3 equals 2 because images. Thus, (1) is sufficient.

    From (2), images is divisible by 3 implies images, where M is an integer. This result implies images. Hence, the remainder when images is divided by 3 equals 2 because images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  50. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), x can take on a range of values. If images, images, which yields an answer of No to the question posed. But if images, images, which yields an answer of Yes to the question posed. Without additional information, you cannot give a definite Yes or No answer to the question posed. Thus, (1) is not sufficient.

    From (2), x can take on a range of values. If images, images, which yields an answer of No to the question posed. But if images, images, which yields an answer of Yes to the question posed. Without additional information, you cannot give a definite Yes or No answer to the question posed. Thus, (2) is not sufficient.

    Taking (1) and (2) together gives images, which implies that images. It follows that images, yielding an answer of No to the question posed. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  51. D. Each statement ALONE is sufficient.

    Let M = the marked-down price. The customer pays images images for the marked-down shoes, including sales tax. From (1), you have images, which you can solve for an exact value of M; and, thereafter, compute images. Thus, (1) is sufficient.

    From (2), you have images, which you can solve for an exact value of M, and, thereafter, compute images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  52. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From the question information, images. From (1), images because the units digit of images is 6 images and the units digit of images is 6 images.

    From (2), images because the units digit of images is 6 images and the units digit of images is 6 images. Taking (1) and (2) together yields images as the only one of the possible values of n that satisfies all conditions given. So 5 is the units digit of imagesimages. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  53. D. Each statement ALONE is sufficient.

    Let M = Mayte’s present age, then images = Mayte’s age in 5 years. From (1), images, which you can solve for M; and, thereafter, determine images. Thus, (1) is sufficient. From (2), images, which you can solve for M; and, thereafter, determine images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  54. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    In (1), no information about y is given, so additional information is needed to answer the question posed. Thus, (1) is not sufficient.

    In (2), no information about x is given, so additional information is needed to answer the question posed. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images, which yields an answer of No to the question posed. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  55. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Let images. Then the sum of the three integers is images. From (1), images implies images, which you already know, so additional information is needed. Thus, (1) is not sufficient.

    From (2), images implies images. You can solve this equation for an exact value of x, and, thereafter, determine 10x, the sum of A, B, and C. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  56. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images implies images, from which you have images. It follows that images. Thus, (1) is sufficient.

    From (2), images implies images, from which you have images, but additional information is needed to determine an exact value of images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  57. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Let L = the larger integer. Then images = the smaller integer. From (1), images. Solving this equation yields

    images

    Thus, (1) is sufficient.

    Statement (2) yields inexact results. For example, images satisfy the condition. And images also satisfy the condition. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  58. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let Q = the number of quarters in the coin bank, and D = the number of dimes in the bank. From (1), images, but additional information is needed to determine an exact value of Q.

    From (2) images, which is one equation with two unknowns, so additional information is needed to determine an exact value of Q.

    Taking (1) and (2) together, you have images, which you can solve for an exact value of Q. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  59. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    The average of R, S, and T is images. Statement (1), gives inexact results because the values of R, S, and T can vary. For instance, images (which satisfy the equation) yield an average of 5. But images (which satisfy the equation) yield an average of images. Thus, (1) is not sufficient.

    From (2), images implies images, which gives inexact results because the values of R, S, and T can vary. For instance, images (which satisfy the equation) yield an average of 15. But images (which satisfy the equation) yield an average of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together and adding the two equations yields images, which implies images, from which you can determine an exact value of images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  60. D. Each statement ALONE is sufficient.

    From (1), images implies images, from which you have images, yielding an answer of Yes to the question posed. Thus, (1) is sufficient.

    From (2), images implies images, from which you have images, so images, yielding an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  61. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Simplify the expression:

    images

    From (1), images leads to inexact results. For example, imagessatisfy the condition and result in

    images

    But images satisfy the condition and result in

    images

    Thus, (1) is not sufficient.

    From (2), images implies images, from which you have images. Factoring yields images. Hence, images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  62. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From the question, you know that each machine will do images of the work. From (1), each machine produces 200 of the 1,200 components. This amount is images of the work, which you already knew, so additional information is needed. Thus, (1) is not sufficient.

    From (2), if it takes images hours for two such machines to produce 1,200 components, then one such machine will take twice as long, or 9 hours. Six such machines will take images as long as one machine takes, or images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  63. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let t = the time, in hours, it will take the two vehicles to be 405 miles apart. Then

    images

    From (1), you have the speed of the truck, but you need the speed of the van also to compute t. Thus, (1) is not sufficient.

    From (2), you have the speed of the van, but you need the speed of the truck also to compute t. Thus, (2) is not sufficient.

    Taking (1) and (2) together yields images, from which you can compute an exact value of t. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  64. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images implies images. It follows that images, which you can solve for an exact value of k. Thus, (1) is sufficient.

    From (2), images implies images. Without additional information, you cannot determine an exact value of k. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  65. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From the question information, images. From (1) images, which yields one equation with two unknowns. Without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2) images, which yields one equation with two unknowns. Without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you have two linear equations with two unknowns. You can solve the two equations simultaneously to obtain exact values for images and d, and, thereafter, determine an exact value of images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  66. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From the question information, make a table of possible paired values of m and n.

    m

    1

    2

    3

    4

    5

    6

    7

    8

    n

    8

    7

    6

    5

    4

    3

    2

    1

    Using the information in (1) and checking through the possible paired values of m and n, only one pair (images) satisfies the double inequality images. With these values, you can compute an exact value of mn. Thus, (1) is sufficient.

    Using the information in (2), six of the possible paired values of m and n satisfy the double inequality. These six pairs result in three different values (8, 14, and 18) for mn. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  67. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images implies images. Without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), images implies images, from which you can determine an exact value of images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  68. D. Each statement ALONE is sufficient.

    Simplify the inequality:

    images

    Hence, the answer to the question posed is Yes if images and No, otherwise. From (1), given that images, then images is true. Thus, (1) is sufficient.

    Simplifying (2) yields

    images

    Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  69. D. Each statement ALONE is sufficient.

    From (1), images. Squaring both sides yields images, which implies images, from which you have images. Thus, (1) is sufficient.

    From (2), images. Square both sides of images to obtain images. Substituting images yields images, which implies images, from which you have images (because images). Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  70. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Let Max = the maximum value and Min = the minimum value of the 15 numbers. Then the range of the 15 numbers is images. From (1), you know only that five images of the 15 numbers equal 25, but you need additional information to determine the range. Thus, (1) is not sufficient.

    From (2), you have the range equals images. This result can vary depending on the value of Max.

    Taking (1) and (2) together provides no additional information that will lead to an exact value of the range. For example, a Max and Min of 100 and 25, respectively, satisfy all conditions and yield a range of 75. While a Max and Min of 80 and 20, respectively, satisfy all conditions and yield a range of 60. Therefore, statements (1) and (2) together are not sufficient.

  71. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    If x and y have opposite signs, the answer to the question posed is Yes; otherwise, the answer is No. Statement (1) indicates that x could be negative, but it does not have to be. Further, there is no information about y given. Thus, (1) is not sufficient.

    From (2), y is positive, but there is no information about x given. Thus, (2) is not sufficient.

    Taking (1) and (2) together, x could be negative, in which case images (yielding an answer of Yes to the question posed) or x could be positive, in which case images (yielding an answer of No to the question posed). Therefore, statements (1) and (2) together are not sufficient.

  72. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images implies images, from which you have images. Thus, (1) is sufficient.

    From (2) images implies images, from which you have images. So images, not an exact value. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  73. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    images will be true if images. From (1), images implies images, from which you can obtain images (because images), but additional information is needed to determine whether images. Thus, (1) is not sufficient.

    From (2), images implies images or, equivalently, images, from which you can obtain images (because images), but additional information is needed to determine whether images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images and images implies images, yielding an answer of Yes to the question posed. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  74. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images, which implies images. Substituting into images yields images. Thus, (1) is sufficient.

    From (2), you have a range of possible values for images. For instance, both images and images satisfy the condition given. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  75. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), Given k is a prime such that images, then images. Without additional information, you cannot determine an exact value of k. Thus, (1) is not sufficient.

    Statement (2) implies that all the positive factors of k are odd (because images, but images). So k is a positive integer that has only odd factors. The list of such integers (1, 3, 5, 7, 9, 11, 15, …) continues indefinitely. Without further information, you cannot determine an exact value of k. Thus, (2) is not sufficient.

    Taking (1) and (2) together indicates images, which satisfies all conditions given. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  76. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images. Solve this equation for x:

    images

    Thus, (1) is sufficient.

    From (2), x is either the least of the four numbers are the greatest (because images). Case I: If x is the least, then images, which implies images. Case II: If x is the greatest, then images, which implies images. Without further information, you cannot determine an exact value of x. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  77. D. Each statement ALONE is sufficient.

    Let M = the number of teachers who have masters degrees. Then images = the number of teachers who do not have masters degrees. From (1), images, which you can solve for an exact value of M. Thus, (1) is sufficient.

    From (2), images, which you can solve for an exact value of M. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  78. D. Each statement ALONE is sufficient.

    Substituting from (1) yields images, which you can solve for an exact value of k. Thus, (1) is sufficient.

    Substituting from (2) yields images, which you can solve for an exact value of k. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  79. D. Each statement ALONE is sufficient.

    From (1), given that 18, the sum of N’s digits, is divisible by 9, then N is divisible by 9. Thus, (1) is sufficient.

    From (2), given that images is divisible by 9, then images, where m is an integer. Then, images, which implies N is divisible by 9. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  80. D. Each statement ALONE is sufficient.

    The perimeter of the triangle is images. Substituting (1) into the Pythagorean theorem yields images. So images. Thus, (1) is sufficient.

    Substituting (2) into the Pythagorean theorem yields images. So images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  81. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    By the triangle inequality images. Substituting (1) into images yields images. So the answer to the question posed is No. Thus, (1) is sufficient.

    From (2), you have a range of possible values of x. For images (values that satisfy the triangle inequality), the answer to the question posed is Yes. But for images (values that satisfy the triangle inequality), the answer to the question posed is No. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  82. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let H = the number of tiles along each of the horizontal boundaries of the wall area, and V = the number of tiles along each of the vertical boundaries of the wall area. Then the perimeter of the wall area is images. From (1), you know the number of tiles is 48, but without knowing the configuration of the 48 tiles, you cannot determine an exact value of P. For example, images yields images, but images yields images. Thus, (1) is not sufficient.

    From (2) images implies images, but further information is needed to determine an exact value of P. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you have images, or equivalently, images, from which you can determine an exact value of V (because the question situation implies that V is a positive integer). Thereafter, you can determine an exact value of images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  83. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From the figure images (because the sum of the measures of the interior angles of a triangle is 180°) and images (because an exterior angle of a triangle is greater than either of the remote interior angles of the triangle). Thus, images. From (1), images, which implies images. So the answer to the question posed is Yes. Thus, (1) is sufficient.

    From (2), images implies images, from which it follows that images. So images, which gives a range of possible values for k. But without additional information, you cannot determine an exact value of x. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  84. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From the question information, images (because the sum of the measures of the interior angles of a triangle is 180°). From (1), images (because base angles of an isosceles triangle have equal measure). Substituting into images yields images. But without additional information, you cannot determine an exact value of x.

    From (2), images. But without additional information, you cannot determine an exact value of x.

    Taking (1) and (2) together, you have images, which you can solve for an exact value of x. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  85. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Let R miles per hour = the speed, at which Tek travels to and from work. Let images = the distance to and from work via route 1, and images = the distance to and from work via route 2. The difference is images. From (1), images. Without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), because 40 minutes equals images, imagesimages. Without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images, which varies depending on the value of R. For example, if images, the difference is 20 miles, but if images, the difference is 15 miles. Therefore, statements (1) and (2) together are not sufficient.

  86. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), if 80 houses do not have four bedrooms, and they make up 40 percent of the houses in the neighborhood, then there are 200 images houses in the neighborhood. 50% of these houses, or 100, are over 30 years old, which means there are also 100 houses that are 30 years old or under. 75% of the 100 houses over 30 years old have four bedrooms, so 25% of 100, or 25, do not. Because 80 houses do not have four bedrooms and 25 are over 30 years old, the remaining 55 without four bedrooms must be 30 years old or under. Thus, (1) is sufficient.

    From (2), you have images of the houses having four bedrooms are two story houses that are more than 30 years old. But further information is needed to determine the total number of houses 30 years or under that do not have four bedrooms. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  87. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images implies images. This result will vary depending on the value of s. For example, if images, then images. But images, so then images. Thus, (1) is not sufficient.

    From (2), images implies images, from which you have images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  88. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), the only way x, y, and z can have a mean of 2 is if they have the values 1, 2, and 3, respectively. The range is images. So the answer to the question posed is Yes. Thus, (1) is sufficient.

    From (2), given that the median is 2, then x and y must have the values 1 and 2, respectively. If images, the range is images. So the answer to the question posed is Yes. But if, for example, images, the range is images. So the answer to the question posed is No. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  89. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Recall that images and images. Because 425,371 is odd, images is odd only if n is even. Hence, the answer to the question posed is Yes if n is even and No otherwise.

    From (1), because 268,865 is odd, then n must be even given that images is odd. This result yields an answer of Yes to the question posed. Thus, (1) is sufficient.

    From (2), because 890,214 is even, then 890,214n is even regardless whether n is even or odd. So you cannot answer definitely Yes or No to the question posed. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  90. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), let 10x = the amount, in grams, of ingredient A, 5x = the amount, in grams, of ingredient B, 4x = the amount, in grams, of ingredient C, and 2x = the amount, in grams, of ingredient D. Then ingredient A is images more than ingredient D. This amount can vary depending on the value of x. Thus, (1) is not sufficient.

    From (2), you are not given information about A or D. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you have images, from which you can determine an exact value of x; and, thereafter, determine an exact value of images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  91. D. Each statement ALONE is sufficient.

    From (1), given that a number is divisible by 4 if its tens and units digit form a number that is divisible by 4, K is divisible by 4 because 36 is divisible by 4. Thus, (1) is sufficient.

    From (2), 12 is a factor of K, which implies that 3 and 4 are factors of K, so K is divisible by 4. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  92. D. Each statement ALONE is sufficient.

    From (1), you have a negative number raised to a negative power. The result will be the reciprocal of a negative number. So the answer to the question posed is No. Thus, (1) is sufficient.

    From (2), images implies images, so images. With this result you can determine that images is negative, yielding an answer of No to the question posed. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  93. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Simplifying (1) yields

    images

    Thus, (1) is sufficient.

    From (2), images implies images, from which you have images. Without additional information, you cannot determine an exact value of images. For example, images satisfy the condition (because images) and yield a value of images. But images also satisfy the condition (because images) and yield a value of images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  94. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Let P = the value of the pendant in 2013. Then images is the value of the pendant in 2015. From (1), you have the value of the pendant in 2014, but you cannot assume that the value of the pendant changed the same amount each year. It’s possible that the value of the pendant may have increased from 2013 to 2014 and then decreased from 2014 to 2013 to 0.5P. So additional information is needed to determine an exact value of P. Thus, (1) is not sufficient.

    From (2), you have images, which you can solve for an exact value of P. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  95. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), images. You need additional information to determine an exact value of a. Thus, (1) is not sufficient.

    From (2), images. You need additional information to determine an exact value of a. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images. Without additional information, you cannot determine an exact value of a. Therefore, statements (1) and (2) together are not sufficient.

  96. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    The sum of the measures of the interior angles of a triangle is 180°. A triangle is equilateral if the measure of each of its angles is 60°. From (1), images, which implies images. So images, indicating that Yes, the triangle is an equilateral triangle. Thus, (1) is sufficient.

    From (2), images, which you already knew because the third angle measures 60°. Without additional information, you cannot determine definite values for x and y. For example, images satisfy the condition and yield an answer of No to the question posed. But images satisfy the condition and yield an answer of Yes to the question posed. Thus, (2) is not sufficient.

    Therefore, statement (1) alone is sufficient.

  97. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), images, which implies images. Without additional information, you cannot determine an exact value of images. For example, if images, then images. But if images, then images. Thus, (1) is not sufficient.

    From (2), images implies images or, equivalently, images. Although the squares of m and n are equal, m and n are not necessarily equal. For example, images yield images. But images yield images. Thus, (2) is not sufficient. Taking (1) and (2) together yields images, which implies images. From this result, you have images, so images and images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  98. D. Each statement ALONE is sufficient.

    Factoring (1) yields

    images

    Given that images, this result implies images, so images. Thus, (1) is sufficient.

    From (2), images implies images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  99. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), the exterior angle that is adjacent to angle Y equals images. Without additional information, you cannot determine whether one of the other exterior angles measures 140°. Thus, (1) is not sufficient.

    From (2), the exterior angle that is adjacent to angle Z equals images. Without additional information, you cannot determine whether one of the other exterior angles measures 140°. Thus, (2) is not sufficient.

    Taking (1) and (2) together, neither of the exterior angles adjacent to angles Y and Z equals 140°. The third exterior angle equals the sum of the measures of the two non-adjacent interior angles. So the measure of the third exterior angle is images, yielding an answer of No to the question posed. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  100. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images. Substituting into images yields images, which simplifies to images, which will equal zero if images. If images, images, yielding an answer of Yes to the question posed. But if images, images, yielding an answer of No to the question posed. Thus, (1) is not sufficient.

    From (2), images implies images, from which you have images, yielding an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  101. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    The question is asking whether images. From (1), images. But without information about S, you cannot determine whether images. Thus, (1) is not sufficient.

    From (2), images, yielding an answer of No to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  102. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), y could be a range of values. For example, y could be 0, which is less than 1 or y could be 2, which is greater than 1. Thus, (1) is not sufficient.

    From (2), given that images, images implies that images or y is negative. Either way, images, yielding an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  103. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient to answer the question asked.

    Recall that images, images, and images images. From (1), given that images is odd and 95 is odd, it follows that n is even. Without additional information, you cannot determine whether n is a prime number. For example, n could be 2, which is the only even prime, or n could be 4, which is not prime. Thus,(1) is not sufficient.

    From (2), you have a range of values of n, some that are prime and some that are not prime. For example, n could be 3 which is prime, or n could be 4, which is not prime. Thus, (2) is not sufficient.

    Taking (1) and (2) together, n is not prime because there are no even prime numbers that satisfy images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  104. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), the customer buys images cans of tomatoes, but you need the original price and the sale price to determine the savings. Thus, (1) is not sufficient.

    From (2), the sale price per can of the store-brand tomatoes is images, but you need the original price and the number of cans purchased to determine the savings. Thus, (2) is not sufficient.

    Taking (1) and (2) together yields images as the sale price of the six-month supply, but you need the original price of the canned tomatoes to determine the savings. Therefore, statements (1) and (2) together are not sufficient.

  105. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), the time for the trip from city A to City B is images. Without additional information, you cannot determine the time Adwoa left city A. Thus, (1) is not sufficient.

    From (2), you know the time at which Adwoa arrived in city B, but without additional information, you cannot determine the time Adwoa left city A. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you can determine that Adwoa left city A at 10 a.m., 4 hours before 2 p.m. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  106. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), section C accounts for images of the total area. But additional information is needed to determine the portion of the total area represented by section A. Thus, (1) is not sufficient.

    From (2), let b = the portion of the total area corresponding to section B. Then b = 3 times the portion of the total area corresponding to section C. But without additional information, you cannot determine the portion of the total area represented by section A. Thus, (2) is not sufficient.

    Taking (1) and (2) together yields images of the total area. So the portion of the total area corresponding to section A is images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  107. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), images implies images. You need additional information about z to determine the value of images. Thus, (1) is not sufficient.

    From (2), images implies images. You need additional information about x to determine the value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, subtract the equation in (2) from the equation in (1) to obtain

    images

    Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  108. D. Each statement ALONE is sufficient.

    From (1), images implies images, from which you have images because 17 is the only prime number in the interval given. Thus, (1) is sufficient.

    From (2), images implies images because images is not a prime number. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  109. D. Each statement ALONE is sufficient.

    From (1), images spectators are residents of the town. Then, because images of the spectators who are residents of the town are close relatives of players in the game, images of the spectators who are residents of the town are not close relatives of players in the game. Thus, (1) is sufficient.

    From (2), let n = the number of spectators at the game, then because images of the spectators are residents of the town, then images, which implies images. Thus, (2) is sufficient because you can complete it as shown in (1). Therefore, each statement alone is sufficient.

  110. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    When the images integers are ordered from least to greatest, the median is located at position images. From (1), images, and the median is located at position images. If images, the median is located at position images, so the median equals the arithmetic average of 400 and 475, which is 475.5. If images, say, for example, images, the median is located at position images, which indicates the median is an integer and, therefore, cannot equal 475.5. Thus, (1) gives inconclusive results, so it is not sufficient.

    From (2), images, and the median is located at position images. If images, the median is located at position images, so the median equals the arithmetic average of 400 and 475, which is 475.5. If images, when say, for example, images, so the median is located at position images, which indicates the median is an integer and, therefore, cannot equal 475.5. Thus, (2) gives inconclusive results, so it is not sufficient.

    Taking (1) and (2) together, the median is located at position images, which indicates the median is 400. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  111. D. Each statement ALONE is sufficient.

    When the numbers are ordered from least to greatest, the median is b. Hence, the question posed can be stated as follows: Is images, or, equivalently, is images? From (1), images, which implies images, from which you have images. Thus, (1) is sufficient.

    From (2), you have images, images or images. Case I: If images, then images. Because images and images, their sum cannot equal zero. So reject images. Case II: If images, then images. Because images and images, their sum can equal zero. So do not reject images. Case III: If images, then images. Because images and images, their sum cannot equal zero. So reject images. Hence, it must be the case that images, which implies images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  112. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), set A contains 4 numbers and thus, set B contains at least 4 numbers. This information leads to inconclusive results. For example, if images and images, then the range of B (which is images) is greater than the range of A (which is images). But if images and images, then the range of B (which is images) equals the range of A (which is images). Thus, (1) is not sufficient.

    From (2), set B contains 5 numbers and thus, set A contains no more than 5 numbers. The same examples given in (1) can be used to show that this information leads to inconclusive results. Thus, (2) is not sufficient.

    Taking (1) and (2) together, the examples given in (1) can be used to show that it cannot be determined whether the range of set A is less than the range of set B. Therefore, statements (1) and (2) together are not sufficient.

  113. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Statement (1) gives inconclusive results. For example, images yield

    images

    But images yield imagesimages

    Thus, (1) is not sufficient.

    Simplify (2) as follows:

    images

    This result yields an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  114. D. Each statement ALONE is sufficient.

    Recall that a circle with radius r has circumference equal to images and area equal to images. From (1), in circle Y, images implies images, so r, the radius of circle Y, is 10 feet. Then given that the circumference of circle X equals images the circumference of circle Y, the circumference of circle X is images, which implies the radius of circle X is 5 feet and its area is images. Thus, (1) is sufficient.

    From (2), you know from (1) that if the circumference of circle Y is known, you can proceed as in (1) to determine circle X’s area. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  115. D. Each statement ALONE is sufficient.

    The triangle is a right triangle, so images. The perimeter of the triangle is images. From (1), given that the area of the triangle is 96, then images, which implies images. Because images, then images. So images and the exact value of the perimeter is images. Thus, (1) is sufficient.

    From (2), images, which implies images or, equivalently, images. Because images is negative, the two roots of this quadratic equation have opposite signs. You can solve the equation for the positive root x, and then determine y; and, thereafter, the exact value of the perimeter, images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  116. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From the question, images and images implies images. From (1), images, which implies images. But without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), images, which implies images. Hence, when images, images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  117. D. Each statement ALONE is sufficient.

    The triangle is a right triangle, so images. The area of the triangle is 24, so images. From (1), images. Then given images, images implies images. Then images, from which you can obtain an exact value of c. Thus, (1) is sufficient.

    From (2), images. Then given images, images implies images. Then images, from which you can obtain an exact value of c. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  118. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let h = the height that is 2 standard deviations greater than the mean height. Then images. From (1), images. Without knowing the standard deviation, you cannot determine an exact value of h. Thus, (1) is not sufficient.

    From (2), images. Without knowing the mean, you cannot determine an exact value of h. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images, which you can calculate to determine an exact value of h. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  119. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let x = the amount, in grams, of Brand X cat food that Sergio’s cat receives each day. Then images = the amount, in grams, of Brand Y cat food that Sergio’s cat receives each day. The amount of fat that Sergio’s cat receives each day from x grams of Brand X cat food plus the amount of fat that Sergio’s cat receives each day from images grams of Brand Y cat food is 103 grams. From (1), the amount of fat that Sergio’s cat receives each day from Brand X cat food is images. But without information about the amount of fat from Brand Y cat food, you cannot determine an exact value of x. Thus, (1) is not sufficient.

    From (2), the amount of fat that Sergio’s cat receives each day from Brand Y cat food is images. But without information about the amount of fat from Brand X cat food, you cannot determine an exact value of x. Thus (2) is not sufficient.

    Taking (1) and (2) together yields images, which you can solve to determine an exact value of x. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  120. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let L = the length, in feet, of the floor, and W = the width, in feet, of the floor. The area of the floor is images. From (1), images, then images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of A. Thus, (1) is not sufficient.

    From (2), images, which implies images, from which you have images and images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of A. Thus, (2) is not sufficient.

    Taking (1) and (2) together yields images, which implies images or, equivalently, images. Given that images (because it’s a measurement of the floor), you can determine an exact value of W and images; and, thereafter, determine an exact value of A. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  121. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Let V = the number of vehicles in the parking lot. From (1), you have that images, but additional information is needed to determine an exact value of V. Thus, (1) is not sufficient.

    From (2), images is the number of sedans in the parking lot, but additional information is needed to determine an exact value of V. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you know that 40 percent of the vehicles in the parking lot are not sedans, and that 5 of those vehicles are pickup trucks. But you cannot assume that only pickup trucks and sedans are in the parking lot. Therefore, statements (1) and (2) together are not sufficient.

  122. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From the triangle inequality, images. From (1), images. But additional information is needed to determine the least value of k in images. Thus, (1) is not sufficient.

    From (2), images. But additional information is needed to determine the least value of k in images. Thus, (1) is not sufficient. Taking (1) and (2) together, images, which implies 22 is the least value of k. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  123. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images implies that n assumes its greatest value when images. Substituting possible values for n yields images; images; and images. So the greatest possible value of n is 4. Thus, (1) is sufficient.

    Statement (2) provides no information about n, so it is not sufficient. Therefore, statement (1) alone is sufficient.

  124. D. Each statement ALONE is sufficient.

    Let S = the number of decorated one-layer cakes sold, and L = the number of decorated two-layer cakes sold. Then images = the total number of decorated one-layer and two-layer cakes sold. From the question information, images. From (1), images. So images, which you can solve for L and images; and, thereafter, determine an exact value of images. Thus, (1) is sufficient.

    From (2), images. So images, which you can solve for S and images; and, thereafter, determine an exact value of images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  125. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let C = the number of chess club members only, and S = the number of swim team members only. Then images = the number of students who belong to either the chess club or the swim team, but not both. Statement (1) tells you only that images. Without additional information, you cannot determine an exact value of either C or S. Thus, (1) is not sufficient.

    Statement (2) tells you only that images. Without additional information, you cannot determine an exact value of either C or S. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images. This result is 13 more than 31, the total number of students who belong to the chess club or the swim team or both. The excess of 13 is the number of members who belong to both the chess club and the swim team. So images, images, and images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  126. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Using (1), the answer to the question posed can be No or Yes, depending on the values of x and y. For example, if images, then images, in which case the answer is No. But if images, then images, in which case the answer is Yes. Thus, (1) is not sufficient.

    From (2), images implies images and images implies images. So images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  127. D. Each statement ALONE is sufficient.

    From (1), because alternate interior angles of parallel lines are congruent, images implies images, from which you can determine an exact value of y. Thus, (1) is sufficient.

    From (2), because corresponding angles of parallel lines are congruent, images implies images, Then, because consecutive angles of a parallelogram are supplementary, images, from which you can determine an exact value of y. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  128. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images could represent multiplication or division because images and images. Thus, (1) is not sufficient.

    From (2), images can only represent multiplication because images, while images. So images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  129. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let M = the number of math majors in Professor X’s physics class, and N = the number of non-math majors in Professor X’s physics class. From (1), images, which is one equation with two unknowns. So without additional information, you cannot determine an exact value of M. Thus, (1) is not sufficient.

    Statement (2) provides no information about M. Thus, (2) is not sufficient. Taking (1) and (2) together yields images, which you can solve for an exact value of M. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  130. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let P = the current membership of the photography club. From (1), images, which implies images. This result gives a range of values of P. For example, P could equal 17 or any integer greater than 17. Thus, (1) is not sufficient.

    From (2), images, which implies images. This result gives a range of values of P. For example, P could equal 17 or any integer such that images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images, from which it follows that images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  131. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Because images, none of the factors are zero. The product xyz will be greater than 0 if it has exactly zero or exactly two negative factors. From (1), images implies that x and z have different signs. Hence, xyz cannot have exactly zero negative factors. If images, then xyz has exactly two negative factors and images is true, indicating a Yes response to the question posed. But ifimages, then xyz has exactly one negative factors and images is true, indicating a No response to the question posed. Thus, (1) is not sufficient.

    From (2), images implies that x, y, and z do not all have the same sign. Hence, xyz cannot have exactly zero negative factors. If there are exactly two negative factors among the three numbers, then images is true, indicating a Yes response to the question posed. If there is exactly one negative factor among the three numbers, then images is true, indicating a No response to the question posed.

    Taking (1) and (2) together, xyz cannot have exactly zero negative factors, but additional information is needed to determine whether the product has exactly two negative factors. Therefore, statements (1) and (2) together are not sufficient.

  132. D. Each statement ALONE is sufficient.

    From (1), images implies images. It follows that images, indicating an answer of Yes to the question posed. Thus, (1) is sufficient.

    From (2), if images then images, which implies that images rounded to the nearest integer is 8. It follows that images, indicating an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  133. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), images implies images. Thus, (1) is not sufficient.

    From (2), images implies images or any integer greater than 2. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images satisfies all conditions given. Therefore, statements (1) and (2) together are not sufficient.

  134. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let images= the initial population of the bacteria. Given that the population doubles every m minutes, in 4 hours, the number of times the population doubles is images. So in four hours, the population of the bacteria colony equals images. From (1), in 1 hour, the number of times the population doubles is images. So images. This is one equation with two unknowns, so additional information is needed to determine an exact value of images. Thus, (1) is not sufficient.

    From (2), in 3 hour, the number of times the population doubles is images. So images. This is one equation with two unknowns, so additional information is needed to determine an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you have two equations and two unknowns that you can solve simultaneously to determine exact values of m and images; and, thereafter, compute an exact value of images. You do not have to actually work out the solution. However, for the purpose of clarity, proceed as follows: images, which implies images or, equivalently, images. It follows that images or images. Substituting images intoimages yields images, from which you have images. So in four hours, the population of the bacteria colony is images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  135. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images implies images or images. If images, then images, yielding an answer of No to the question posed. But if images, then images, yielding an answer of Yes to the question posed. Thus, (1) is not sufficient.

    From (2), images implies images, from which you have images or equivalently, images, yielding an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  136. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), n divisible by 12 implies images, where k is a positive integer. If k is even, then n is divisible by 24, yielding an answer of Yes to the question posed. But, if k is odd, then n is not divisible by 24, yielding an answer of No to the question posed. Thus, (1) is not sufficient.

    From (2), n could be any even number such as 20, which is not divisible by 24, or 72, which is divisible by 24. Thus, (2) is not sufficient.

    Taking (1) and (2) together is not sufficient because the possibilities for n are the same as described for statement (1). Therefore, statements (1) and (2) together are not sufficient.

  137. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let y = the price of one 64-ounce container of Brand Y ice cream, and x = the price of one 48-ounce container of Brand X ice cream. From (1), images. This is one equation with two unknowns. Without additional information, you cannot determine an exact value of y. Thus, (1) is not sufficient.

    From (2), you have two possibilities because 192-ounces is either 3 times 64 ounces or 4 times 48 ounces. No other combination using 64 ounces and 48 ounces will sum to 192 ounces. Case I: The customer bought 4 48-ounce containers of Brand X ice cream for $18. So images. Case II: The customer bought 3 64-ounce containers of Brand Y ice cream for $18. So images. Without additional information, you cannot determine the value of y. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you have two cases. Case I: images. Substituting into images yields images, which implies images. Case II: images. In either case, images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  138. D. Each statement ALONE is sufficient.

    Let m = the number of students who are taking mathematics only, and p = the number of students who are taking physics only. Then the percent of students who are taking only mathematics or only physics and no other class is images. From (1), images. You can solve this equation for images; and, thereafter, obtain images. Thus, (1) is sufficient.

    From (2), images and images. Then images, from which you can determine images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  139. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Solving the equation in (1) yields

    images

    Without additional information, you cannot determine and exact value of x. Thus, (1) is not sufficient.

    From (2), images implies images. This result indicates that x can be any number such that images. Thus, (2) is not sufficient.

    Taking (1) and (2) together is not sufficient because either –4 or 3 satisfies all conditions given. Therefore, statements (1) and (2) together are not sufficient.

  140. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), you have images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of q. Thus, (1) is not sufficient.

    From (2), you have images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of q. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you have two equations and three unknowns. Without additional information, you cannot determine an exact value of q. Therefore, statements (1) and (2) together are not sufficient.

  141. D. Each statement ALONE is sufficient.

    Let D = the total distance, in miles, that Rylon drove, and T = the total time, in hours, that Rylon drove. Then Rylon’s average speed, in miles per hour, was images. From (1), because 1 hour 48 minutes is 1.8 hours, images, which is greater than 55 miles per hour. Thus, (1) is sufficient to answer the question posed.

    From (2), images and imagesimages, so images is the same as in (1). Thus, (2) is sufficient to answer the question posed. Therefore, each statement alone is sufficient.

  142. D. Each statement ALONE is sufficient.

    From (1), images implies images or, equivalently, images. This result gives images. Thus, (1) is sufficient.

    From (2), given that images, images implies images or, equivalently, images. This result gives images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  143. D. Each statement ALONE is sufficient.

    Let S = the cost of the sweater, excluding sales tax. Then the total amount of Vinod’s purchase, including sales tax, is imagesimages. From (1), images, from which you can determine S; and, thereafter, determine an exact value of images. Thus, (1) is sufficient.

    From (2), images, from which you can determine S; and, thereafter, determine an exact value of images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  144. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let images = the first term of sequence A, and images = the hundredth term of sequence A. From (1), images. But without additional information, you cannot determine subsequent terms, including an exact value of images. Thus, (1) is not sufficient.

    From (2), images and so on. Hence, images. But without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, the exact value of the 100th term is images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  145. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Create a two-way table to organize the information. Put variable expressions in empty cells:

    on-campus

    off-campus

    Total

    senior

    x

    50

    images

    junior

    y

    z

    images

    Total

    images

    images

    S

    From (1), images, which implies images. Use this information to update the table:

    on-campus

    off-campus

    Total

    senior

    30

    50

    80

    junior

    y

    z

    images

    Total

    images

    images

    S

    From the table, images. This is one equation with three unknowns. Without additional information, you cannot determine an exact value of S. Thus, (1) is not sufficient.

    From (2), images, which implies images. Use this information to update the table:

    on-campus

    off-campus

    Total

    senior

    x

    50

    images

    junior

    y

    70

    images

    Total

    images

    120

    S

    From the table, images. This is one equation with three unknowns. Without additional information, you cannot determine an exact value of S. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you have the following updated table:

    on-campus

    off-campus

    Total

    senior

    30

    50

    80

    junior

    y

    70

    images

    Total

    images

    120

    S

    From the table, images. Without knowing y, the number of juniors who live on campus, you cannot determine an exact value of S. Therefore, statements (1) and (2) together are not sufficient.

  146. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), imagesimages This result implies images is even. However, without additional information, you cannot determine whether it is positive or negative. If z is positive, then images is a positive even integer. But if z is negative, then images is a negative even integer. Thus, (1) is not sufficient.

    From (2), images. This result implies images is even. However, without additional information, you cannot determine whether it is positive or negative.

    Taking (1) and (2) together, given z is negative, then images is a negative even integer. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  147. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), images, which implies images. Substitute into images. Then the question asks: is images? or, equivalently, is images? Without additional information about X, you cannot determine a definite Yes or No response to the question posed. Thus, (1) is not sufficient.

    From (2), images, which implies images. Substitute into images. Then the question asks, is images? or, equivalently, is images? Without additional information about R, you cannot determine a definite Yes or No response to the question posed. Thus, (2) is not sufficient.

    Taking (1) and (2), together, you have images and images. So you can compute RX; and, thereafter, determine a definite Yes or No response to the question of whether images? Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  148. D. Each statement ALONE is sufficient.

    Make a sketch.

    image

    © John Wiley & Sons, Inc.

    The figure shows that the diagonal of the square is the diameter of the circle (because the measure of the inscribed angle of 90° is images the measure of the arc that it subtends). Because the radius of the circle is images, the area of the circle is images. From (1), because the area of a square is images the square of the length of its diagonal, images, which implies images. It follows that images and images. Thus, (1) is sufficient.

    From (2), because the circumference of the circle is images times its diameter, images, which implies images and images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  149. D. Each statement ALONE is sufficient.

    Let M = the number of men at the ceremony and W = the number of women at the ceremony. Then images = the ratio of the number of men to the number of women at the ceremony. From (1), images, so images. Thus, (1) is sufficient.

    From (2), images, which implies images or, equivalently, images. It follows that images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  150. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Let X = the amount invested at P percent simple annual interest. Then the total amount invested is images. From (1) imagesimages, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), the interest earned by the two investments in one year is images. This result does not lead to an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images, which implies images or, equivalently, images and images. This result does not lead to an exact value of images. Therefore, statements (1) and (2) together are not sufficient.

  151. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), h could be 5, 6, 7, 8, or 9 because each of 0.458, 0.468, 0.478, 0.488, and 0.498 rounded to the nearest tenth is 0.5. Thus, (1) is not sufficient.

    From (2), when images is rounded to the nearest hundredth, because 8 is the digit in the thousandths place, the digit in the hundredths place increases by 1. So images, which implies images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  152. D. Each statement ALONE is sufficient.

    Recall that images, images, and imagesimages. And images, images, and images. From (1), because images is odd, then m is even. It follows that mn is even. Thus, (1) is sufficient.

    From (2), because images is odd, then m and n cannot both be odd (because images). It follows that at least one of m and n is even, so mn is even. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  153. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    It is given that net proceeds increase as the number of tickets sold increases. From (1), you know only that net proceeds exceeded $40,000 on 4,000 tickets sold. But because you have no way of knowing how net proceeds increase as a function of tickets sold, you cannot assume that net proceeds exceeded $80,000 on 7,600 tickets sold. Thus, (1) is not sufficient.

    From (2), given that the net proceeds on 7,000 tickets sold exceeded $100,000, then, because net proceeds increase as the number of tickets sold increases, sales of images tickets will also have a profit exceeding $100,000, which is greater than $80,000. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  154. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    It is given that x and y are integers such that images. From (1), images and images. These results imply that images and images. Hence, images and images. Given that images, which is a rational number, neither x nor y can equal 2, 3, 5, 6, 7, or 8 because the square roots of these integers are positive irrational numbers. The sum of a positive irrational number and a positive rational number or the sum of two positive irrational numbers is irrational. Hence, given images, the possible values of x are 1 or 4, and the possible values of y are 4 or 9. Only the values images and images will satisfy images and images. So images. Thus, (1) is sufficient.

    From (2), given images, the possible values of x and y are the pairs 1 and 9; 2 and 8; 3 and 7; or 4 and 5; respectively. Without additional information, you cannot determine an exact value of xy. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  155. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Let P = the original price of the computer and D = the discounted price of the computer. Then the percent discount is images. From (1), images. Substitute this result into images to obtain images. Thus, (1) is sufficient.

    From (2), images, which implies images. Substitute this result into images to obtain images. Without additional information about P, you cannot determine an exact value of images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  156. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let F = the number of favorable responses from former customers and P = the number of favorable responses from potential customers. Then the percent of favorable responses is images. From (1), images, which you can substitute into images to obtain images. The value of this quantity can vary, so without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), images, which you can substitute into images to obtain images. The value of this quantity can vary, so without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  157. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images. Multiply both sides of this equation by 3 to obtain images, which implies images. Thus, (1) is sufficient.

    From (2), images implies images and images. The value of this result will vary. Without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  158. D. Each statement ALONE is sufficient.

    Let a = the number of components produced by machine A in 20 minutes, and b = the number of components produced by machine B in 20 minutes. Then images. From (1), images. Solving this equation simultaneously with images yields images and images. Hence, machine B works at a constant rate of  images So working alone, machine B would have taken images. Thus, (1) is sufficient.

    From (2), given that machine B’s rate is 150% of machine A’s rate, then images. Solving this equation simultaneously with images yields images and images, which leads to the same result as obtained in (1). Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  159. D. Each statement ALONE is sufficient.

    You can answer the question by solving images for the least positive value of x. From (1), substitute images into images to obtain images, which you can solve for the least positive value of x that makes the inequality true. Thus, (1) is sufficient.

    You can solve (2) for k, substitute the result into images, and then solve for the least positive value of x that makes the inequality true. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  160. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images implies images, from which it follows that images. Additional information is needed to determine an exact value of xy. For example, if images and images, then images. But if images and images, then images. Thus, (1) is not sufficient.

    From (2), there are only two pairs of integer values for which images. These are images and images images and images and images images. In either case, images. Therefore, statement (2) alone is sufficient.

  161. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), images implies images. Without additional information about c, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), images implies images. Without additional information about a, you cannot determine an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you can eliminate b from the two equations by subtracting images from images to obtain images. But without additional information, you cannot determine an exact value of images. For example, images satisfy all conditions given and yield images. But images satisfy all conditions given and yield images. Therefore, statements (1) and (2) together are not sufficient.

  162. D. Each statement ALONE is sufficient.

    To use (1), first write images divided by images as follows: images. Next, substitute images and simplify images. Thus, (1) is sufficient.

    To use (2), first write images divided by images as follows: images.

    Then, images implies images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  163. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let S = the number of restaurants that serve shrimp; let C = the number of restaurants that serve crab; and let B = the number of restaurants that serve both shrimp and crab. Then the number of restaurants in the city that serve shrimp but not crab is images, and the number of restaurants in the city that serve crab but not shrimp is images. Hence, the number of restaurants in the city that serve neither shrimp nor crab is imagesimages. From (1),imagesimages. The value of this quantity will vary, depending on the value of B. If images, then the number of restaurants that serve neither shrimp nor crab is images. But if images, then the number of restaurants that serve neither shrimp nor crab is images. From (2), images. The value of this quantity will vary depending on the values of S and C. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images, which you can calculate to determine an exact value of the number of restaurants in the city that serve neither shrimp nor crab. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  164. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    It is given that b is an integer. From (1), images is an integer implies a is an integer (because b is an integer). Additional information is needed because the number of values of b that satisfy images can vary. For example, if images and images, then four values of b satisfy images. But if images and images, then nine values of b satisfy images. Thus, (1) is not sufficient.

    From (2), images implies images. Additional information is needed because the number of values of b that satisfy images can vary. For example, if images and images, then six values of b satisfy images. But if images and images, then seven values of b satisfy images. Thus, (2) is not sufficient.

    Taking (1) and (2) together implies that only six values of b satisfy images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  165. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), Let T = the total of the selling prices of the 21 home security systems. Then Nio’s compensation is images. This quantity will vary depending on the value of T. Without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), you know only that the total of the selling prices of the 21 home security systems is $52,500. But you need additional information about how Nio’s compensation is determined to answer the question. Thus, (2) is not sufficient.

    Taking (1) and (2) together, Nio’s compensation is images, which you can calculate to answer the question. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  166. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images implies images, which establishes that images. But additional information is needed to determine whether images. For example, if images and images, then images, which implies images, yielding an answer of Yes to the question posed. But if images and images, then images, which implies images, yielding an answer of No to the question posed. Thus, (1) is not sufficient.

    From (2), images implies images, yielding an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  167. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Recall that images, images, and images And images, images, and images. From (1), images is even. This result implies images is odd, so K must be odd, yielding an answer of No to the question posed. Thus, (1) is sufficient.

    From (2), images, which is even regardless whether K is odd or even. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  168. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), the percent increase in Nayeli’s salary is images images. But without information to determine Tristan’s percent increase, you cannot answer the question. Thus, (1) is not sufficient.

    From (2), without knowing Tristan’s salary last year, you cannot determine Tristan’s percent increase. Further, without information to determine Nayeli’s percent increase, you cannot answer the question.

    Taking (1) and (2) together, Nayeli’s percent increase is 5 percent, but you do not have sufficient information to determine Tristan’s increase to make the comparison required to answer the question. Therefore, statements (1) and (2) together are not sufficient.

  169. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let C = the country’s current national debt in dollars, and I = the amount the national debt increases each day. Then images is the country’s national debt in 30 days. From (1), the country’s national debt in 30 days is images. This quantity will vary depending on the value of C. Thus, (1) is not sufficient.

    From (2), the country’s national debt in 30 days is imagesimages. This quantity will vary depending on the value of I. Thus, (2) is not sufficient.

    Taking (1) and (2) together, the country’s national debt in 30 days is images, which you can calculate to answer the question. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  170. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let V = the value of the stock fund. Then images = the amount invested in U.S. companies. From (1), images = the amount invested in Texas companies. Without additional information, you cannot determine an exact value of V. Thus, (1) is not sufficient.

    From (2), you can determine that images. But additional information is needed to determine an exact value of V. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images, which you can solve for an exact value of V. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  171. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images implies images. So k could equal images. Thus, (1) is not sufficient.

    From (2), because images, images, and images, only images satisfies images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  172. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images implies images. Hence, t could be 0, 1, 2, or 3, all of which would result in images when rounded to the nearest hundredth. Thus, (1) is sufficient.

    From (2), X could be, for example, 0.0135 or 0.0175. In the first case, images when rounded to the nearest hundredth. But in the second case, images when rounded to the nearest hundredth. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  173. D. Each statement ALONE is sufficient.

    Let D = the flight distance, in kilometers, from city A to city B. From (1), images, which you can calculate to determine an exact value of D.

    From (2), images, which you can solve for an exact value of D. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  174. D. Each statement ALONE is sufficient.

    Let R = the length of the radius of the larger circle, and r = the length of the radius of the smaller circle. From (1), images, which implies that the ratio of R to r is 4 to 1. Hence, the ratio of the area of the smaller circle to the area of the larger circle is images to images. It follows that the total area of the smaller circle is images of the total area of the larger circle. Thus, (1) is sufficient.

    From (2), the ratio of R to r is 4 to 1. You can complete (2) as shown in (1). Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  175. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Let X = the value of products labeled gluten-free in the grocery in 2015, and Y = the value of products labeled gluten-free in the grocery in 2017. Then the percent increase in value from 2015 to 2017 is images. From (1), if V is the value of all products sold in the grocery store in 2015, then images. But without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), if W is the value of all products sold in the grocery store in 2017, then images. But without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images. This expression gives inconclusive results. For example, if images, then images. But if images, then images. Therefore, statements (1) and (2) together are not sufficient.

  176. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    It is given that Hachi read for 15 days. From (1), Hachi read images pages during the first 10 days. But without additional information, you cannot determine the average number of pages read for 15 days. Thus, (1) is not sufficient.

    From (2), Let x = the average number of pages Hachi read during the first 10 of the 15 days, and y = the average number of pages Hachi read during the last 5 of the 15 days. Then images and the average number of page read for 15 days is images. This expression gives inconclusive results, depending on the value of y. For example, if images, images. But if images, images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images, from which you can determine y; and, thereafter, an exact value of images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  177. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE.

    Recall that if images is the prime factorization of a non-prime integer Z, then the number of positive factors of Z is the product images. From (1), images implies that X has images factors. But no information about Y is given. Thus, (1) is not sufficient to answer the question posed.

    From (2), images implies that Y has images factors. But no information about X is given. Thus, (2) is not sufficient to answer the question posed.

    Taking (1) and (2) together, given that images, then every positive factor of X is a factor of Y. Because Y has two more factors than X does, two positive factors of Y are not factors of X. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  178. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Given that images is equivalent to images, the question asks: is images?

    From (1), information about a is not helpful because a can be eliminated from the inequality given in the question without altering its meaning. Thus, (1) is not sufficient.

    From (2), images implies images. It follows that images. Hence, images and images. So images, yielding an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  179. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let A = the number of workers over the age of 40 at company X, and B = the number of works age 40 years and younger at company X. From (1), images and images have 401(k) accounts. But without additional information, you cannot determine whether the percent of the workers over the age of 40 years who have 401(k) accounts is at least 40 percent. Thus, (1) is not sufficient.

    From (2), images. But without additional information, you cannot determine whether the percent of the workers over the age of 40 years who have 401(k) accounts is at least 40 percent. Thus, (2) is not sufficient.

    Taking (1) and (2) together, consider, for a moment, the implications if A and B were equal, then images = the number of workers over the age of 40 who have 401(k) accounts and images = the number of workers age 40 years and younger who have 401(k) accounts. But it’s given in (1) that 16% of B have 401(k) accounts. This percent is images below the average of 29%. So in the hypothetical case of images, the percent of A that have 401(k) must be images to maintain an overall average of 29%. It’s given in (2) that images, from which you can infer that more than 42% of workers over the age of 40 years must have 401(k) accounts in order to pull up the average for all workers to 29%. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  180. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    It is given that images. From (1), images implies images. Hence, because images, then images, yielding an answer of Yes to the question posed. Thus, (1) is sufficient.

    From (2), images gives inconclusive results. For example, images and images yield an answer of Yes to the question posed images. But images and images yield an answer of No to the question posed images. Thus, (2) is not sufficient. Therefore, state-ment (1) alone is sufficient.

  181. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let R = the number of red chips in the box initially, and B = the number of black chips in the box initially. From (1), images, which is one equation with two variables. Without additional information, you cannot determine an exact value of B. Thus, (1) is not sufficient.

    From (2), images, which is one equation with two variables. Without additional information, you cannot determine an exact value of B. Thus, (2) is not sufficient.

    Taking (1) and (2) together, because images, let images and images. Then substitute into images to obtain images, which you can solve for x; and, thereafter, obtain an exact value of images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  182. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), images because if two non-vertical lines are perpendicular, their slopes are negative reciprocals of each other. Hence, images. Without additional information, you cannot determine whether images contains the point images. Thus, (1) is not sufficient.

    Substituting (2) into images yields images or, simply, images. Hence, images. Without additional information, you cannot determine whether images contains the point images. Thus, (2) is not sufficient.

    Taking (1) and (2) together images and images, confirming that the line contains the point images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  183. D. Each statement ALONE is sufficient.

    From (1), of the images beads remaining in the bag, half or 38, are blue. Thus, (1) is sufficient.

    From (2), let x = the number of blue beads removed, and 3x = the number of pink beads removed. Then images or, equivalently, images. Hence, images and images blue beads are left in the jar. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  184. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let h = the number of hours that Cerenity and Jas rented the jet ski, x = the rental fee for the first hour, and y = the rental fee for each additional hour. It is given that images and images. From (1), images, which implies images. Substituting into images yields images or, equivalently, images. This equation eliminates images as a possible value of x because division by 0 is undefined. And it eliminates images as a possible value for h because images implies images, which contradicts images. Hence, images. But without additional information, you cannot determine an exact value of h. Thus, (1) is not sufficient.

    From (2), because you have no way of knowing how many hours came before the last three hours, you cannot determine an exact value of h. Thus, (2) is not sufficient.

    Taking (1) and (2) together, because images, the last three hours does not include the first hour. Hence, images, which implies images. Substituting into images yields images, which you can solve for an exact value of h. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  185. A. Statement (1) ALONE is sufficient.

    It is given that k is a prime number. From (1), you have that the common factors of 24 and 36 are 1, 2, 3, 4, 6, and 12. Because k is prime, images, the only common factors to consider are 6 and 12. Of these factors, only images, or images, results in a prime number value for k. Thus, (1) is sufficient.

    From (2), k could be 2 or 3. Without additional information, you cannot determine an exact value of k. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  186. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Let x = the cost of one item of type 1, and y = the cost of one item of type 2. To answer the question posed, determine whether images. From (1), images, which implies images, or, equivalently, images. This inequality does not necessarily guarantee that images. For example, if images and images then images and images. But if images and images then images and images. Thus, (1) is not sufficient to answer the question posed.

    From (2), images, which implies images, yielding an answer of Yes to the question posed. Therefore, statement (2) alone is sufficient.

  187. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    It is given that the arithmetic average cost of the three items is $25. Hence, the total cost of the three items is images. From (1), one item cost $50. The remaining two items cost a total of images and thus were not taxed (because each would have a cost less than $40). Only the $50 is taxed, resulting in a total sales tax of images. Thus, (1) is sufficient.

    From (2), one item is $5. The remaining two items cost a total of images. Without additional information, you cannot determine an exact value of the sales tax on the three items. For example, if the remaining two items cost $35 and $35, then none of the items is taxed, resulting in a total of $0 tax on the three items. But if the three items cost $5, $60, and $10, then the total sales tax on the three items is images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  188. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let images = the probability Harper will get a job offer from both companies, images = the probability Harper will get a job offer from exactly one of the two companies, and images = the probability that Harper will get a job offer from neither company. Given that one of these three events is certain to happen, then images, from which you have images. From (1) images. Without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), images. Without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  189. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Standard deviation is a statistical measure that is used to quantify the amount of deviation from the mean in a set of data values. If all the values of a data set are equal, the standard deviation is 0; otherwise, the standard deviation is positive. From (1), x is 0 because all the data values equal 50. Two cases for y are possible. Case I: If images, then images is false because images is false. Case II: If images, then images is false because images. Therefore, statement (1) alone is sufficient.

    From (2), images because the values in the data set are not all equal. But without additional information, you cannot determine whether images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  190. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), it is given that the probability is images that the chip drawn will be green or red, meaning images of the chips are green or red. Hence, images of the chips are black or blue. So the probability that the chip drawn is black or blue is images. Thus, (1) is sufficient.

    From (2), it is given that the probability is images that the chip drawn will be black, meaning images of the chips are black. However, there is no information about how many of the remaining 16 chips are blue, green, or red. Without additional information, you cannot determine an exact value of the probability that the chip drawn is black or blue. Therefore, statement (1) alone is sufficient.

  191. D. Each statement ALONE is sufficient.

    From (1), given images and images (because consecutive angles of a parallelogram are supplementary), then images, which you can solve for b; and, thereafter, determine an exact value for images. Thus, (1) is sufficient.

    From (2), given images and images (because opposite angles of a parallelogram have the same measure), then images, which you can solve for an exact value of a. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  192. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Let P = the original price of the computer, and N = the new price of the computer. Then images = the increase in price, which as a percent of the new price is images. From (1), images, which implies that images. Substituting into images yields images. Thus, (1) is sufficient.

    From (2), images and images. The value of this expression will vary, depending on the value of P. Without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  193. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let M = Makayla’s current age, and G = Gilbert’s current age. From (1), images, which is one equation with two unknowns, so additional information is needed to determine an exact value of M. Thus, (1) is not sufficient.

    From (2), images, which is one equation with two unknowns, so additional information is needed to determine an exact value of M. Thus, (2) is not sufficient.

    Taking (1) and (2) together, you can solve images and images for an exact value of M. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  194. D. Each statement ALONE is sufficient.

    It is given that images. Hence, images, images, and images. From (1), images implies images, so images. You can substitute this value into images to determine an exact value of images. Thus, (1) is sufficient.

    From (2), images implies images. Substituting either of these values into images will lead to the same results for the value of images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  195. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), t could be 5, 6, 7, 8, or 9 because each of 0.5658, 0. 5668, 0.5678, 0.5688, and 0.5698 rounded to the nearest hundredth is 0.57. Thus, (1) is not sufficient.

    From (2), when images is rounded to the nearest thousandths, because 8 is the digit in the ten-thousandths place, the digit in the thousandths place increases by 1. So images, which implies images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  196. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), in terms of ordered pairs, images could be images, images, images, or images. Thus, (1) is not sufficient.

    From (2), in terms of ordered pairs, images could be images, images, images, images, images, images, or images. Thus, (2) is not sufficient.

    Taking (1) and (2), together, there are still two possibilities for images. These are images or images, meaning images could be images or images. Therefore, statements (1) and (2) together are not sufficient.

  197. D. Each statement ALONE is sufficient.

    From (1), the car is traveling images miles per hour faster than the van. Given that the car is already 4 miles ahead of the van, the time it will take the car to be 10 miles ahead of the van is images. Thus, (1) is sufficient.

    From (2), the car gained images miles on the van in 1 hour, so it is traveling 5 miles per hour faster than the van. This result leads to the same calculations as performed in (1) to obtain a time of 1.2 hours for the car to be 10 miles ahead of the van. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  198. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), given that one apartment has more than three occupants, you know only that there are 39 apartments left to accommodate the remaining occupants. But without additional information, you cannot determine how many occupants are left to distribute among the 39 apartments. Thus, (1) is not sufficient.

    From (2), the apartment manager and family account for 1 apartment and 4 occupants, leaving 39 apartments to accommodate 79 occupants. The only way to distribute 79 occupants among the 39 apartments is 38 apartments with 2 occupants and 1 apartment with 3 occupants. So there is a total of 2 apartments that have more than two occupants (the apartment manager’s apartment being one of those two). Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  199. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    It’s given that images. From (1), there are only 8 possible values of X, depending on the possible values of the ordered triples images. The possible values for images are images, images, images, images, images, images, images, and images. Hence, X can equal only the values images. Given that images is not among this list, then the answer to the question posed is No. Thus, (1) is sufficient.

    From (2), given that images is less than images, additional information is needed to rule this value out as a possible value of X. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  200. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), images implies images, from which you have images or –6. This result yields images equal to 6 or images. Thus, (1) is not sufficient.

    From (2), images implies images, from which you have images or –14. This result yields images equal to 6 or –18. Thus, (2) is not sufficient. Taking (1) and (2) together, images satisfies all conditions given, resulting in images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  201. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Statement (1) is not sufficient because all of the possible fractions given are less than 0.5.

    From (2), images because, of the possible fractions given, only images is greater than 0.25. Therefore, statement (2) alone is sufficient.

  202. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), images leads to inconclusive results. Without additional information, you cannot determine a definite Yes or No answer to the question posed because there are multiple values for x and y that satisfy this condition. For example, images and images yield a Yes response. But images and images yield a No response. Thus, (1) is not sufficient.

    From (2), images is inconclusive because no information about x is given. Without additional information, you cannot answer the question posed. Thus, (2) is not sufficient.

    Taking (1) and (2) together yields inconclusive results. For example, images and images yield a Yes response. But images and images yield a No response. Therefore, statements (1) and (2) together are not sufficient.

  203. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    It is given that images. From (1), you cannot determine a definite Yes or No answer to the question posed because, for example, X could be images, which yields a No answer to the question posed, or X could be images, which yields a Yes answer to the question posed. Thus, (1) is not sufficient.

    From (2), images implies images, which yields a Yes answer to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  204. D. Each statement ALONE is sufficient.

    It is given that images. Hence, images. From (1), images implies images, from which you have images. Thus, (1) is sufficient.

    From (2), given images, then images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  205. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), given images, then triangles ADB, ADC, and BDC are isosceles. Given that base angles of isosceles triangles have equal measure, images, images, and images. Note: images denotes the measure of angle X. Given that the sum of the measures of the interior angles of a triangle is 180°, images and images. Also, images, so images, which implies images. Hence, images, from which you can determine that images. Thus, (1) is sufficient.

    From (2), given images, images. But additional information is needed to determine an exact value of x. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  206. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    It is given that images for the integer k. Hence, images. From (1), images implies images, which you already knew. Thus, (1) is not sufficient.

    From (2), k is divisible by 16 implies images is an integer. Given that images, then images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  207. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), because images is an integer, then images is an integer. Thus, (1) is sufficient.

    From (2), images. Without additional information, you cannot determine whether images is an integer because, for example, if images, images is an integer. But if images, images is not an integer. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  208. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images implies images. Because an odd root of a negative number is negative, then images, yielding an answer of Yes to the question posed. Thus, (1) is sufficient.

    From (2), images implies images. This result is true regardless whether x is positive or negative, leading to inconclusive results. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  209. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    It is given that the total amount of the bonuses is $5,600. Let B = the amount of Benjamin’s bonus. From (1), Let X = the amount of Sian’s bonus = the amount of Lin’s bonus. Then images, which implies images. This is one equation with two unknowns. Without additional information, you cannot determine an exact value of B. Thus, (1) is not sufficient.

    From (2), if X = amount of Sian’s bonus, then images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of B. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images, which you can solve for X; and, thereafter, determine an exact value of B. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  210. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images implies that k must be odd. This is true because the only way that images can be negative is if m is a negative integer raised to an odd power. Otherwise, if k is even and m is negative or positive, images. Thus, (1) is sufficient.

    From (2), images is odd leads to inconclusive results. This is true because (2) would be true for both odd and even values of k. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  211. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), images leads to inconclusive results because images could be the sum of any two factors whose product is 36. For example, if images and images, then images. But if images and images, then images. Thus, (1) is not sufficient.

    From (2), images leads to inconclusive results because images could be the sum of any two integers that satisfy the inequality. For example, if images and images, then images. But if images and images, then images. Thus, (2) is not sufficient.

    Taking (1) and (2) together also leads to inconclusive results because both images and images and images and images satisfy all conditions given, yet yield different values of images. Therefore, statements (1) and (2) together are not sufficient.

  212. D. Each statement ALONE is sufficient.

    It is given that a, b, and c are positive integers and images. Thus, a, b, and c constitute a Pythagorean triple. From (1), given images, then images and images because there is no other positive integer solution of images. Hence, images. Thus, (1) is sufficient.

    From (2), given images, then images and images because there is no other positive integer solution of images. Hence, images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  213. D. Each statement ALONE is sufficient.

    Let H = the number who have lived in their current home for at least 10 years. Then images= the number of homeowners who have not lived in their current home for at least 10 years. From (1), images, which you can solve for an exact value of H. Thus, (1) is sufficient.

    From (2), images, which you can solve for an exact value of H. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  214. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Let x, y, and z be the costs, in dollars, of the individual shirts; and, for convenience, let images. Then images. From (1), either images, in which case images; images, in which case images; or images, in which case images. Either way, you have one equation with two unknowns. Without additional information, you cannot determine an exact value of z. Thus, (1) is not sufficient.

    From (2), either images, in which case images; images, in which case images; or images, in which case images. Either way, you have one equation with two unknowns. Without additional information, you cannot determine an exact value of z. Thus, (2) is not sufficient.

    Taking (1) and (2) together leads to inconclusive results. For example, if images and images are true, then images, which you can solve for y; and, thereafter, determine an exact value of z. But if images and images are true, then images, from which you cannot determine an exact value of z. Therefore, statements (1) and (2) together are not sufficient.

  215. D. Each statement ALONE is sufficient.

    From (1), images implies images, which, in turn, implies images. Thus, (1) is sufficient.

    From (2), you have images, which implies images, which, in turn, implies images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  216. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Note: images denotes the measure of images. From (1), images implies images. Given that the sum of the measures of the interior angles of a triangle is 180°, images equals images. Hence, triangle ABC is a right triangle, and, by the Pythagorean theorem, images. Thus, (1) is sufficient.

    From (2), given that the sum of the measures of the interior angles of a triangle is 180°, images, which implies images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  217. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    Simplify the equation in (1) as follows:

    images

    This result yields an answer of Yes to the question posed. Thus, (1) is sufficient.

    From (2), images implies images. This result is not sufficient to answer the question posed. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  218. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    From (1), images leads to inconclusive results because no information is given about r. Thus, (1) is not sufficient.

    From (2), images leads to inconclusive results because no information is given about p. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images implies images. Hence, images. Because p, q, and r are positive integers, you can determine a solution for images by finding the least common multiple of 2, 4, and 11, which is 44. Let images, which yields images. Thus, the least possible value of images is images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  219. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Let A = the amount, in gallons, of water added to the barrel, and let B = the barrel’s capacity, in gallons. Then images = the amount, in gallons, of water already in the barrel. From (1), images, implies images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of B. Thus, (1) is not sufficient.

    From (2), images, which is equivalent to images, the same equation as in (1). Thus, (2) is not sufficient.

    Taking (1) and (2) together results in images, which leads to the same conclusions as in (1) and (2). Therefore, statements (1) and (2) together are not sufficient.

  220. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Let M = the number of math teachers in the group of 9 teachers, then images is the percent of math teachers in the group. From (1), images, which leads to inconclusive results because you can’t assume there are only two math teachers in the group. So M could be a range of values. Thus, (1) is not sufficient.

    Statement (2) provides no information about M. Thus, (2) is not sufficient.

    Taking (1) and (2) together leads to inconclusive results because you cannot determine an exact value of M from the information given. Therefore, statements (1) and (2) together are not sufficient.

  221. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images leads to inconclusive results. For example, if images and images, then images is true, yielding answer of Yes to the question posed. But if images and images, then images is false, yielding answer of No to the question posed. Thus, (1) is not sufficient.

    From (2), images implies images. Hence, images is true, yielding an answer of Yes to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  222. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    Let D = the number of people in the group who own a dog, and C = the number of people in the group who own a cat. Then images = the number of people in the group who own either a dog or a cat or both, images = the number of people in the group who own both a dog and a cat, and images = the number of people in the group who own neither a dog nor a cat. From (1), images implies images. But without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), images implies images. But without additional information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    Taking (1) and (2) together, you have images. So without additional information, you cannot determine an exact value of images. Therefore, statements (1) and (2) together are not sufficient.

  223. D. Each statement ALONE is sufficient.

    From (1), images implies images. Thus, (1) is sufficient.

    From (2), images implies images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  224. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    From (1), images implies images, or, equivalently, images. Given that m and n are positive integers, images; otherwise, m would be negative. To assure that m is an integer, the possible values for n are 2 and 4, in which case images or 3, respectively. Hence, images or images. Thus, (1) is not sufficient.

    From (2) images implies images or, equivalently, images. Hence, images, which implies images. (It cannot equal –3 because m and n are both positive). Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  225. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Let images = the first term of sequence G, images = the nth term of sequence G, and images = the 51st term of sequence G. From (1), images. But without further information, you cannot determine an exact value of images. Thus, (1) is not sufficient.

    From (2), because images, and so on, then images, from which you have images. Hence, images. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  226. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), images implies images. Without knowing whether b is positive or negative, you cannot give a definite Yes or No answer to the question posed. If images, then images, yielding an answer of No to the question posed. But if images, then images, yielding an answer of Yes the question posed. Thus, (1) is not sufficient.

    From (2), images leads to inconclusive results. If images and images, then images, yielding a Yes answer to the question posed. But if images and images, then images, yielding a No answer to the question posed. Thus, (2) is not sufficient.

    Taking (1) and (2) together, the examples in (2) satisfy all conditions given and lead to inconclusive results. Therefore, statements (1) and (2) together are not sufficient.

  227. D. Each statement ALONE is sufficient.

    From (1), images, which implies images. Thus, (1) is sufficient.

    From (2), because 4 members left team B, images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  228. E. Statements (1) and (2) TOGETHER are NOT sufficient.

    From (1), images implies that images tenths digit is 0, 1, 2, 3, or 4. Thus, (1) is not sufficient.

    From (2), images implies that images tenths digit is 3, 4, 5, … , or 9. Thus, (2) is not sufficient.

    Taking (1) and (2) together, images implies images tenths digit can be 3 or 4. Therefore, statements (1) and (2) together are not sufficient.

  229. D. Each statement ALONE is sufficient to answer the question.

    It is given that images and images. From (1), images implies images. Because images implies x, y, and z are three different odd integers, then images. Hence, images, which you can solve for an exact value of z. Thus, (1) is sufficient.

    From (2), given that images, then images and images. Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  230. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    From (1), images implies images. Because any number raised to an even power is positive, images. Hence, images, yielding an answer of Yes to the question posed. Thus, (1) is sufficient.

    From (2), images leads to inconclusive results. For example, images can be positive if, say, images and images. Or images can be negative if, say, images and images. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

  231. D. Each statement ALONE is sufficient.

    From (1), images implies images. Given images, then images. Similarly, images implies images. Given images, then images. Hence, images. Because a and b are both positive this equation implies images or, equivalently, images, yielding a Yes answer to the question posed.

    From (2), images leads to the same results as shown in (1). Thus, (2) is sufficient. Therefore, each statement alone is sufficient.

  232. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

    Let x, y, and z be the prices of the three chairs. And, for convenience, let images. From (1), images implies images. This inequality leads to inconclusive results. The prices of the chairs can be under $600, yielding a No response to the question posed, if images, images, and images. And the prices of the chairs can be over $600, yielding a Yes response to the question posed, if images, images, and images. Thus, (1) is not sufficient.

    From (2), images implies images, yielding a Yes response to the question posed. Thus, (2) is sufficient. Therefore, statement (2) alone is sufficient.

  233. C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

    Let B = the number of tokens that Blake has, and K = the number of tokens that Kylie has. Then images equals the total number of tokens that Blake and Kylie have. From (1), images. Hence, images. The value of this quantity will vary, depending on the value of K. Thus, (1) is not sufficient.

    From (2), images, which implies images could be 20, 21, 22, 23, or 24.

    Taking (1) and (2) together, if images, then images and images. None of the other possible values for images yield integer values for B, K, and images. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

  234. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    It is given that machines A, B, and C, working together, can complete the job in 24 hours. Thus, the portion of the job the three machines, working together, can complete in 1 hour is images. Let T = the time it would take machine A to complete the job, working alone. Hence, the portion of the job that machine A can do in 1 hour is images. From (1), given machines B and C, working together, can complete the job in 36 hour, the portion of the job they can do in 1 hour, when working together, is images. It follows that images, which you can solve for an exact value of T. Thus, (1) is sufficient.

    From (2), given machines A and C, working together, can complete the job in 48 hour, the portion of the job they can do in 1 hour, when working together, is images. Let K = the time it would take machine C to complete the job, working alone. Then images, which is one equation with two unknowns. Without additional information, you cannot determine an exact value of T. Thus, (2) is not sufficient. Therefore, statement (1) alone is sufficient.

Chapter 5

  1. B. Literature in the United States changed dramatically in the second half of the 20th century.

    Essentially, you’re looking for the thesis of the passage, so it will most likely be fairly broad, but be careful not to select an answer [like Choice (A)] that’s too broad. Choice (B) walks the line between capturing the entirely of the passage but also being specific to the two paragraphs here. It’s the best choice.

  2. A. The aftermath of the war.

    The last sentence is a complicated one with many clauses, which is why the GMAT test-makers have chosen it to ask this question, hoping you will read through it too quickly and choose the wrong answer. However, a careful read reveals that Choice (A) is the main subject of the sentence, and other choices describe what happened during the aftermath. It’s the best choice.

  3. D. An emphasis on plain character and plain language.

    The answer to this question is factual. You need only find it in the passage itself. Choice (D) is taken directly from the passage.

  4. A. … historical events in each country radically changed their writers in non-analogous ways.

    Inference questions are tricky. Simply answering with a fact isn’t enough. You must find the step beyond what’s said in the passage. Here, Choice (B) is a fact from the passage, while Choices (C) and (D), whether true or not, are factual responses. Choice (A) is best here because it points to a trend that is hinted at but not explicitly stated in the passage.

  5. E. To recognize as different or unique

    Even if you can’t figure out what the word means, it is clearly used as a verb in the sentence, and only Choice (E) is a verbal definition.

  6. D. It provides a turn from the topic of the first paragraph, clarifying what the purpose of the passage will be.

    The word “however” in the second paragraph should be a hint that it’s contradicting or turning away (even slightly) from the first paragraph. A careful read shows that the second paragraph clarifies what the passage will be about, as it turns slightly away from the premise of the opening. Choice (D) is thus the best.

  7. B. While an incandescent lamp may produce heat, many people will continue to use them because the light is familiar and comforting.

    With an inference question, you always want to make a short jump, not a long leap. Choice (D) represents a long leap — it may be true, but it’s not implied in the passage. Choice (B), however, is a very small hop that even uses words from the passage, making it the best choice.

  8. D. It provides additional factual information about the topic of the passage.

    The topic of the passage is the incandescent lamp. The last sentence provides additional information about the light given off by such lamps. Choice (D) is best.

  9. C. About 95 percent

    So long as you read the question carefully and take a moment to a brief calculation, you’ll choose correctly. If 5 percent or less of the lamp’s energy is given to producing light, that means that 95 percent or more is given to other tasks. Choice (C) is best.

  10. C. Despite their inefficiencies, there are reasons why incandescent lamps remain popular.

    The passage is not a screed against incandescent lamps. In fact, suggesting that they be eliminated isn’t even suggested. Choice (C) is the closest to capturing the real point of the passage.

  11. A. Visible, obvious

    The best definition of apparent as used here is Choice (A). The whiteness is visible or obvious.

  12. E. The first paragraph describes Fischer’s prowess in chess at the height of his career, and the second paragraph describes the fall he experienced.

    The answer here is fairly obvious if you’ve read the passage, but the question is designed to keep you reading for as long as possible. Choice (E) is ultimately the best answer.

  13. B. He finds Fischer’s ultimate fate tragic, but also finds fault with Fischer.

    Only Choice (B) fits the tone of the passage. Fischer’s withdrawal is described as “tragic” but the use of the word “unfortunately” hints at the idea that the author thinks the chess master should have made different decisions.

  14. D. José Rail Capablanca was also a successful chess player with a high degree of self-confidence.

    Choice (D) is best here. The author’s reference to Capablanca means that he sees a connection between Fishcer and the other chess player. It’s not too much of a stretch to infer that they shared some characteristics, as seen in Choice (D).

  15. C. Anxiety about playing a match against Fischer that was so extreme that it causes physical illness.

    This is a factual question, so don’t try to infer what the symptoms of the “fever” are, beyond what the passage describes. That's best captured in Choice (C).

  16. B. Crafting characters and structures, and gathering resources.

    The answer is in the passage — you just need to take the time to read it and the answer choices carefully to find one that matches. Choice (B) is correct. Remember not to bring your outside knowledge into the game. You might play Minecraft, but you can only respond based on what the passage says.

  17. D. An overview of the game of Minecraft, aimed at those who might want to try playing it.

    The author is seeking to explain how to play the game. It is clear from the first sentence, which explains Minecraft in extremely simple terms, that her audience is intended to be people who are not very familiar with the game. Choice (D) is best.

  18. A. Minecraft is a game that allows players to change in their focus the more they play it.

    The inference of the last sentence is that the game will change as you play it, because it will be “less about surviving” and “more about building… . ” Choice (A) is a logical step in inferring — the game can become what the player wants.

  19. B. Creating a physical object or a representation of a physical object

    Choice (B) is best here. Choice (A) is a type of craft, which is not the same thing. Choice (D) has some merit, but in a virtual world “sculpting” is less likely to be the meaning as Choice (B). Choices (C) and (D) represent ways to craft, but they’re not quite right for this question. People playing Minecraft would not need to program computer code.

  20. E. Some Stars Aren’t What You Think!

    The best title captures some understanding of the main point of the passage, which is that the Evening and Morning Stars are not actually stars at all. Choice (E) is the best of the answers here.

  21. B. Mercury and Venus

    This is a factual question, so all you need to do is read the passage to find the correct information carefully. Choice (B) is the right answer.

  22. D. Many Americans may have ideas about the sky that show their interest but lack of understanding about astronomy.

    The only reasonably inference you can make about the writer has to be rooted in what he’s written here. Choice (D) is a safe assumption — it’s clear from the passage that the writing is correcting misapprehensions, but in a friendly way.

  23. C. A group of people on a boat spot what they think is a pack of dolphins in the ocean in the distance, but the captain informs them they’re actually looking at buoys bouncing in the water.

    The passage describes mistaking one thing for another, which is clarified by an expert (in that case, the author). Choice (C) describes a similar phenomenon.

  24. E. Wrong names

    The best alternative for misnomer is incorrect names. It is incorrect to name a meteor a “shooting star,” making Choice (E) the best answer. Notice that Choice (A) is correct but too broad. A misnomer is a kind of mistake — Choice (E) explains which kind.

  25. C. Allowing one of the branch of the government to be tied to a hereditary monarch and aristocrats.

    It is strongly implied in the passage that the Americans saw the British monarchy and hereditary aristocrats to be a flaw that kept their government from being a true republic. Choice (C) is best.

  26. D. Factual and learned

    You may be thinking “What tone?” because the author here has avoided a strong personal tone. The best answer, therefore, is Choice (D) because the passage sticks to the facts intelligently.

  27. D. It provides historical proof of the assertion the author has made earlier.

    The bolded portion is factual, and a careful reading shows that the facts are included to provide support for the idea mentioned in the sentence before it: “Most did not last very long.” Choice (D) is best.

  28. B. The American who set up the country’s government tried to do something uniquely long-lasting yet based in the historical example of republics that came before.

    Choice (B) best captures the main idea of this long passage. The Americans who set up the government the country still uses were aware of republics that came before, as well as the government of Britain, and created their new government in response to those examples.

  29. D. A dictatorship

    As clearly stated in the passage, the republic was followed by a dictatorship, making Choice (D) correct.

  30. E. Landowners

    The passage states that “Large landowners controlled the House of Commons” so Choice (E) is best.

  31. D. Including video elements in a website is increasingly common, and may be a good choice for your site.

    The passage suggests (but does not insist upon) including video on one’s website. Choice (D) thus expresses the main idea of the passage the best.

  32. C. Business owners who are deciding what elements to include in their web pages.

    The passage is clearly aimed at business owners, but the emphasis is not on those who are deciding about whether to have an online presence, as in Choice (A), but rather those who have decided to have one and now want to figure out what to include. That makes Choice (C) the best answer.

  33. A. It increases.

    The passage includes the following: “Research supports the idea that video increases customer engagement… . ” That makes the answer Choice (A).

  34. D. Video should be used carefully on a website, as it can work against the site’s accessibility and enjoyment.

    In the last sentence of the passage, it is suggested that website owners should “weigh the pros and cons of video” and use it in a way that “supports, rather than detracts.” That points out the correct answer as Choice (D).

  35. D. The ever-increasing interest in YouTube

    This is an unusual variation on this type of question, but you might see it on the test. The point is for you to find a phrase that best matches the original phrase in meaning. Here, Choice (D) is best because it means something akin to “soaring popularity.”

  36. B. Swollen and damaged

    The last section of the passage, in the bullet points, answers this question. The passage advises avoiding cans that are swollen and damaged. Choice (B) is right.

  37. E. They provide a helpful list of characteristics to look for that is drawn from the main paragraph.

    In this case, the bullet points flow from the main paragraph, adding more information, not contradicting or repeating it. In this case Choice (E) is thus the best.

  38. A. Botulism is a serious health hazard, but there are steps you can take to avoid the risk of mistakenly consuming it.

    The correct answer is Choice (A) which captures the main idea of the entire passage in a tone that is factual.

  39. C. Anhydration

    The passage defines anaerobic to show that an- means without. Applying this rule (and knowing that hydration must be the other part because it is in every answer), the correct answer must be Choice (C).

  40. E. Poison

    Even if you are not familiar with the word toxin, its use in the passage makes it clear that it is a type of poison, so Choice (E) is correct.

  41. C. Carefully check cans for swelling, damage, rust or deep dents, and do not consumer the food therein if you notice any of these.

    The answer is in the passage, but you must take the time to read it carefully, not just skim it. Choice (C) is best.

  42. C. Personal Real Estate Is Not a Foolproof Investment

    Choice (C) best gets to the tone of the piece, which suggests that individual real estate can plummet in price. That hints at the idea of the title, that real estate is not a foolproof investment because it can sour.

  43. D. Both towns were sites of carcinogenic toxic waste contamination.

    Here, you’re asked to find the factual information as listed in the passage. It’s clear that Choice (D), which includes language taken directly from the passage, is the best answer.

  44. B. Pursued legal action against the real estate agencies that did not disclose known contaminants to them before selling them property in the towns.

    In an inference question, you want to make a small step away from facts and into supposition. The trick is not to wander too far away from what is already known. Here, the best choice is Choice (B), because it can be inferred from the final sentence of the passage that legal action was most likely taken. All of the other choices might be true, but there is not as much justification in the choices as in Choice (B).

  45. A. Cautious and factual

    The author’s tone here is cautious, as is clear from the first sentence when he points out the pitfalls of individual real estate property as an investment. In the rest of the passage, he provides facts to prove his point. That makes Choice (A) the best selection.

  46. D. It clarifies that some property owners were eventually compensated for their losses.

    The best choice here is Choice (D) because the bolded sentence offers clarification about information presented in the passage. It suggests that while the property owners did lose money on their investment, they were eventually compensated for at least part of the lost money.

  47. E. It summarizes attempts to fix a problem before asserting that the problem is not yet fixed.

    The best choice here is clear: Choice (E). The passage explains a problem in “the world of intellectual property” as well as attempts to fix that problem, but concludes that the problem is not yet resolved.

  48. B. By producing guides to initial patent application.

    It’s clearly stated in the passage that the Patent Offices “have recently intensified their efforts to be more accessible” by publishing “guides to initial patent application.” Thus, Choice (B) is the best answer.

  49. D. Intellectual property management must do a better job of connecting legal procedure with technological development and business strategy.

    In this main idea question, the trick is to avoid choosing an answer that identifies an idea from the passage, but not the main idea. Choice (D) is the only one here that correctly explains the main idea of the passage.

  50. C. Of a whole, more than the sum of its parts

    In the sentence from the passage, holistic is used in its standard meaning, to suggest more than the sum of its parts. Choice (C) is correct.

  51. D. They will have further suggestions about how intellectual property management can be approached.

    The passage reads like the opening to a longer piece of writing about intellectual property management. It seems clear that further suggestions will come, making Choice (D) the most accurate of those offered here.

  52. A. Zoos are not very well understood. Zookeepers, administrators, and veterinarians have to work together at a zoo, but often they are unable to see how their efforts appear to visitors to the zoo, even after making efforts to make the zoo accessible. Their efforts need to be combined better.

    The passage identifies an area where three groups must work together, which is difficult. They’ve made improvements, but the overall picture is still very hard to see, and they must improve. That’s the same logic as we see in Choice (A).

  53. D. The author is gently teasing readers about the items that they might be storing on their kitchen counters instead of using them for cooking.

    Choice (D) is the best answer here. The author’s tone is gentle and humorous, suggesting that these items don’t belong on a kitchen counter. It’s too much to think the author is suggesting you get rid of these items permanently or should never have owned them at all.

  54. C. Cleaning Off Your Counter Gets Your Ready to Cook!

    The best answer here is Choice (C), which is neither too narrow, as in Choice (B), nor too broad, as in Choice (A). It captures the main idea of the passage.

  55. B. Unsure about keeping their deep fryer on their kitchen counter, even though they only use it once a month.

    The advice in the second paragraph specifically urges people to store their seldom-used appliances off their counters. Thus Choice (B) is best.

  56. E. Maintaining a clutter-free kitchen so it is usable whenever cooking inspiration strikes.

    The answer choices provided read like a list of commonly asserted ideas from cooks and cookbook writers, so it’s easy to get confused. However, if you pay attention the passage, only Choice (E) is truly justified as an inference. The authors write “A clean, clear counter space can inspire the creation of a great meal.”

  57. D. Not specified, but not on a kitchen counter.

    This is a supporting idea question. You just need to read the passage carefully to find the answer. Here, no system is advocated, except that the kitchen counter should not be used, so Choice (D) is best.

  58. E. A compiled language.

    The last sentence of the passage reads, “Software you install on your computer … are coded using compiled language.” Choice (E) is thus the best.

  59. C. As the speed advantage that compiled languages have continues to decline, both languages will offer equal incentives to be used.

    Choice (C) is just a small extension from the passage, which points out that the “speed advantage compiled languages have is starting to fade in importance.” If that is true, it is safest to say that the languages will be continue to be equally appealing for different reasons.

  60. B. There are two types of programming languages, and each offers advantages and disadvantages.

    Choice (B) best captures the main idea of the passage: There are two main types of languages, and each has distinct characteristics to recommend them.

  61. C. Factual and helpful

    The choice between Choice (C) and Choice (E) is a little tricky here. Keep in mind the somewhat negative meaning of rote, which is typically used to describe going through the motions. Disinterested also implies a lack of true engagement with the topic. That’s hard to prove here, so Choice (C) is better. The tone is definitely factual and helpful.

  62. C. A computer translates the code into an executable file, and then it is distributed via the internet, CD-ROMs, or other media.

    Choice (C) is correct. The language is taken directly from the passage, but the test-taker must carefully read both the passage and the answer choices to make the correct pick.

  63. D. Javascript, Ruby, and C++

    A half-dozen high-level programming languages are listed in the passage. Choice (D) collates three of them into a list and thus is the best choice.

  64. E. The first paragraph provides an overview of how beneficial bees are to our world, so as to make the impact of losing them clearer when presented later.

    The best choice here is Choice (E). The opening paragraph can be summed up in this sentence: “You may not have thought much about the role honey bees play in our everyday food supply.” The rest of the paragraph works to prove that point, so that the next paragraph’s concern about the loss of honeybees has more of an impact.

  65. B. Beef and dairy

    It’s certainly possible that all of the food products mentioned here could be negatively affected by the decline of bees. However, the passage makes specific reference to “meat and dairy” as well as “cattle” so Choice (B) is the best of the answers here.

  66. A. The health of honey bees has been so compromised in recent years that a spring without them is a possibility.

    The passage mentions that honey bees have been compromised and then goes on to mention a “spring without bees” that could endanger our food supply. Choice (A) makes a reasonable inference that a spring without bees is therefore a possibility.

  67. C. Concerned and alert

    While the author is neither scheming nor hysterical, he does seem to be both concerned and alert, to judge from the tone of the second paragraph, so Choice (C) is best.

  68. D. Scientists who have been studying bees should provide suggestions about how the rest of us can help, including keeping hives.

    In this inference question, the author’s tone is key. It is too urgent for Choice (A) and too calm for Choice (B). Choice (E) is not justified by the text, and Choice (C) seems like the exact opposite of what the author wants. Choice (D), therefore, is correct.

  69. E. To expose to danger in some way

    In any sentence with a bolded word, you must look carefully at the context in which it is used. Here, several accurate definitions of the word compromise are offered, but only Choice (E) is a verb version that makes sense in the sentence.

  70. A. Cerro Tololo in the Chilean Andes

    The passage notes that at Cerro Tololo you “can see even more stars” than the other places listed in the passage, so Choice (A) is right. Notice that the question is not asking for the best place in the world, but the best place mentioned in the passage.

  71. C. The sky is a busy place, and no matter where you watch it from, you can see interesting things.

    Choice (C) sums up the two main points of the passage the best. First, there are many interesting sights in the night-time sky, and secondly, no matter where you watch, you’ll be able to see something worth your time.

  72. B. The Hubble Space Telescope

    The passage specifically states that space satellites, like the Hubble Space Telescope, and airliners can be mistaken for each other. Notice that while it’s certainly possible that any of the choices provided could also fool an amateur, the passage is specifically referring to this comparison, so Choice (B) is right.

  73. C. It explains the phenomenon mentioned in the sentence before it.

    The bolded sentence explains what the “beautiful pearly swath across the heavens” is, as mentioned in the sentence before it. That makes Choice (C) the best.

  74. C. “Starry Night” may have been painted in an area that the author would deem a “great observation place” like Cerro Tololo.

    Choice (C) is the best inference of those offered here, because it connects to the text of the passage. “Starry Night” is mentioned as depicting a scene that is similar to what one might see at a place like Cerro Tololo, so Choice (C) makes sense.

  75. E. Average adults interested in learning more about the night sky.

    The passage is clearly aimed at people who do not already know quite a bit about the night sky, which eliminates Choices (A), (B), and (C). The students mentioned in Choice (D) are too young to understand language of this complexity, so Choice (E) makes the most sense.

  76. E. America’s Democratic Republic System

    Choice (E) is best here. The passage explains why America is not a democratic republic in a factual tone.

  77. A. They are democracies.

    The example of a New England town meeting is used in the passage as an example of a vestige of democracy, so Choice (A) is the right one.

  78. D. It turns the paragraph back to the main topic after a series of sentences that provided exceptions to the topic under discussion.

    Choice (D) is best because the passage seeks to build an argument that America is a democratic republic. In order to do so fairly, several examples of a true democracy are offered, and the bolded sentence acknowledges them before turning the paragraph back to the topic.

  79. B. Referendum; Democracy

    A silly question, perhaps, but one you’ll need to double-check the passage to make sure you’ve chosen the correct answer for. It’s stated that the ballot initiative is “also called the referendum” so Choice (B) gets it right.

  80. C. The Board of Trustees, chosen by election, vote on the next steps for an insurance company.

    You’re looking for a situation similar to what is explained within the passage, where a group of people elect a smaller group to make decisions for them. Choice (C) presents such an example.

  81. D. To alert readers that something paradoxical has been noted.

    The author makes use of the phrase In contradictory language to note that she is aware of what readers will surely notice: the paradox between the rise in temperature measurements and the colors we perceive them in. Choice (D) is best.

  82. E. Yellow

    Choice (E) is correct, which follows the statement in the passage that “Temperatures around 2,700 – 3,000 K … are perceived as warm in color, tilting toward yellow and red.”

  83. B. Colloquial language about light often reflects actual observation about the color of hot things.

    The end of the passage notes that the “heat-light-color relationship is recognized in colloquial language.” The safest inference, then, is that it has been observed closely. Choice (B) is best.

  84. D. The relationship between heat, light, and color is sometimes counter-intuitive.

    The best answer notes the relationship between heat, light, and color [not just heat and color, as in Choice (A)], as well as some characteristic of that relationship that is expressed in the passage. Choice (D) is best.

  85. B. Metal burning “white-hot.”

    The type of item burning doesn’t matter; the passage states that something burning “white-hot” is hotter than something burning “red-hot” so Choice (B) is best.

  86. C. A brief biography of a memorable American.

    Choice (C) is the best answer. The passage gives a very brief biography of Huey Long.

  87. D. Polls showed he would secure enough of the Democratic vote to swing the election to the Republican party.

    According to the passage, the principal reason that the Democratic party would have been concerned was Long’s likelihood of splitting the vote. Choice (D) is the best answer.

  88. A. Long’s policies hurt some of the people who he was supposed to represent as an elected official.

    The safest inference is to take the words of the last sentence — that Long had “ruined” the family of the man who shot him — and draw a conclusion that he had hurt people whom he was supposed to help. Choice (A) is best.

  89. E. “Kingfish”

    The question is simple, so long as you read the passage for the answer. Huey Long was called “Kingfish.”

  90. C. Reminds or informs readers that Long did some good things on the way to his eventual demagoguery.

    The use of the word “actually” is key here. It has a tone of revelation, teaching readers that Long did good things as well as bad. Choice (C) is thus the correct answer.

  91. D. Wealthy people with annual incomes of over $1,000,000

    It’s not a guess: The passage states that Long’s “Share Our Wealth” program would redistribute wealth of people with an annual income of over $1,000,000. It’s a logical inference that those people would dislike Long.

  92. C. Enthusiastic and supportive

    The authors strike a tone of enthusiasm and support, as can best be seen in the last sentence of the passage: “Why shouldn’t one of those people be you?” Thus, Choice (C) is the best offered.

  93. E. It develops the main idea beyond the initial example to show another way it applies.

    Choice (E) is the best answer here. The bolded sentence adds an additional idea to the support the thesis that “an Internet-based business model has proven to be a worthwhile investment.”

  94. D. Consider Starting an Online Business

    The purpose of the passage is to explain why starting an online business might be a good choice for readers. Choice (D) is the best pick to capture that idea.

  95. D. Smartphones

    The passage specifically refers to smartphones as a technology that has made shopping online “as easy as ever.” Choice (D) is thus the best.

  96. E. It invites readers to give an Internet-based business a try.

    The use of a sentence at the end of the passage can create several different effects. It could be rhetorical, as in Choice (A), or suspenseful, as in Choice (D). But here, the question serves as an invitation to read and explore more about the topic, so Choice (E) is correct.

  97. D. Businesses of all sizes

    The passage includes this sentence: “Increasingly, businesses of all sizes are also buying products and services online.” That makes Choice (D) the best answer.

  98. A. To set up a contrast between the appealing smell of apple pie baking and the less pleasant smell of cruciferous vegetables being cooked.

    Here, you must look at the context of the sentence in bold. Notice how it is followed by the word “But … ” in the next sentence. You can tell that it is setting up a contrast from that alone. Choice (A) is best.

  99. C. Sulfur Is the Smell of Cruciferous Vegetables Cooking

    Of the choices presented here, Choice (C) is the best. It refers to a main idea of the passage, which is that cruciferous vegetables release a sulfurous scent.

  100. D. Plexin

    Choice (D), Plexin, is not listed in the passage, so it is the best choice. Remember to read the question carefully — so you know you’re looking for the name that is NOT a sulfur compound — and also check the passage for the right answer.

  101. B. The crucifix at the front of the sanctuary.

    The word crux is defined in the passage as “the Latin word meaning cross.” Thus, the best answer here is one that uses the prefix in the same way, as in Choice (B).

  102. D. Interested in one of their distinctive characteristics

    Choice (D) is correct. The author is pointing out an interesting characteristic of this type of vegetable, not dismissing them or discouraging use of them.

  103. E. The smell of sulfurous compounds in cruciferous vegetables is heightened by heat.

    The passage indicates but never explicitly states that heating cruciferous vegetables makes the sulfuric smell worse. (It states that the smells “are liberated” but you must infer the rest). That makes Choice (E) the best.

  104. D. Carrots

    Choice (D) is best because carrots are not in the passage’s list of cruciferous vegetables.

  105. C. The brain’s minicolumns are key to how it works, as are the inputs it receives.

    While Choices (D) and (E) contain factual information from the passage, they don’t represent the main idea of the passage. Choice (C) is better at that.

  106. A. A repeated neural circuit in the brain

    You’re presented with two choices that are correct — Choices (A) and (C). A quick review of the question asked, though, reveals that you’re to find the “most specific” answer, which must be Choice (A).

  107. D. It supplies further details and information about a general concept presented in the first paragraph.

    The second paragraph develops the idea of the first paragraph, providing more information about how minicolumns work in the neocortex of the brain, the main idea presented in the introduction. Thus, Choice (D) is the best.

  108. E. Auditory

    The context gives you the clues you need to understand this unusual usage of audition. It’s used here as opposing vision, indicating that it’s an adjective too. That makes Choice (E), auditory, also an adjective relating to hearing, the best.

  109. B. A phone system is built out of a single type of wire which adjusts to respond to the location of the call being placed.

    Choice (B) most closely mimics the idea presented in the second paragraph: The brain is not build out of differing structures of minicolumns; instead, the input received and the output sent by the minicolumn defines its role.

  110. D. Respond differently to different inputs from vision or hearing.

    Choice (D) gets at a reasonable inference from reading the passage. If, as the passage suggests, minicolumns are the same in the brain and respond to become part of a certain area because of the input from a different sense, it stands to reason that they might also be able to change based on those inputs. Thus, it is correct.

  111. D. Factual and explanatory

    The author may feel wonder or be aggrieved, but that’s not clear from this passage. It’s factual and full of information, so Choice (D) is best.

  112. B. It’s important to find a balance between your work life and your personal life.

    Choice (B) is the best conclusion. The paragraph develops the idea that even people who really love their work sometimes neglect other aspects of their lives. Choice (B) finishes that thought well.

  113. C. To introduce in an interesting way an idea the author intends to develop.

    This type of question is really an inference question: you need to infer why the author might use a quotation at this point in the passage. Here, the most likely answer is Choice (C) because the author wants to capture the attention of readers and use the quotation to introduce the main point of the passage.

  114. B. An excessive amount of time for a small-business owner to work.

    Choice (B) is best here. It’s possible that the author feels that several other choices here are also true, but in a GMAT inference question, you always want to choose the small hop in logic, not a leap.

  115. E. You may want to consider hiring an employee to help with the business.

    Choice (E) is best here. The passage states, “You may need to start hiring people.” Choice (D) seems like a good idea, but an accountant is not specifically referred to in the passage, so it cannot be correct.

  116. E. A thoughtful exploration about finding a balance between a rewarding small business and a personal life.

    Choice (E) is best. The passage does include a quotation and seems slightly discouraging of putting too much effort into business, but Choices (A) and (D) are too extreme. The passage mostly seems to be about finding a balance between work and personal life.

  117. C. Enterprising

    The use of inventive in the passage suggests a person who is enterprising, so Choice (C) here is best.

  118. D. Baked

    The passage suggest that kale is “traditionally sautéed, baked, or simmered,” so a restaurant that prepares it in a traditional way would serve it baked, as in Choice (D).

  119. E. Kale, which has several types, can be prepared in a myriad of ways, including an innovative new form.

    Choice (E) is best. The passage does indeed indicate that there are several kinds of kale as well as a multitude of ways to prepare and serve it.

  120. A. It is less fibrous and grassy tasting that curly kale.

    A close re-read of the passage will remind you that the authors state, “Lacinato is less fibrous and grassy tasting than curly kale.” Choice (A) is thus correct.

  121. D. Competing in a chess tournament can be emotionally grueling for children, but doing so can also teach them resilience and other valuable lessons.

    The author’s position is that “Chess is a good was to help children deal with” loss and similar issues, and that crying after a grueling loss is natural. Thus, he is most likely to agree with the sentence in Choice (D).

  122. B. At any age so long as the child is ready.

    According to the passage, “Kids begin competing at all ages. When a child is ready for individual or team competition depends on many factors.” Thus, Choice (B) is closest to what the author believes.

  123. A. Straightforward, gently leading

    The test-makers have provided answer choices with higher-level vocabulary in hopes of confusing you. Don’t fall for it. The tone of the passage is best described by Choice (A): straightforward and gently leading.

  124. C. The child is reacting to a loss in a natural way.

    The author states that crying is a “natural response to loss.” Therefore, the correct answer is Choice (C).

  125. D. Chess Will Teach Children Valuable, If Sometimes Painful, Lessons

    Choice (D) best gets at the author’s main purpose in this passage, which is to convince parents that playing competitive chess may be hard on their child but still worth their time.

  126. C. They do not produce pollen and thus do not attract bees.

    The passage states “Watch out for the hybrid that is pollenless because it is of little use to the bees.” That means that Choice (C) is correct.

  127. D. The widely-loved sunflower is more complex than you may know.

    Of the choices given here, Choice (C) is the best. It’s clear that the passage is about sunflowers, but a couple of the choices — (A) and (C) — are too specific. Choice (B) is an opinion that goes further than the passage itself, and Choice (E) is never actually stated. That leaves Choice (D), which aptly explains the main idea of the passage.

  128. B. A principal reason for maintaining a garden is to provide pollen for bees.

    The most reasonable inference is to extend the author’s statement to “watch out for” hybrid sunflowers that are pollenless and provide “little use” to the bees. It is not too far a jump to assume, therefore, that the author thinks garden should provide pollen for bees. Choice (B) is correct.

  129. A. The author feels that they are an important part of the ecosystem.

    Choice (A) is best here. It is clear that the author feels bees are important enough in the ecosystem that plants which do not support them should be avoided. Notice that while Choice (D) feels like it is likely true (especially given the source of the passage as stated), there’s no actual proof that it is correct in the passage itself. Choice (A) is the more justified and thus, correct, choice.

  130. B. The author’s experience in trying to transplant sunflowers has taught him that using peat pots is a smart move.

    The general tone of the passage is to give advice, which indicates that the author is an expert in his field. Choice (B) makes the most sense here: The author is giving advice he’s learned, perhaps the hard way. The context of the sentence supports this idea.

  131. C. To show how the concept of a republic is an ancient ideal.

    The use of the term res publica is most likely to show how the idea of a republic is an ancient one, which gives it greater meaning and esteem. Choice (C) is the best.

  132. D. The concept of a republic now used in America has been developed for thousands of years.

    The passage essentially traces the historical precedent of the American concept of a republic, so Choice (D) is best.

  133. E. It was felt that short terms of office reduced the likelihood of corruption.

    Choice (E) is taken directly from the passage: “No one held office for a long period of time, because when citizens rotate in and out of office they avoid corrupting influences.”

  134. A. Virtue

    The passage states that “virtue” was “the highest ideal a republican citizen could achieve.” Choice (A) is best.

  135. C. The American republic grew out of a number of historical precedents.

    We may hope that the author believes Choice (E) and suspect that he thinks Choice (A), but Choice (C) is the safest answer. It is reasonable to assume that the author believes the American republic grew out of a number of historical forbearers.

  136. D. What Is an Asterism?

    There are other choices here that point out facts mentioned in the passage, but only Choice (D) gets at the main point of it: explaining what an asterism is and where readers might encounter them.

  137. A. It provides an example so that readers can relate to the main idea of the passage.

    Choice (A) best reveals the purpose of the first sentence: It gives an example of an asterism, the main topic of the passage, to set up the idea that the rest of the passage will explain what an asterism is.

  138. E. It is a named star pattern.

    The passage reads, “An asterism is a named star pattern that’s not identical to one of the 88 recognized constellations.” Choice (E) is thus the best.

  139. B. An asterism may straddle several different constellations.

    Reviewing the passage, Choice (B) is clearly supported by the ideas within it, so it is the best choice. Other answer may be correct, but Choice (B) is definitely correct.

  140. C. The ocean was vitally important to the development of multicellular life.

    Refer to the last sentence of the passage: “The processes that lead to multicellular life all took place in the earth’s oceans.” It is a reasonable inference to say that the author agrees, as Choice (C) suggests, making it the best answer.

  141. C. Since the earth’s formation 4.5 billion years ago, the development of life has been a complex process.

    Of the choices provided, Choice (C) combines specificity (in the 4.5 billion years figure) with the general outline of the passage. It’s the best answer here, beating out Choice (A), which is correct but also very broad.

  142. E. Prokaryotic cells

    It’s clear from the passage that another term for cells without a cell nucleus is “prokaryotic cells.” Choice (E) is thus the best.

  143. D. Intrigued, informative

    The author is intrigued by his topic, as the phrase “What’s remarkable is … ” alone indicates. But the author is also well-informed. That makes Choice (D) the best.

  144. A. Two billion years

    If you follow the passage’s math, it took two billion years for humans to develop after Eukaryotic life (cells with nuclei) appeared. Choice (A) is right.

  145. C. Life did not have to begin at the moment it was sustainable.

    If it’s “remarkable” that life began at the earliest moment it could on our planet, the possibility that life did not have to start at that exact moment must also be true. Thus, Choice (C) is the best answer.

  146. B. Innovations in electrical safety continue to be developed by Americans.

    The passage begins with mention of Edison, but isn’t actually about the man. The rest of the passage focuses on the development of electrical safety, and Choice (B) captures that the best.

  147. E. Direct Current

    The passage clearly defines DC as “direct current”; a careful read of the passage and answer choices will keep you from choosing any answer but Choice (E), the correct choice.

  148. C. A passage exploring the history of containing nuclear power, beginning with a brief look at the first time it was safely processed.

    Choice (C) best captures the flow of the passage: It begins with an innovation that increased the safety of the power source, and it then chronicles additional innovations that increased safety. The original passage does this as well.

  149. A. Steam engines were responsible for a significant portion of factory accidents before electrical engines were put into use.

    The safest inference is that steam engines were the cause of a significant portion of factory accidents, because the final sentence of the passage states that electrical engines improved safety on factory floors. Thus, Choice (A) is the best.

  150. E. Serviceable

    We’re used to hearing the word practical as meaning something similar to Choice (A), sensible. But the word has another meaning, used here. Choice (E) captures that.

  151. B. The first makes a general statement about events; the second offers evidence that proves that statement.

    The first sentence is an overview of what the rest of the passage — including the second bolded sentence — will prove. Choice (B) is best.

  152. C. The way light interacts with color profoundly affects the way we see.

    Some of the answer choices provided here are on the right track, but are too broad, as in Choice (A) and Choice (B). Choice (C) does a better job of capturing the general point of the passage without being so broad as to be almost meaningless.

  153. A. Blue ink

    The passage lists colorants “like paints, inks, or dyes” so Choice (A) makes the most sense here.

  154. D. Watching a streaming service on a laptop.

    Reading the passage carefully will allow you to note the sentence “The colors on a monitor screen are seen as direct light.” Whether you understand the science involved or not, you can tell that only Choice (D) offers a similar situation to that one.

  155. D. Attendees at a design conference, attending a workshop on choosing colors for their graphic work.

    The material presented here is introductory, so a group of scientists [Choice (C)] would be unlikely to need to know it. But it’s too complex for a group of children, as in Choice (A). That makes Choice (D) the most likely audience.

  156. E. Reflected and direct

    The passage mentions direct and reflected light as the two colors of light. Choice (E) is thus correct.

  157. E. It introduces a key concept in understanding light but is not the thesis.

    The first sentence is often assumed to be the thesis of a passage, but that’s not true here. Instead, Choice (E) is correct: The first sentence sets boundaries for the discussion about light but isn’t the main point to be proven by the passage.

  158. B. The era of human vs. robot had begun.

    Only Choice (B) presents a continuation of the idea in the second paragraph: that of a human in opposition to a non-human. It’s the best choice.

  159. D. To back up her point with a list of examples that prove it.

    Although it may seem quite obvious, the truth is that in this inference question, the safest answer is Choice (D) — to provide examples that prove her point. It’s the best answer.

  160. A. The idea of “politics” in American literature changes in the second half of the 20th century.

    Choice (A) is best. The passage is difficult to follow, but the overarching point is clear from the first sentence.

  161. C. American critical reception that was influenced by the poor review from Europe.

    Remember than in an inference question, the idea is not to wander too far down the path from the passage. Choice (C) goes just a bit further than the passage itself and thus is the best choice.

  162. D. What Was the Missouri Compromise?

    Choice (D) captures the topic of the passage best. Choice (E) is a little too vague to work — it could refer to many different events — while Choice (D) is specific to this topic.

  163. A. New states located above a certain latitude could not practice slavery.

    As the last sentence makes clear, “slavery would be excluded from any new states or territories above latitude 36 degrees, 30 minutes,” so Choice (A) is best.

  164. D. Calm statement of fact

    The author is not sneering or accepting — he merely restates the historical facts. Thus, the only answer that fits here is Choice (D).

Chapter 6

  1. C. can always differentiate among the three signatures.

    The correct answer is Choice (C). When the sentence involves two choices between is correct. Here, there are three signatures, so among is correct, which is only found in Choice (C). Notice that Choices D and E change the meaning of the sentence, and Choice (B) adds in an unnecessary word.

  2. B. but until we know what they think, we can’t move forward.

    The best answer is Choice (B), because it matches the correct pronoun (they) with everyone, and the verb is correct as well. Choices A and D do not use the correct pronoun (and Choice (C) doesn’t use the correct verb for that incorrect pronoun, anyway). Choice (E) needlessly makes the sentence more complicated by changing the word order of a common phrase.

  3. D. but neither he nor anyone else knew the how his invention of the telephone would change the world.

    This is a question about pronoun choices, so ignore those answers which do not address this, including Choice (B) and Choice (E). The sentence as is contains a pronoun error: they does not refer back to Alexander Graham Bell correctly. Choice (C) matches the pronouns correctly, but changes the meaning of the sentence, which refers to how Bell’s invention would go on to change the world in the future. Choice (D) does the best job of matching the pronoun and making it clear (by the addition of the phrase nor anyone else) that the sentence is meant to show that no one, including Bell, foresaw how his invention would change the world.

  4. A. dissolved into a debate over

    The sentence is correct the way it’s written, so Choice (A) is best. The idiomatic expression is debate over and the test always wants you to choose the most standard English language expression, even if other choices sound fine.

  5. C. to speak with

    Choice (C) is the only answer that uses a common English idiom, to speak with. Choices A, B, and D do not render the idiom correctly, and Choice (E) lacks the needed preposition.

  6. B. Because she was the first to arrive at the cabin,

    Choice (B) is the best, because the being construction shown in every other choice is wrong. Being is only properly used as a verb.

  7. A. Either the Pirates or the Orioles are the winners;

    The original sentence is correct, so Choice (A) is the best. When either … or is used with plural nouns, the verb in the sentence must match the noun closest to it. In this case, that’s Orioles, which is plural, making are the best choice. Choice (B) changes the meaning of the sentence.

  8. E. rather not

    Choice (E) presents the idiom correctly as commonly used in the English language. No other choice makes sense in the sentence.

  9. B. With a mountain forming the perfect backdrop, Adil went for a run yesterday morning.

    Choice (B) is the best of the sentence options offered, since it add a preposition (with) to make the phrase a mountain forming the perfect backdrop work as the introduction. The original sentence allows it to modify Adil, making him the mountain! Choice (D) is technically correct but is less streamlined than Choice (B).

  10. A. Who do you think is the better dancer,

    Choice (A) is correct because the sentence is correctly written. When the options are only two (Monique or Enrique) you must use the word better not best, which is reserved for three or more options. Choices C and D are written correctly but change the meaning of the sentence slightly.

  11. B. more effective than the exhaust fan in the second examination room.

    Of the choices provided, Choice (B) is the best. It clarifies that the comparison is between the exhaust fans in two examining rooms, whereas the original leaves it unclear as to what the second is referring to.

  12. E. Seeing her running to catch the train,

    Because you can only modify the first, underlined, part of the sentence, Choice (E) is the best. It makes clear that the people on the platform were watching Suzie, not running themselves.

  13. D. doesn’t quiet down

    Because of lacrosse players is a prepositional phrase, it is not the subject of the sentence. The subject is group which is singular and thus needs a singular form of the verb, which is only found in Choice (D). Choice (C) changes the meaning of the sentence.

  14. E. To say that Andrew likes ice cream is to understate the truth!

    Choice (E) is the best because it balances To claim with to understate, which is the error in the original sentence. The test makers are hoping that you will think the mistake is with the verb, so it offers a few choices in that realm in Choices B and C.

  15. B. to wait quietly by the door

    Never split an infinitive verb, which in this case is to wait. Only Choice (B) puts the adverb (quietly) after the verb phrase. It is the only correct choice.

  16. C. is the better ballplayer.

    Remember, when you have two nouns being compared (in this case, Juan and Almanzo) you can only choose the better of them. Three or more allows you to choose the best. With this rule in mind, only Choices C and D can be considered, and Choice (D) repeats unnecessary information with the addition of of the two of them. That makes Choice (C) the best.

  17. A. Xu wishes she could join us,

    Choice (A) is correct. The sentence is fine as it is.

  18. D. The dispute over who owned the land affected five generations of the Longfellow family.

    The popular idiom is the dispute over as in Choice (D). Notice that Choice (E) offers incorrect punctuation — there’s no need for a possessive — and Choice (C) misuses re: in a sentence.

  19. B. The cookies in my lunch are smaller than those in Justin’s lunch.

    The sentence as is presents a false comparison by comparing the cookies to Justin’s lunch. Choice (B) fixes this problem by comparing the two sets of cookies.

  20. E. On her first visit to Paris, Parah wanted to visit the Louvre, walk by the Seine and shop in the Latin Quarter.

    Balancing phrases with the same verb is the issue in this sentence. In the original, the last phrase (shopping in the Latin Quarter) doesn’t match the first two. You can see the problem if you put the sentence together without the first two phrases: On her first visit to Paris, Parah shopping in the Latin Quarter. Choice (E) is the only rewrite that makes sense.

  21. B. The girls and their coach eat together after the game.

    Choice (B) matches the verb eat to the subject The girls and their coach correctly. Remember that even though coach is a singular noun, it is combined with The girls with the conjunction and, making the subject plural.

  22. D. As we wandered through the trees, we saw spectacular scenery.

    The best answer is Choice (D), which re-words the sentence so that the subject is we. The original sentence implies that the scenery was wandering through the trees, which, of course, does not make sense. Only Choice (D) fixes the problem.

  23. A. The first and only person I thought of was you.

    The sentence is correct as written, so Choice (A) is right. The test-makers are hoping that you might remember the rule to always use the plural form of a verb with you. But in this case, the subject of the sentence is The first and only person so the verb must be the singular was.

  24. D. Belle, like many cows, eats a great deal of grass.

    This is a subject-verb matching question. It’s natural to match the word cows to the verb eat, but the subject of the verb is Belle, not cows. That makes Choice (D) the only correct answer.

  25. A. The McCutcheons or the Jacksons were

    The sentence is correct as written, so Choice (A) is appropriate. The subject is joined by the conjunction or, but both parts of the subject are plural, so the plural noun were is still correct.

  26. C. Either Brenda or Xiu might like to tell that story.

    The problem in the original sentence is that a plural verb, might likes, is paired with a singular subject in Either Brenda or Xiu. A simple way to tell what to do is to eliminate the names and consider Either on its own. It’s clearly singular and should get a singular verb. This makes Choice (C) the best.

  27. B. The audience was euphoric upon receiving their prizes.

    Choice (B) is correct because The audience is a collective noun. These are almost always treated as a singular noun on the test. Choice (D) seems like it could be correct because the sentence has been reworded. However, notice that they no longer clearly refers to the audience.

  28. E. Nobody wants more dessert.

    This the type of question the GMAT throws at you sometimes in hopes that utterly confusing you will make you guess wrong. Don’t fall for it! The sentence is incorrect, eliminating Choice (A), and the only fix for it is to change the verb to match a singular noun. That makes Choice (E) correct because it makes the verb wants. Choice (C) was close, but there’s no need to make dessert plural.

  29. C. after he stopped by.

    This is a verb tense agreement question. The problem with the original sentence is that the first verb gave is in past tense, while the second verb would stop is in conditional tense. The best fix is to make both verbs past tense, and Choice (C) does that.

  30. C. Dennis wanted to take Neil shopping for a birthday gift, but Neil wasn’t available on Tuesday.

    The original sentence has several pronoun errors: It’s not clear whose birthday gift they’re going shopping for, nor it is clear who isn’t available on Tuesday. While Choice (B) partially fixes this problem, Choice (C) is the best choice. It makes the sentence much more clear. Notice that Choice (D) and Choice (E) don’t eliminate the confusion but make it worse.

  31. A. Annie asked Bill if he would tell her the truth.

    The sentence is correct as written. Because the original sentence involves a man and a woman, the pronouns he and her are correct as written. While it’s possible that tell her the truth is referring to a woman who is not Annie, you can assume by the answer choices that this is not correct. All of the answer choices only involve Annie and Bill.

  32. D. Because it was sunny and warm that morning, Takeya couldn’t wait to get to the beach.

    The modifier of the original sentence, sunny and warm, needs to be properly placed. It’s a slightly confusing that either the beach or Takeya could be described as sunny and warm, so reading the other choices is necessary. That makes it clear that beach is being described making Choice (D) the best. Notice that while Choice (E) makes a simple, clear sentence, it isn’t logical: the beach isn’t sunny and warm because Takeya’s going to it!

  33. B. Jade was a weaver with a fine sense of color, so her throws were exquisite.

    Choice (B) fixes the problem in the original sentence: the adjectival phrase, a weaver with a fine sense of color, is modifying the throws instead of Jade. No other choice fixes this problem.

  34. A. I brought three things to work that morning: my lunch bag, my laptop, and a copy of the report.

    The sentence is correct as written, so Choice (A) is the best choice. Choice (E) is very close to being correct, but notice that it adds an unnecessary phrase (with me) that is already clear and does not need to be restated. Choice (C) similarly adds in an extra my which isn’t needed.

  35. C. In wonder, Richard stared at the polar bear, the large creature with snowy white hair.

    The original sentence has a misplaced adjectival phrase, making it seem that the large creature with snowy hair is Richard. Choice (C) fixes that problem and is the only choice to do so without adding in extra words as Choice (D) does.

  36. D. Choose from

    The idiomatic expression is Choose from, so even if other choices seem reasonable, Choice (D) is correct.

  37. B. The winner will be determined by

    The idiomatic expression is determined by. Choice (B) is thus the best choice. Notice that Choice (C) changes the meaning of the sentence.

  38. E. Rather than

    The standard idiomatic expression is Rather than, making Choice (E) the correct choice.

  39. C. We have to determine a winner between the two semi-finalists.

    The best answer is Choice (C) because it follows the grammatical rule than when the quantity in question is two (two semi-finalists) the correct phrasing is between. Choice (D) also uses between but needlessly complicates the rest of the sentence.

  40. D. The costumes for the musical are more elaborate than those of the musical last year.

    This is the rare instance in which making a sentence more wordy is correct. The problem with the original is that it compares The costumes for the musical with last year. Only Choice (D) makes it clear that the comparison is between two musicals.

  41. A. I’m trying to determine the better of the two routes suggested, because I want to find the best way to travel to Dublin.

    The original sentence, for all its complexity, is correct, so Choice (A) works well here. Remember that better is used when determining between two nouns, while best is used when there are more than two (including an indeterminate amount such as way).

  42. D. I prefer the second of the two flavors of ice cream more.

    Choice (D) is the only suggestion that correctly uses the grammatical rule. When only two things are being compared, the correct wording is more. Most can only be used when three or more things are being compared.

  43. A. Jim was the least entertaining at the party.

    To choose the correct answer, you have to infer that the party had more than two people. That seems a safe bet, which means that Jim could be the least entertaining person, not just the less entertaining person. So Choice (A) is correct. Choices (C) and (D) are correct sentences, but they slightly change the meaning in each case, making Choice (A) the best.

  44. A. A number of people stopped by my table to ask if I was OK

    The sentence is fine as it is, so Choice (A) is correct. A number of is the correct term for a countable group of people, and it’s safe to presume that in a restaurant, the speaker could count the number of people who stopped by. Notice that Choice (B) and (C) sound wrong — that’s not always a good hint on the GMAT, but in this case, it is.

  45. D. Much of the food was thrown out after five days,

    Choice (D) is the best choice. In the original sentence, Many of the food is incorrect. When the amount is uncountable, it’s grammatically correct to use Much instead, as Choice (D) does. While Choice (E) also makes this switch, after five days is also changed incorrectly.

  46. B. Bria gave Ebron fewer cookies than she gave Nadine.

    Choice (B) is the best of those offered. The original sentence misuses less cookies, which should be fewer cookies. Both Choice (B) and Choice (C) correct for this error, but Choice (C) is needlessly repetitive. That makes Choice (B) the best.

  47. A. It took me more time than I expected, but I was able to buy more towels at the sale.

    The sentence is correct as written, so there’s no need to make any changes. Choice (A) is correct. Don’t be fooled into not following your gut!

  48. B. It took Sally less time at the doctor than she expected, and she was able to buy fewer pills to complete her treatment.

    The key question here is whether there is an error in the original sentence and, if so, whether it’s in less time or less pills. If you remember that we use fewer when the amount is countable — as presumably pills would be — that makes Choice (B) clearly the correct one.

  49. C. Bob missed much of the discussion, and many of the key points.

    Choice (C) is the best choice, because it fixes the error in the original sentence. When writing about a countable amount (as in the key points), we use many of … not much of … Notice that Choice (B) is a correctly composed sentence, but it slightly changes the meaning of the original sentence. That makes Choice (C) the better choice.

  50. D. Ma started to pick her way carefully through the stones.

    Choice (D) is the best, because it fixes the error in the main sentence. That’s a split infinitive — to carefully pick. Choice (C) might have fooled you, but notice that it moved the adverb, carefully, to the wrong place.

  51. B. Too many people think they can start to complain angrily about the poor service after one mistake.

    The sentence is a mess, but the main error in the original version is the split infinitive: to angrily complain. Only Choice (B) fixes it by moving angrily to after the infinitive phrase.

  52. B. If Shelly were a nice person,

    This is a very tricky question. It makes use of the subjunctive mood verb tense. What you must remember about this sentence is that the subjunctive verb form of to be is always were even if the subject (Shelly) is singular. That makes Choice (B) correct. Choice (D) also employs were but changes the meaning of the sentence to nonsense.

  53. A. That’s my professor.

    There’s nothing wrong with this sentence. It uses a possessive correctly (That’s). That makes Choice (A) the best because it correctly replaces the missing letter with an apostrophe. Although it sounds very strange, Choice (E) could be considered grammatically correct, but it’s obviously not the best answer.

  54. E. I found its match in the pile of socks.

    Choice (E) is correct, because it fixes the apostrophe error in the original sentence. When using its as a possessive (that is, belong to it), there’s no need for an apostrophe. It’s not replacing a letter.

  55. A. but I know it’s just up the road.

    The sentence is correct as written. Choice (A) correctly uses an apostrophe in it’s because the word is replacing it is. Whether the meaning is that the destination is just up the road, or that the GPS is just up the road, the punctuation would remain the same.

  56. D. Because she’s the CEO, Maya likes to get to the construction site early.

    The error in the original sentence is the use of Being. Unless it is being used in a phrase like human being or state of being, it’s almost always incorrect. In Choice (D), that error is fixed by replacing Being with Because.

  57. D. because he was nervous about his wife’s delivery.

    Choice (D) fixes the incorrect use of being in the sentence. Choice (C) replaces the pronoun he with Johann, but that’s unnecessary. It’s clear in the sentence who he refers to.

  58. C. and hold a meeting with his staff.

    Choice (C) is the best answer. The original sentence doesn’t balance phrases: drop off and pick up are both verb phrases, and also a meeting is a noun phrase. It needs to be changed to a verb phrase as well, and the word also isn’t needed.

  59. B. Kate, like many vet technicians, works very long hours.

    The prepositional phrase like many vet technicians is meant to trip you up, since it is plural. But the subject of this sentence, Kate, is singular, and should be matched with a singular verb, as in Choice (B).

  60. D. I’m not sure why you were so upset by the phone call.

    The original question mismatches the subject, you, to the verb, was. You is always matched with a plural verb even when being used as a singular pronoun.

  61. B. the penguin wasn’t going to emerge to find its food again

    Choice (B) fixes the error in the sentence. The original uses it’s when its is correct.

  62. D. but David got bored and wanted to go home.

    The fixed sentence is less than ideal, but remember that on the test, you can only fix the underlined portion of the sentence. Given that constraint, Choice (D) is the best because it makes clear that he is referring to David.

  63. E. As he screamed for the goalie to block the net, Tom was escorted from the stadium by Security.

    Choice (E) is the best because it clarifies that Tom was escorted from the stadium while he screamed, while the original sentence implies that Security was screaming.

  64. A. If she were taller, Shakiya could have been a ballerina.

    The sentence, which is in that tricky subjective mood, is correct as written. We choose Choice (A) because it uses a plural verb, were, which is always correct with the subjective mood.

  65. E. but neither she nor anyone else realized her over was broken.

    Choice (E) fixes the main problem in the original sentence, which is that the pronoun they is unclear. By substituting neither she nor anyone else in attendance, Choice (E) makes clear who exactly did not realize her oven was broken.

  66. B. from the better of two schools’ offers

    Choice (B) fixes the error in the original sentence. Remember, you can only choose between the better of two options. And Choice (B) maintains the correct possessive form of schools from the original. Choice (E) needlessly adds in the word between.

  67. B. To say that Acadia National Park is a beautiful place is to understate the truth.

    Choice (B) fixes the error in the original, which is not balanced. It begins with a to statement: To say that … and thus needs to be balance with another to statement, as in to understate the truth!

  68. A. I asked Mo’chelle and her brothers to help with the fair.

    There is no error in the original sentence, so Choice (A) is the best. It’s typical for sentences that are completely correct to appear as if they must have errors after working on questions like these. Stay focused!

  69. D. I was the last to leave the testing center.

    The original sentence contains a subject/verb agreement error, because I should not be paired with were. Choice (D) fixes this mistake.

  70. E. The clowns, even Dani, were not the children’s favorite act.

    Choice (E) fixes the error in the original sentence. The clowns is plural, but the verb in the sentence is was, which is singular. The correct choice is were. Remember that even Dani is a phrase, not the subject of the sentence.

  71. A. Despite Elsie’s reluctance, her family is asking for donations.

    There’s no error in the original sentence. The use of the phrase her family makes clear how the subject is connected to the introductory phrase Despite Elsie’s reluctance. Choice (A) is best.

  72. B. You lift me up as a class.

    The key issue here is matching the subject, You, with the correct verb. In Choice (B), You is correctly treated as a plural verb, which makes it the best choice. There’s no need to alter anything else in the sentence as in Choice (D).

  73. D. Either Renee or Todd will take you

    Choice (D) is the best offered here because it fixes the subject/verb agreement issue. Remember Either always makes the noun singular, so it must be used with will take.

  74. C. Nobody wants to go to that club again.

    Choice (C) correct fixes the subject/verb agreement problem in the original sentence. Nobody is a singular, collective pronoun and must be matched with wants.

  75. B. Everybody loves music.

    Choice (B) corrects the mistaken subject/verb agreement to Everybody loves. Everybody is a singular, collective noun. Note that Choice (D) is a correctly composed sentence but does not have quite the same meaning as the original.

  76. E. We will play when the field is dry,

    Choice (E) is the only one here that correctly fixes the subject/verb agreement error. We, which is plural, should be matched with will play.

  77. B. after I learned the basics in high school.

    The original cannot be correct because learning in high school must have come before learning in college chronologically. The conditional tense (would learn) cannot be paired with the past tense (learned). Choice (B) fixes this error.

  78. A. Ida fixed Bruce’s bike chain after he asked her to help.

    Choice (A) is correct because there aren’t any errors in the sentence. Both verbs — fixed and asked — are in past tense.

  79. A. I should be the last person you ask.

    Choice (A) is correct. There’s no need to change anything in the sentence. While Choices (D) and (E) are both acceptable sentences, they slightly change the meaning of the original and are thus incorrect.

  80. A. I asked Miguel if Lilly would be late.

    There’s no error in the original sentence. Choice (A) is therefore correct. Choice (B) might seem like the better choice, but do make sure to read the entire sentence: late has been changed to later.

  81. D. after extensively researching vampires, publishing several other books, and crafting several early drafts.

    Choice (D) fixes the parallelism error of the original sentence. While after extensively researching vampires and publishing several other books are both verb phrases, and also several early drafts is a noun phrase. Choice (D) changes it to a verb phrase.

  82. E. subject to her availability.

    Choice (E) is the best sentence. The common idiom is subject to, and that is what the test-makers are looking for you to know.

  83. B. As great as the diner’s breakfast is,

    Choice (B) correctly renders the idiomatic phrase, As great as so it is the best choice. Notice that Choice (D) and (E) can be eliminated because they do not include the proper punctuation.

  84. A. Because he is in danger of failing, Gomez went to tutoring.

    The original sentence renders the idiomatic phrase in danger of correctly. Choice (A) is correct.

  85. C. This argument is different from what we’ve seen before.

    Choice (C) correctly places the idiomatic expression different from in the sentence.

  86. D. Western Pennsylvania is usually defined as Pittsburgh and further west.

    Choice (D) correctly uses the idiomatic expression defined as in the sentence.

  87. B. Gretel and I agreed that the pink bubble tea tasted better than the blue bubble tea tasted.

    Choice (B) is the best because it matched the comparison in a correct parallelism. The phrase the pink bubble tea tasted must not be matched to just the blue bubble tea but to the blue bubble tea tasted.

  88. A. were prohibited from diving.

    There aren’t any errors in the original sentence, so Choice (A) is correct. The common phrase is prohibited from.

  89. C. were larger than the eggs gathered in the other coop.

    The original sentence has a false comparison. It compares The eggs to the other coop. Choice (C) fixes this problem by making it clear that The eggs are being compared to the eggs gathered in the other coop.

  90. D. rather than going out to eat.

    The correct idiomatic expression is rather than, and only Choice (D) uses it.

  91. E. Marie wanted to circle the block slowly until we found a parking spot.

    The original sentence splits the infinitive phrase to circle by inserting an adverb, slowly. Only Choice (E) fixes the error in a sentence that is grammatically correct.

  92. A. George Washington had to choose the better of two men when selecting a personal secretary.

    The sentence is correct as written, so Choice (A) is the best choice. Remember that when selecting between two choices, better is the correct word.

  93. D. That’s the worst of it.

    The sentence incorrectly uses worse. Because of it implies more than two — or an uncountable number — worst is the correct choice, as found in Choice (D).

  94. C. was the least interesting.

    Choice (C) is best because the three movies are compared in the original sentence. When three or more things are compared, it’s appropriate to use least. Do note that Choice (E) makes a false comparison because it doesn’t complete the idea of what the last movie is being compared to, while Choice (D) makes a correct sentence but changes the meaning.

  95. A. Many more people signed up for the class than I expected.

    There is no error in the original sentence, so Choice (A) is correct. When writing about a countable number, the use of many is correct, and it can be assumed that the number of people who signed up for the class is countable. Note that Choice (E) is an acceptable sentence but does not convey the same meaning as the original.

  96. B. a number of times.

    When the amount is countable — as we can presume the physician asking the family was, it’s proper to use the word amount. That makes Choice (B) correct. Quantity and amount are for non-countable things.

  97. B. because of his many achievements.

    The error in the underlined phrase is not the appearance of a lot, which is so controversial that the GMAT will never present it as a usage error, but in awkwardness of the phrase. Choice (B) is simpler and much more elegant. Remember that Washington’s achievements are countable, so many is used.

  98. E. I saw the play you’re talking about.

    The error in the original sentence is easy to spot: seen had been substituted for saw. That makes Choice (E) the correct one. Don’t be thrown off by Choice (D), which “fixes” a prepositional mistake which is not always considered an error anymore.

  99. A. The squirrel dropped its birdseed when we startled it.

    The original sentence is correct, so Choice (A) is the best. The use of its without an apostrophe is correct because it is a possessive, not replacing it is.

  100. E. It takes a long time to walk Hadrian’s Wall, but it’s worth it.

    The error in the original sentence is the substitution of its when it’s is needed. Choice (E) fixes the error. Remember that it’s, with the apostrophe, is the correct substitute for it is.

  101. C. It’s about time that Carolyn realizes it’s dangerous.

    Choice (C) makes clear that both it’s in the sentence are substituting for it is and thus should have an apostrophe. The easiest way to figure this out is to substitute it is into the sentence. In this case, it would read: It is about time that Carolyn realizes it is dangerous, which is correct.

  102. E. Given that he was the only nominee, it’s not surprising

    The error in the original sentence is not with its use of it’s, but in the use of Being, which is almost never correct. Choice (E) fixes this error. Notice that Choice (D) doesn't make sense — the word although doesn’t work with it’s not surprising.

  103. B. From what we could see, Jill’s team lost points for lack of originality, not being on the beat, and starting too late.

    Choice (B) best fixes the parallelism problem in the original sentence by changing they weren’t on the beat to not being on the beat so that the phrases match.

  104. C. The pipes hiss when water runs through them.

    The original sentence has an error in how the subject, pipes, matches with the verb, hisses. Only Choice (C) fixes this error. Notice that Choice (B) is a correct sentence but changes the meaning of the original, which involved pipes, not one pipe.

  105. A. They are her best friends

    You may feel that the second part of the sentence, despite all of the fights the four of them had had over the years they’ve known each other is poorly written — and we wouldn’t disagree — but there are no errors in the first part, so Choice (A) works best! Notice that the comma is not underlined, so its placement, whether correct or not, cannot be part of the solution to the problem.

  106. D. Carlos, like many science teachers, explains evolution very clearly.

    Despite how the answer choices may mislead you, the problem in this sentence is in the subject/verb agreement. The subject is Carlos, and that must be matched with explains. Choice (D) does this correctly. That the subject ends in –s and that the sentence includes a plural phrase, like most science teachers, doesn’t change the answer.

  107. B. You, despite the other qualified candidate, are my first pick for the job.

    Choice (B) is correct. You is always matched with a plural verb. Notice that while Choice (E) does so, it also uses the word candidates, although the original sentence mentions only one candidate.

  108. B. Beverley’s choice is the green; Mindy chose the gold.

    Choice (B) best fixes the error in the original sentence, which substitutes a comma for a semi-colon. Semi-colons are used when two sentences that could stand independently are linked together.

  109. C. Penelope, as is the case with many researchers, loves the library.

    There’s most likely an even better way to phrase this sentence, but of the choices offered here, Choice (C) is the best. It matches the subject of the sentence, Penelope, to the verb, loves, correctly. Notice that while Choice (E) is a correctly formed sentence, it changes the meaning of the original, making it not entirely clear that Penelope is a researcher herself.

  110. B. either Susan or Daveed decides to perform the surgery.

    The use of either in the original sentence means that the subject is rendered singular, and the verb must agree with a singular noun. Thus, Choice (B) is the best, with the verb decides.

  111. D. Nobody understands the directions, so please go over them again.

    Choice (D) is the best. Remember that a collective noun like nobody is almost always (and always on the GMAT) treated as a singular noun.

  112. C. Monica sent Rachel an invitation before Rachel complained about it.

    Choice (C) best reconciles the unmatched verbs in the original sentence, sent, which is past tense, and would be complaining, which is in the conditional tense. Choice (C) puts both verbs in the past tense with sent and would complain.

  113. B. Despite trying everything she could, Dr. Geller could not save the patient.

    The original sentence features a misplaced modifier: Despite trying everything she could should modify Dr. Geller, not the patient. Choice (B) is the only option that fixes this effectively.

  114. D. Despite being an astronaut with seven missions under her belt, Rhonda still felt excited about the next one.

    Choice (D) best fixes the misplaced adjectival phrase in the original sentence, which implies that An astronaut with seven missions under her belt describes the next mission, not Rhonda.

  115. B. Before swimming the require laps, the team enjoyed a hearty breakfast.

    In the original sentence, a misplaced participial phrase means that Before swimming the required laps, is modifying a hearty breakfast. Choice (B) fixes the error so that the phrase correctly modifies the team.

  116. A. That old man is acting like a child!

    Choice (A) is correct. This sentence preys on uneasiness about whether to use like or as. Remember that when two things are compared (man to child), the best choice is like.

  117. B. Not everyone can learn to bake the way my mom does.

    In the original sentence, the sentiment is expressed in the way we commonly speak. But to be grammatically correct, the sentence cannot include like because there is a verb after the words my mom.

  118. E. The campsite appeared welcoming to the sad and scared hikers.

    Choice (E) fixes the misplaced adjectives in the original sentence, making it clear that sad and scared modify the hikers, not the campsite.

  119. B. known for her use of color, strong lines, and collage in her work.

    The original sentence fails to use parallelism correctly in the three phrases. Choice (B) best fixes this error, correcting she uses collage in her work to collage in her work. This makes all three phrases match.

  120. A. Ricardo is required to design products, create mock-ups for review, and approve the samples for production.

    There are no errors in the original sentence so Choice (A) is best. Notice that while Choices (D) and (E) are tempting, Choice (D) misplaces the phrase for production, while Choice (E) incorporates a parallelism mistake.

  121. E. To say that Ronald was an excellent dad is to give credit where it is due.

    Choice (E) best fixes the error in the original sentence, which fails to balance the phrases in a parallelism structure. To say must be balanced with to give credit.

  122. B. rather than the Steelers.

    Choice (B) uses the idiomatic expression rather than correctly, so it is the best choice.

  123. A. The race course will be defined as

    The sentence renders the idiomatic phrase, defined by, correctly, so Choice (A) is correct.

  124. D. I can conclude from your expression that your team won.

    The idiomatic phrase is conclude from, so Choice (D) is the best.

  125. E. A debate over

    Choice (E) renders the idiomatic expression A debate over correctly, so it is the best choice.

  126. D. prohibit them from

    Choice (D) is the only option that correctly renders the common phrase prohibit them from, making it the correct answer.

  127. A. The play that has always been attributed to

    The original sentence correctly uses the idiomatic expression attributed to, so Choice (A) should be chosen.

  128. D. The entrée was different than what I expected

    The original sentence contains an idiomatic expression error. The correct expression is different than not different by. Choice (D) fixes this mistake. Choice (E) forms a correct sentence, but the meaning is changed with the phrase than what I expected is dropped.

  129. C. As great as Brooklyn is, Benji prefers Pittsburgh.

    The idiomatic expression is as great as, and only Choice (C) uses it correctly.

  130. D. Dr. Huardo felt the results were the best she’s seen

    The error in the sentence is in the better, which is only used when comparing two items. Since the experiment has been performed for 8 years, we can assume that more than two results are being compared, and we can use the best she’s seen construction, which you’ll only find in Choice (D).

  131. B. Between the two of us,

    Choice (B) is the best choice because the correct phrasing is Between the two of us. When speaking of two items, we use the between construction instead of the among construction.

  132. C. The reports have been printed for over a week, at least.

    The idiomatic expression is at least, which is correctly used in Choice (C), making it the best answer.

  133. E. The recommendations from the customer service department are more helpful than those from the human resources department.

    The original sentence contains a false comparison by comparing The recommendations from the customer service department to the human resources department. Choice (E) fixes this error by adding in the clarifying phrase those from.

  134. C. It’s easy to find the answer when you’re looking for it.

    The original sentence contains a mistake in Its, which is substituting for It is and thus should have an apostrophe. Choice (C) fixes the mistake without changing the correct you’re to the incorrect your.

  135. E. Liu was forced to agree that the cars traveled more quickly on the highway than the buses traveled.

    The flaw with the original sentence is a false comparison: the cars traveled more quickly is compared to the buses. Choice (E) makes it clear that the buses traveled. It’s the best choice.

  136. D. They’re the ones asking for a replay.

    The error in the original sentence is replacing They’re with Their. Choice (D) fixes the problem. Remember that they’re = they are.

  137. E. Most orchid growers obsessively worry over their plants.

    The error in the original sentence is in the misplacement of an adverb, obsessively. It should not split the phrase worry over. There’s no problem in using Most, so Choice (E) is the best fix.

  138. A. A number of laptops were missing from the cart,

    The sentence is correct as written, so Choice (A) is best. When writing about a countable number — and presumably the laptops that were missing is a countable number — it is correct to use A number instead of An amount or A quantity.

  139. B. Jovan applied to five colleges and now has to choose between two of them.

    Choice (B) is the best answer. The original sentence uses among when between is the correct choice, as it is used for when two things are being compared.

  140. A. Much of the project was scrapped, but our division kept all of the blueprints.

    There is no error in the original sentence. It’s correct to use Much in this context, when the number is not countable. The project is not a countable number. Choice (A) is the best.

  141. C. We saw less of an increase than we were expecting after the new logo was unveiled.

    Choice (C) is the best here because it uses the wording less of an increase, which is correct for an uncountable number. Notice that while Choice (D) is a correctly worded sentence, it changes the original sentence’s meaning. Far less of an increase is not the same as a decrease.

  142. A. The drive took less time than Maddie expected, so she arrived early for the meeting.

    Choice (A) is correct. The sentence does not have any errors: less time is the correct phrasing.

  143. D. You did not take time to read the instructions carefully

    The original sentence splits the infinitive to read with the adverb carefully. Choice (D) fixes that error.

  144. B. If Jim were a nice guy, he would have asked for forgiveness.

    The sentence uses the subjunctive mood, expressing something that the writer wishes was true, but is not. In that tense, the verb is always were, even if the subject is singular, like Jim. Choice (B) is the only one that renders that correctly.

  145. E. The shopping trip took Tony and Deven less time than they expected, but they ended up buying fewer shoes at the sale.

    Choice (E) is the only one available that fixes the error at the end of the sentence. When writing about a countable number (such as shoes), it’s correct to use fewer, not less.

  146. C. Delores called the theater to complain angrily about the audio problems

    There are several issues with this sentence, but in the underlined portion, the biggest error is splitting the infinitive to complain with angrily. Choice (C) fixes this mistake.

  147. A. The cow chewed through its rope

    The original sentence correctly spells through, as well as uses the possessive form of its. It’s would only be used if substituting for it is. Thus, Choice (A) is correct.

  148. D. Helen, the most affluent of my friends, gives lavish gifts.

    The original sentence involves a subject-verb agreement error, since the subject of the sentence is Helen (not friends). Choice (D) fixes the verb to gives which correctly matches Helen.

  149. D. After selecting Joseph, John, and Marni to lead the project, Sam regretted choosing John.

    The original sentence contains a pronoun error: It’s unclear whether Sam regretted choosing Joseph or John. Choice (D) clarifies which him is meant. Notice that while Choices (B), (C) and (D) all form correct sentences, they slightly change the meaning of the original and thus cannot be the best choice.

  150. B. I didn’t like the colors offered, but I had to pick one, so I chose it.

    Choice (B) is the best of the answer choices offered. It correctly uses the pronoun it as a substitute for one of the colors. The error in the original sentence is to replace that phrase with them.

  151. C. Because they were excited and happy, the soon-to-be graduates were not deterred by the gloomy day.

    The original sentence contains a misplaced set of adjectives, Excited and happy. The way the sentence is worded makes it appear that the gloomy day is also excited and happy. Reorganizing the sentence and making the subject the soon-to-be graduates appear shortly after the adjectives solves this problem. Choice (C) does that.

  152. E. As a nurse with a background in chemistry, Becca easily understood the patient’s records.

    The original sentence has a misplaced adjectival phrase. A nurse with a background in chemistry modifies Becca, but appears to be connected to the patient’s records in the original. Choice (E) rewords the sentence to be clearer, so it is correct.

  153. E. Having prepared the lunch, Jean left for the picnic.

    Choice (E) best fixes the mistake in the original, a participial phrase that’s misplaced. Before leaving for the picnic modifies Jean, not the lunch.

  154. A. The skills we’re looking for in our new hire are excellent customer service experience, a willingness to brainstorm, and a background in finance.

    Choice (A) is the best because there aren’t any errors in the original sentence. It balances the parallelism correctly, since all three phrases are nouns. Notice that while Choice (E) also forms a complete sentence, it changes the meaning of the original, so it cannot be the correct choice.

  155. C. Dax, an outstanding researcher, often takes his staff to lunch, gives plenty of vacation days, and is sure to remember birthdays as well.

    The original sentence contains an error in parallelism: Two of the phrases (often takes his staff to lunch, gives plenty of vacation days) are verb phrases, while he is sure to remember birthdays is a noun phase with the subject he. Choice (C) fixes this error by making all three verb phrases, so they are parallel.

  156. B. If you are in danger of failing,

    The original sentence does not correctly use a common idiom, in danger of. Choice (B) fixes that error.

  157. A. We can conclude from the results

    The original sentence is correct: The idiom is conclude from. Thus, Choice (A) is best.

  158. D. The statistics appear to

    The original sentence does not use an idiom correctly. It is common to write appear to, which is what Choice (D) offers. Thus, it is correct.

  159. D. because of the regulations.

    Only Choice (D) uses the correct idiomatic expression: because of. Thus, it is correct.

  160. B. to contribute to the discussion.

    Choice (B) uses the idiomatic expression contribute to correctly, which makes it the best choice.

  161. D. The temperature in Austin is higher than the temperature in Dallas today.

    This is a false comparison question. In the original sentence, The temperature in Austin is falsely compare to in Dallas. Choice (D) fixes the sentence so that The temperature in Austin is compared to the temperature in Dallas. The comparison is no longer false.

  162. A. The questions on the GMAT are more challenging than the questions on the SAT.

    The original sentence correctly uses a comparison by comparing The questions on the GMAT and the questions on the SAT. Thus, Choice (A) is best, since no changes are needed.

  163. D. We don’t know yet if it’s a boy or a girl.

    The original sentence contains its, which is used incorrectly. When replacing it is, use the version with an apostrophe: it’s. Choice (D) does this without making any other changes, so it is correct.

  164. E. The penguins swim more gracefully than the polar bears swim.

    The original sentence contains a false comparison: How the penguins swim is compared to the polar bears. In Choice (E), the comparison is corrected so that how each animal swims is compared. It’s the best choice.

  165. A. Think of your assignment as an opportunity,

    The original sentence uses the common idiom construction Think of … as correctly, so it does not need to be changed. Choice (A) is best.

  166. C. To admit you’ve erred is to admit you’re human.

    The original sentence contains a parallelism error. The phrase To admit you’ve erred requires another to … phrase to balance the sentence. Only Choice (C) does so.

  167. B. Anna carefully tried to pick her way through the glass shards.

    Choice (B) fixes the error in the original sentence: a split infinitive. To pick should not be split by the adverb carefully.

  168. A. To begin paying quickly,

    In this case, the infinitive — To begin paying — is not split by an adverb because quickly appears after it in the sentence. This is correct, so Choice (A) is also correct.

  169. D. Mary and Rick took Takeya and Leroy to the store, but Leroy didn't want to buy anything.

    Choice (D) best fixes the error in the original sentence, which is the unclear use of the pronoun he. It could refer to Leroy or Rick in the original. Choice (D) shows that Leroy is meant. Don’t be fooled by the fact that Choice (B), Choice (C) and Choice (E) form what appear to be correct sentence: They change the meaning of the original.

  170. D. As he yelled that even he could see that the ball was fair, Bobby was taken away from the stadium by Mom.

    In the original sentence, the phrase Yelling that even he could see that the ball was fair is misplaced because it appears to modify Mom, not Bobby. Choice (D) fixes the mistake.

  171. D. gasps when the curtain rises

    Remember that collective nouns like the audience are almost always treated as singular. The original sentence does not do that, but Choice (D) does. Notice, too, that there is no error in the curtain rises.

  172. E. Despite our invitation, you seem surprised

    Remember that you is always treated as a plural noun, even when referring to one person. Thus, it should be paired with seem. Choice (D) forms a correct sentence, but changed the verb to the past tense, which is not in line with the original. Choice (E) is the best choice.

  173. B. works long hours.

    Choice (B) best fixes the issue in the original sentence, which mistakes the subject as nurses. In fact, the subject is Mitchell, which needs the verb works.

  174. C. and reschedule her visit to her dentist.

    Choice (C) best fixes the parallelism error in the original sentence: buy a wedding gift and resole her dancing shoes are both verb phrases, while and the visit to her dentist needs to be rescheduled is a noun phrase. You can’t change the first two because they are not underlined, so you’re left fixing the last phrase. Choice (E) is tempting, but doesn’t convey the idea needs to be rescheduled.

  175. E. to wait quietly by the door before entering

    The complicated sentence structure should not fool you into failing to notice the split infinitive: to quietly wait. Fixing it, as in Choice (E) means moving the adverb to after the phrase: to wait quietly.

  176. A. This is its cage, but it’s hiding.

    There’s no error in the sentence. The first its is correctly possessive: The cage belongs to it. The second it’s replaces it is. Thus Choice (A) is correct.

  177. B. Fewer classmates came to the show

    Choice (B) is correct because we use fewer when considering a countable number of classmates. Since the rest of the sentence tells you that it was a class of 10, it seems reasonable that Roberto would be able to count the number of classmates exactly.

  178. D. If I were younger,

    Remember that when a sentence employs the subjunctive mood, expressing something that the speaker or writer wishes were true but is not, we always use the were form of the verb to be, even if only one person makes up the subject. Thus, Choice (B) is correct.

  179. D. Between you and me,

    The original sentence uses among when between is the correct choice for a sentence that compares two things. Choice (D) is correct. By the way, Between you and I is not how the idiomatic phrase is correctly rendered.

Chapter 7

  1. E. It introduces a premise that the argument goes on to oppose.

    The bolded portion of the passage is a premise that the rest of the argument goes on to contradict, or prove wrong. Only Choice (E) shows itself as a premise, and must be the correct answer.

  2. E. Autopsies of coyotes killed by cars or found in dead in Keystone State Park revealed that nearly all of them had recently consumed deer meat.

    Choice (E) is the best answer because the evidence it reveals helps to support the idea that coyotes have contributed the decline of the deer population in the park. Choice (A) merely restates the argument, while Choice (D) argues against it.

  3. B. Two years ago, a dip in home mortgages dropped inflation temporarily below its stable level of 2% in recent years.

    In order to weaken the conclusion in the argument, you have to find a reason for it to not be, or come, true. Choice (B) does that the best here because it provides information that indicates the rate of inflation from two years ago was a one-time blip, and that inflation has already returned to as steady rate of 2% per year.

  4. B. In two years’ time, the inflation rate will be higher than 4%.

    This question is tricky because it’s asking you nearly the reverse of the question before it. You must throw out the arguments made in that question and look only at the initial reading passage. If you do so, you’ll see that if the passage is true, it must also be true that the inflation rate will rise to greater than 4% in two years’ time, which is Choice (B). There’s nothing in the argument that suggests the rate of inflation, which eliminates Choices (A) and (C). While Choices (D) and (E) might seem to intuitively true, we don’t have proof of them from the initial passage.

  5. D. Taking a protein supplement has been shown to hurt, not improve, memory.

    The question asks you to find the reason that will weaken Ryan’s chance of success. Only Choice (D) does that. While Choice (C) is not likely to earn him that 4.0, which Choice (E) says he wants, neither of these weaken his likelihood of success. Choice (A) might, but we don’t learn if he prefers to study in the library. In Choice (B), we see a possible reason why his plan might now work, but we are not given enough information. Choice (C) is a bad habit, but Choice (D) shows a direct contradiction to his plan: He plans to take a protein supplement in order to help him improve his grades, but if Choice (D) is true, it’s clear that they may not help, and, in fact, hurt his plan.

  6. C. Ryan’s Physician’s Assistant suggested the protein supplement based on her observation of its success for other student-athletes at Ryan’s college.

    The best answer is Choice (C) because it provides evidence from a medical professional that a similar plan has recently worked for students very like Ryan.

  7. A. It’s possible to bottle milk without preservatives in a way that still makes it safe to drink.

    If everything in the argument is true, then Choice (A) must be inferred. A dairy that has eliminated preservatives must have found a way to bottle milk without them. The other choices are either a leap in logic that are not supported by the argument, as in Choices (B) and (C), or restate elements of the argument, as in Choice (D), or are simply too broad to be inferred from the argument, as in Choice (E).

  8. C. Several stores will no longer carry Lange Farm milk because customers have returned too many bottles in which the milk spoiled several days before the “Sell by” date stamped on the lid.

    The basic premise of the argument is that Lange Farms says that their milk will be good and tasty for at least a week after it is bottled. Choice (C) shows that they have not been able to guarantee that their milk will not spoil without preservatives. It is thus the best choice.

  9. B. There are no advantages to buying stamps at a shop instead of a post office.

    The argument states that the people of the town are making an odd choice. In order to make that argument, it must be assumed that there are no advantages to buying stamps at a shop instead of post office, which is Choice (C). Choice (D) is a good reason to argue against the premise, but that’s not what the question asks you to do.

  10. A. What reason do the citizens of Bohlburg give when asked why they prefer to buy stamps in shops instead of the post office?

    The conclusion that must be supported is that it’s odd for the people of Bohlburg to buy their stamps at shops instead of the post office. The only question that will provide helpful information is Choice (A) because it directly asks why this is so. The other choices make assumptions about why people don't go to the post office — because of the distance or because certain products aren’t offered there — but without input from the people of the town, these are not justified assumptions.

  11. C. The company’s workforce in Country X can be paid 15% less than the anticipated workforce in Country Y.

    Choice (C) is best because it shows the financial logic that could justify remaining in Country X. While Choice (A) and Choice (D) might be important to the company, these are not logical reasons to stay in Country X. Choice (B) has no merit since the company exports its product, and Choice (E) is helpful but not a better reason than Choice (C).

  12. C. The 5% tariff will increase by 1% every year until it reaches 10%, at which point, it will surpass the company’s savings on workforce cost by remaining in Country X.

    In a question like this one, it’s worth your time to seek out the answer that most directly addresses the premise of the statement. Choice (C) does that here, but taking the one number in the question — 5% — and building on it to create a scenario in which the company would be foolish to stay. All the other answer choices are far too vague to be correct.

  13. C. Pineapples grow in a three-year cycle, in which one heavy harvest is followed by two less abundant harvests.

    The question asks you to support the argument that farmers should hold back a portion of an over-abundant harvest. Choice (C) best supports that particular line of logic by showing that any given pineapple farmer is sure to have two years of lean harvests after a flush one. Holding back the plentiful harvest will even out their supply.

  14. A. Pineapples can be kept in refrigerated warehouses for a month to six weeks at maximum.

    The question asks you to weaken the conclusion presented. To do that, you’ll need to find the argument that presents the best roadblock to the idea of keeping extra pineapples in refrigerated warehouses to drive up the price. Choice (A), if true, shows that this plan is not likely to work because the pineapples will spoil. It is the best answer.

  15. E. Stabilizing the riverbank in the area that belongs to J & B Warehouse would help to counteract the yearly floods.

    The concern here is not why the flooding is happening, but why the town of Bettyville has decided to pursue litigation against J & B Warehouse for their role in the flooding. Choice (E) best suggests an assumption that must have been made: J & B Warehouse is particularly culpable for the flooding and their property must be stabilized.

  16. D. Jen has been served that brand of soda at her favorite restaurant for years without realizing that she was consuming it, and has never felt sick afterwards.

    Choice (D) most weakens Jen’s argument, which is that the brand of soda makes her feel sick. If she was correct, she should feel ill after consuming the soda whether she knows she is doing so or not. Choice (D) shows that this is not the case.

  17. D. “Come to think of it, in my journal, I noted that you often complained of a stomachache after we ate at restaurants that served you that brand of soda.”

    Dialogue questions, while a little strange, do occasionally appear on the GMAT. Here, you need to think of finding the best evidence to support Jen’s assumption. Vic offers her own evidence, as in Choice (D), that strengthens Jen’s assumption. That’s the best choice.

  18. B. It is a premise that will be proven by the rest of the argument.

    The bolded portion of the passage is a premise that the rest of the argument goes on to prove. That means that Choice (B) must be correct. Notice that it cannot be the evidence, since it does not provide any. It must be a premise or idea.

  19. C. The news channel based its conclusion on only 3 percent of registered voters’ responses.

    Here, you’re asked to find the most significant mistake in the news channel’s logic — in other words, where did they most go wrong with their prediction? Choice (C) is the best answer because it reminds us that the news channel polled a very small portion of registered voters. Choice (B) is a mistake as well, but less important than the extrapolating a town-wide result from 3 percent of its population.

  20. B. It provides evidence to support a premise of the argument.

    The bolded portion of the passage is evidence that supports the premise of the argument. The news channel’s argument was that Stewin would win, premised on the poll results. Therefore, the registered voters polled provided evidence to support that premise. That’s Choice (B). Notice that this is true even if the argument is wrong or flawed: The news channel was incorrect, but its argument was supported by a premise and evidence.

  21. C. A recent Twitter survey of local people shows that they report finding Hitchjaw eels more disgusting than snakes or rats.

    The best choice is Choice (C). The argument presented in the reading is that the zoologist thinks local people won’t help to save the Hitchjaw eel because they find it off-putting. Choice (C) give evidence to support that idea, in showing that people do, indeed, find them disgusting.

  22. B. Recent efforts by locals have helped stabilize the population of long-eared rats, a deeply disliked local pest.

    The premise of the argument is that people haven’t helped to save the Hitchjaw eel because they don’t like them. Choice (B) points to a recent effort by locals to preserve another animal that they don’t like, which argues against their logic in the passage. It best disproves the passage.

  23. A. The zoologist should start a campaign to help people understand and grow to admire Hitchjaw eels.

    The conclusion must logically flow from the argument presented. Here, the zoologist has concluded that people won’t help animals that they find off-putting. However, if he was able to convince people that Hitchjaw eels are not off-putting — as in Choice (A) — public interest might turn toward helping them. That makes Choice (A) the best choice. Notice that Choice (C) is essentially restating the zoologist’s conclusion in the passage.

  24. E… . accept the gift card from Danielle and wait for the white paint to go on sale or to be able to pay an additional $10 for it.

    In this question, the GMAT test-makers hope that you’ll get confused by the choices. But the premise of the argument is clear: Lucy can’t spend more than $30. If that is true, only Choice (E) is a logical choice because it recognizes that premise. Choice (A) might seem like a good choice, but the other premise of the argument is that Lucy wants to paint her kitchen white and it is in no way indicated that that premise is less important.

  25. E. Luis’s neck brace will be removed next week, and he will be able to resume his training schedule without further delay.

    In this question, test-takers must find a premise that would help the argument make sense. In this case, Choice (E) does that because it provides an explanation that directly shows how Luis could still be the favorite. Choices (A) and (C) hint toward other reasons why he would be, but they are not as clear or convincing as Choice (E).

  26. C. The local newspaper that made the prediction that Luis would win the annual city marathon is unaware of his injury.

    The best way to weaken this argument is to attack the conclusion that Luis will win. If it can be shown, as in Choice (C), that the prediction is not based on a full understanding of Luis’ situation, that would seriously weaken the conclusion. It is the correct choice.

  27. D. The vegetable distributor principally ships to vegetable juice production companies that have no use for the leafy green tops.

    To improve profits is the ultimate goal of the logic in the passage. In order to achieve that goal, only Choice (D) is helpful, providing a clear reason why eliminating the leafy green tops of the carrots would be helpful to the company buying the most carrots.

  28. A. Many customers prefer to buy carrots with their leafy green tops, which can be used in cooking.

    The question asks you to find the evidence that would most weaken the plan to cut the leafy green tops off of carrots before selling them. Choice (A) does that the best by providing evidence that carrots without their leafy green tops would be less desirable to many consumers.

  29. D. Because of the extreme stress of the testing process, any windbreaker design that has more than two-thirds of its prototypes functional at the end of the tests is considered sufficiently durable for the consumer market.

    The company’s decision is based on logic that is not clear to readers. Choice (D) best provides an explanation that shows why the company decided to put the windbreaker on sale. If the test process is so extreme that it is typical for one-third of the products tested to be ruined, that only 20 windbreakers were ruined shows this product to be superior to the average.

  30. E. Consumers often prefer to buy windbreakers that have scored much better in the tests described.

    To weaken the logic behind the company’s plan to put their windbreakers on sale despite the poor test results, it must be shown that those test results can weaken the potential sales. Only Choice (E) does that by showing that potential customers may be reluctant to buy windbreakers which have not scored well on such tests.

  31. D. The other newspaper in city, the Dubsville Tribune, also reported a similar spate of complaints from their readers in the same month.

    That another newspaper in the same city experienced a similar drop in subscriptions at the same time best supports the newspaper’s case, so Choice (D) is best. Keep in mind that you may find the newspaper’s case dubious, but you’re asked to complete its logic, not attack the premises.

  32. C. Dirk: You know as well as I have that we’ve eaten here every Saturday night for years, and usually there are twice as many employees working.

    You want to complete the dialogue in a way that proves Dirk’s point as logically as possible. If he has prior evidence that the restaurants is frequently busy on Saturday nights and usually has more staff at work, his case that they can plan for a particularly busy night is stronger. That's Choice (C).

  33. B. We’ve eaten here before on a Saturday night at this time and been the only customers!

    You want to improve Ellen’s logic. Choice (B) does this best, by offering evidence that proves her thesis: that there is no way to predict how many people will visit the restaurant on a given Saturday night.

  34. D. A house built on a concrete foundation will definitely survive a tornado.

    The argument presented in the passage moves from a “likely” premise (the house is likely to survive) to a “definite” premise (the house will survive any tornados.) This is only possible if the assumption is that likely really means definitely, which is best expressed in Choice (D).

  35. B. Within five miles of the house in the passage, dozens of houses with concrete foundations were destroyed in a tornado three years ago.

    In order to weaken the argument, it must be shown that the assumption that a concrete foundation renders a house impervious to a tornado isn’t true. Choice (B) supplies direct evidence to counteract that assumption.

  36. B. As Muir’s need for water grows, it would have no other water resources except Lake Onnipi.

    In order for the argument in the passage to make logical sense, it’s necessary for Lake Onnipi to be the only water resource available to the town of Muir. That argument is presented in Choice (B). If the town could access any other water supply, the concern over Lake Onnipi would be lessened.

  37. E. If the town of Muir wants to preserve the fragile trout population of Lake Onnipi, they should consider finding other sources for water in the next few years.

    Choice (E) is the best choice. The key in choosing between Choices (A) and (E) is the time frame. The passage tells you that the trout population will be affected in 20 years. Therefore, the rush to curb water usage “immediately,” as in Choice (A), seems too rash. Choice (E) presents a more appropriate time frame.

  38. C. A recent scientific study shows a strong correlation between the increase of water consumption in Muir and the decrease in the trout population in Lake Onnipi.

    The question asks you to extend the argument presented. What further information would make the argument stronger? In this case, Choice (C) does so by presenting a scientific study that connects the overuse of water and the decrease of trout. It’s the best answer.

  39. B… . avoid overconsumption of carrots.

    This question seems very simple, and it is. The best choice is Choice (B). People should avoid overconsumption of carrots. No other advice is justified by the passage, and Choice (E) merely repeats a statement in the passage.

  40. E… . eat carrots to excess.

    Here, you're tasked with finding a conclusion that most poorly finishes the paragraph’s logic. If the paragraph is building a logical case for nutritionists to warn people not to eat too many carrots, Choice (E) is the most illogical conclusion. It encourages people to eat carrots.

  41. D. It’s unlikely that Sammy will win the collegiate championship this year.

    While we can look at the situation as given and perceive that Sammy most likely won’t win the championship, we do not know enough about the situation to absolutely predict that or to make predictions about the probably winner. Thus, Choice (D) is the best answer.

  42. C. The Downintown Police Department has technology that allows it to film most of the fire alarm boxes and see who pulled them.

    To support the Mayor’s argument with evidence, you need to know what it is: He or she is proposing that the fire alarm boxes be removed because they’re a nuisance that keep fire fighters from responding to real emergencies. The best evidence to support that is Choice (C), which would provide actual evidence of people pulling the alarms without reason. The cost of a false alarm, Choice (A), could be a nuisance, but the Mayor has not mentioned anything about the monetary cost of a false alarm so it’s not as good a choice.

  43. A. In a recent poll, only 40 percent of the residents of Downintown owned cell phones.

    The Mayor’s entire argument is premised on the idea that citizens of Downintown won’t need to use fire alarm boxes because they’ll be able to call for help on their cell phones. Choice (A) is a direct rebuttal to this idea, making it clear that the majority of citizens do not have a cell phone to use. It’s the strongest argument against the Mayor’s plan.

  44. C. The fire alarm boxes could be fitted with cameras that take photos of those citizens pulling them.

    Of the choices provided, Choice (C) is the best. It provides a selection of data that could be sorted into helpful photos of people pulling false alarms. Choice (A) is a step after Choice (C): First the perpetrators need to be caught before they can be fined. Choices (B) and (D) are not logically consistent, and Choice (E) not direct enough to solve this problem.

  45. C. The word “Non-Transferrable” is a significant deterrent to customers who might have otherwise sold their vouchers online.

    The logic shown by the marketing department is that marking the vouchers as “Non-Transferrable” will be, by itself, a significant deterrent. Thus, Choice (C) is the best answer.

  46. A. A competing chain found that marking their free drink coupons “Non-Transferrable” did little to change customers’ habits of selling those coupons online.

    The chain does not want to pursue a court case against people who sell the vouchers. From the passage, it’s clear that they just want to keep the vouchers from being sold as often as possible. The plan to mark the vouchers “Non-Transferrable” hits a snag if Choice (A) is true, as it’s direct evidence that marking coupons “Non-Transferrable” did little to stop the practice of selling them.

  47. B. Xinyuan wants to earn an A in her class. Her professor told her that she should try to get As on most of her exams. Xinyuan was able to earn an A on all of her exams, and thus, expects an A in the class.

    This kind of question is rare on the GMAT, but you’ll probably get one of them. Instead of asking you to look at the argument itself, it asks you to think through the logic used in the argument and then find another argument that most resembles the passage. Here, that’s Choice (B). Even though the setting is a college instead of a workplace, the logic shown is the same (and as equally flawed, by the way), as in the main passage.

  48. C. It is the conclusion to the argument.

    This is an easy one. Choice (C) is correct because the bolded portion is the conclusion to the argument.

  49. D. There might be a reason why Jane’s boss wanted her to sell three, not four, houses.

    It seems likely that if Jane was tasked with selling three houses in order to get a promotion, four houses would be even better. However, we don’t know that for sure, and Jane has changed the criteria under which she was to be promoted. As Choice (D) suggests, there might be a reason that was a bad idea.

  50. D. Scientific studies have consistently shown that yogurt does indeed help create a healthful environment in the digestive tract.

    The argument presented is that yogurt if helpful to maintain microbes a person’s digestive system. Only Choice (D) provides evidence — in the form of scientific studies — that help to prove that argument is correct. It’s thus the only good choice.

  51. A. The source of the nutritionists’ belief about yogurt turns out to be a widely-discredited article from the 1950s.

    If the argument is that nutritionists are recommending yogurt because it will be helpful to patients’ digestive systems, that needs to be scientifically validated. Choice (A) shows that, in fact, the advice is based on a scientifically invalid piece of evidence. It most weakens the argument.

  52. E. Surveys of park visitors show that they consistently asked for a cell phone ban, writing things like “Save us from ourselves!”

    The basic premise of the argument is that people are avoiding the park because they can’t tear themselves away from their cell phones long enough to enjoy being there. The administrator suggests that by banning cell phones, people may return to the park in greater numbers. The logic here is shaky, but Choice (E) best supports the idea that people want to spend time in a place where their smart phones must be put away.

  53. B. Three years ago, there was a widely publicized incident in the park in which a hiker was hurt and unable to call for help because he didn’t have a phone with him.

    To attack the argument, one must find reasons why the administrator’s logic is flawed, so you can either find another reason why attendance is down or find a reason why people would want to have their phones with them in the park. Choice (B) does both, so it beats Choices (A) and (C), which answer one or the other need.

  54. C. The administration noticed that the 80 seniors who had taken two or more AP classes all were accepted into their first-choice college. The colleges reported that their AP credits strongly influenced their acceptances.

    Here, you must find evidence to support the administration’s decision to add five more AP classes. Choice (C) is the best answer because it shows why the administration would add courses that are not widely requested by the student body. Choice (A) makes a similar point, but with less specificity and no actual proof. Choice (E) presents another reason to add AP courses, but is likely to be less convincing than Choice (C).

  55. B. A comparison of the number of graduates from next year’s class who got into their first choice college, and the number of graduates from this year’s class who got into their first choice college.

    The most helpful evidence would be a comparison of the rate of getting into one’s first choice colleges between this year’s senior class and next year’s, so Choice (B) is best. Notice that both Choices (D) and (E) are too vague and can be eliminated immediately.

  56. D. My favorite band strictly follows an every-other-summer tour schedule, and have done so for over 20 years.

    Despite appearing to be about music, this short passage is really about logic. In order to make the argument true, you have to find logic that would support the idea that if the band didn’t tour last summer, they will this summer. Choice (D) best does that, by showing the pattern: if they don’t tour one summer, they do the next.

  57. A. The band has always followed a “two summers off, one summer on” touring schedule since their founding 15 years ago.

    Choice (A) is the clearest evidence that the band won’t tour this summer: It’s not in their well-established pattern. Notice that Choice (E) is misleading: Since you know nothing about the band, the lead singer’s injury may or may not be a factor. You can’t tell for sure.

  58. D. No significant changes have been made to help protect Bridgeton from flooding since 1957.

    The argument made in the passage can only be true if nothing much has changed since the last time the town faced a flood. That makes Choice (D) the best answer.

  59. B. Since 1957, Bridgeton has undertaken multiple steps to improve the town’s protect against the next flood, including raising the river walls by three feet.

    In order to attack the argument, it’s necessary to show that the premise that the flood will be more destructive is unlikely to be true. Choice (B) does that best by showing that the town is less vulnerable to a flood than it used to be.

  60. E. Hypoloss carries a high risk of serious complications, including internal bleeding and death.

    Notice that most of the choices explain why obesity is a risk factor, but the argument is about why doctors won’t prescribe Hypoloss. Choice (E) best gives a reason why that may be. The drug itself carries a “high risk” of serious complications, even death. That’s most likely why doctors are reluctant to prescribe it.

  61. D. Three recent scientific studies have found that taking Hypoloss is no less dangerous to a patient than non-prescription weight loss techniques.

    It’s most likely that doctors, who are scientists, would be most convinced by scientific evidence that argues for a medication that they found dubious. Choice (D) best provides that evidence.

  62. B. Scientific studies on the safety of Hypoloss have not been conducted yet.

    Doctors wouldn’t want to prescribe a medication that may not prove safe to their patients. Choice (B) indicates that the jury is still out on that question.

  63. D. Gladys: You know as well as I do that the factory on Main Street changes shifts at 5:00 p.m., and that slows traffic to a crawl every day at that time.

    Gladys needs to present the best evidence she can to prove her argument is correct. Choices (A) and (B) provide evidence, but they’re slimmer than Choice (D), which provides much more clear and convincing evidence.

  64. A. It is a request that Gladys prove her argument.

    Although it sounds like a sentence one might hear in a disagreement, the bolded sentence does have a role to play: It is a request that Gladys provide evidence to prove her argument that they will not get there until 6:30. Thus, Choice (A) is best.

  65. B. The university’s definition of “most deserving” is not solely based on financial need.

    Since we are told almost nothing about the university’s scholarship program, we can only use the information we’ve been given. Choice (B) best does that. Notice that all of the other choices make assumptions that we might be sure are correct, but which are not justified by the language of the passage.

  66. A. A clear explanation of how the scholarship committee defines “most deserving.”

    The missing evidence that is most needed here is an understanding of how the university defines “most deserving.” If given that, we might better understand the choice that was made. Choice (A) is the best answer.

  67. D. The guidelines for the scholarship clearly define “most deserving” as being a student who cannot contribute more than $12,000 a year to their education.

    For the decision to be weakened, evidence showing that the scholarship committee chose to award a student who should not have received the scholarship. Choice (D) demonstrates that the committee ignored one of the terms of the scholarship’s rules.

  68. B. The majority of customers bought dishes of ice cream, and 80% of those bought vanilla or a vanilla-based flavor.

    While Choice (A) has some merit in weakening the argument, the best choice is Choice (B), because it provides evidence that the argument presented is not comprehensive enough. If the idea is to find out whether chocolate flavors are more popular than vanilla flavors overall (and not just in scoop form), Choice (B) gives the best evidence to be considered.

  69. C. It is the evidence that Li uses in his argument.

    The information in the bolded sentence is the evidence Li presents in order to support his argument, so Choice (C) is correct. Whether or not we think that the argument is a good one, that is the evidence Li is presenting to support it.

  70. E. Green is a color people like more than red or blue.

    Every answer except Choice (E) is an assumption that Li makes. With Choice (E), however, the assumption may not be correct. Li states that people buy more books with a green cover than any other color, but he doesn’t indicate that he believes people like green more than any other color.

  71. D. Business C produced more than 80% of the waste City A had to dispose of in the last year.

    Don’t get distracted! Business C’s assertion that it should not have to pay a tax to help offset the fee paid to City B is the premise here. The best argument against it is Choice (D) which makes it clear that Business C does, in fact, produce far more garbage than City A’s homeowners.

  72. B. City A’s homeowners contributed 60% of the town’s waste last year. The year before that, they contributed 68%.

    Business C needs to prove that homeowners in City A are contributing more to the trash problem than it is in order for the argument to work. Choice (B) does that best.

  73. D. Many of the creative writing faculty members who’ve left Wadsworth College have continued teaching at nearby schools for higher pay.

    Here, you want to find a reason to support the chairperson’s plan. Choice (D), which indicates that creative writing faculty are leaving Wadsworth College because they can do the same work for more pay elsewhere, supports the plan the best.

  74. E. Exit interviews with creative writing faculty members who’ve left the college indicate that course assignments and inadequate health benefits were the most common reasons they left Wadsworth College.

    The idea here is to find the flaw in the chairperson’s logic, not merely find a reason why his or her plan is not likely to be approved, as in Choice (C). Choice (E) is the best answer because it indicates that faculty members may not be more likely to stay merely because of a pay increase.

  75. B. “Sure, but we have five months until wedding season this time.”

    The basic premise of the argument Chip is making is that inexperienced clerks do not help during the wedding season. But Jackie is arguing that they will have more time to train the new clerks this time. Choice (B) best shows that she’s right because there is more time to train new clerks this year.

  76. C. It is the evidence that Chip is presenting to bolster his argument.

    The bolded portion is evidence that Chip is presenting to strengthen his argument against Jackie. Thus, Choice (C) is the best.

  77. D. The “10 patients per hour” statistic is misleading because it is an average. Daytime nurses sometimes treat 15 patients per hour while night nurses may only see 5 patients per night.

    The nurses’ union’s grievance attacks the premise of the administrator’s offer. If all of the ER nurses do not actually see 10 patients per hour, some will be much more likely to earn a bonus than others. Choice (D) shows that this is true.

  78. A. Mystique Auto charges a finance rate that is three times the rate charged by Miracle Cars, and customers must get their financing in-house when buying at Mystique.

    Michael Sanchez can feel confident if he has a tangible reason in mind as to why customers would want to shop at his auto dealership instead of Mystique Auto. Only Choice (A) gives a clear, compelling reason why consumers would choose his dealership and thus justifies his belief. It is the best answer.

  79. D. Sanchez does not know that Miracle Cars’ CFO has ordered that they raise interest rates on their in-house loans, which had been well below market average.

    Sanchez makes his statement with the assumption that nothing will change at Miracle Cars, so they remain in good standing, even when compared to Mystique’s new offer. But Choice (D) shows that Sanchez does not have all of the information and that there is good reason to feel less confidence.

  80. B. Meghan: “My coworkers wouldn’t stop asking me where I was going on vacation. I finally made them a deal: If they would stop bothering me for an hour, long enough for me to get my report written, I would tell them all about my trip. They left me alone, and when my hour was up, I told them it was none of their business where I traveled!”

    Here, you’re asked to figure out the logic in an argument in the passage. Hannah’s logic seems to run as follows: If I want A, I promise B if he does C. He did C, but I took away B. The closest mirror to this logic is in Choice (B), where Meghan employs the same logic. Notice that Choice (A) seems appealing because it’s about a similar situation, but Steve does not use the same logic.

  81. E. It is the conclusion to the argument.

    The bolded sentence shows how the argument concluded, so it is the conclusion, as stated in Choice (E).

  82. A. The new racquet costs 200 times the amount of the most expensive racquets made now.

    All of the choices presented could weaken the expectation that the new racquet will sell well, but Choice (A) is the largest threat. It practically guarantees that the racquet will sell poorly because the price difference is so large. It is the best choice.

  83. C. The manufacturer has secured the support of three top tennis players to act as ambassadors for the racquet. One was recently quoted as saying the racquet improved her game “more dramatically than I thought possible.”

    The manufacturer wants to support the idea that the racquet will sell well. Their confidence would like be well-placed if Choice (C) is correct, and several top players are endorsing the product so vociferously.

  84. B… . time how long it takes you to read and respond to a couple of emails in your in-box and that recalculate the time you’ll need?

    The point of Andrew’s argument is that he wants to empty his email in-box in as little time as possible, but he does not know how long it will take do so. Choice (B) is the best suggestion Diane can make. Following it would allow Andrew to make a reasonable guess on how long it will take him to empty his email box while also responding as needed.

  85. E. A survey of Factory B’s workers reveled that 78 percent would like to see technological improvements on their assembly line.

    Choice (E) best supports the argument that Factory A is more advanced than Factory B. If the workers of Factory B want to see improvement that will be similar to what is already in place at Factory A, that’s good evidence to support the argument as stated in the passage.

  86. D. It presents a possible cause of a condition as the only cause of that condition without considering other causes.

    The argument is clearly flawed, but figuring out where the major flaw is located is tricky. Choice (D) is best because the argument’s biggest error is using one reason to explain why Factory B’s output us lower than Factory A’s. It may well be because of the technology of the assembly line, but that is not proven yet.

  87. D. Chemicals used in the creation of fabrics are far more damaging to the environment than fabric scraps created in traditional clothing manufacture.

    The premise of the argument is that zero waste manufacturing of clothing is not as kind to the environment as some might think it is. The best facts to support that premise is in Choice (D), which shows that a major environmental problem in manufacturing is not addressed by zero waste clothing.

  88. D. Underage drinking has been on a steady decline for the last 25 years, long before the campaign to reduce the portrayal of it on television.

    The argument that reducing the portrayal of underage drinking in films can be tied to the reduction of the same in real life becomes questionable if underage drinking has been on a steady decline for many years. Thus, Choice (D) most seriously weakens the argument.

  89. E. There is a direct correlation between seeing an activity on television and taking part in that activity.

    As strange as it may seem, there indeed must be a belief that there’s a direct correlation between the portrayal of underage drinking and the rise of underage drinking to make the argument work, so Choice (D) is the best.

  90. C. In a poll of graduating high school seniors, 60 percent reported that they did not drink alcohol on a regular basis because of negative portrayals of the same in television and movies.

    Poll results are the kind of evidence that provide figures to boost an argument. Choice (C) does that for this argument.

  91. A. Readers are not interested in distinguishing between a well written essay and a hastily written short article.

    The basic premise of the argument holds that people cannot or will not distinguish between quality writing and poor writing, so long as something is provided for them to read. That makes Choice (A) the best answer.

  92. B. Subscriptions to print-based journals that publish long, well written essays are at an all-time high.

    The fact that people are buying more journals that publish essays would seriously weaken the argument that people do not care what they read. Thus, Choice (B) is best.

  93. A. When the dosage of the drug was half of what was used in the latest round of tests, the reoccurrence rate was still 60%.

    The assumption is that upping the dosage will also lower the rate of reoccurrence. Choice (A) demonstrates that there’s no connection between the dosage and the reoccurrence rate. That’s where the assumption is.

  94. A. Thyroid cancer is considered a relatively small impact disease. Most people recover from it.

    Choice (A) may be true, but the impact thyroid cancer has on people who have it is not a factor in the plan to double the dosage.

  95. E. Construction of the bypass is controversial, and most town residents have signed a pledge not to use it.

    Of these choices, Choice (E) provides the clearest argument for why the businesses may be wrong. If local residents have pledged not to use the bypass, it is less likely to be used, which would mean that traffic would continue as normal, passing the local businesses.

  96. C. “Because the soda won’t go bad, I can drink it tomorrow. I’m paying a little more for two sodas today, but I won’t pay anything for tomorrow’s soda.”

    The fact that the soda isn’t perishable is the key to Sam’s logic. Choice (C) explains that he will be able to consume the soda tomorrow and thus spread the savings into the next day.

  97. D. It is evidence that supports the premise of his argument.

    Sam’s argument is that it’s better to buy two sodas now instead of one soda each day because he will save money. The bolded portion is evidence that supports the premise that he will save money. Choice (D) is best.

  98. E. The book is incorrect. Not all animals, including dogs, can see colors.

    If Sparky can’t see that the room is blue, it is unlikely to have a soothing effect on him. Thus, Choice (E) is best.

  99. D. Sparky began barking a lot after Tyronicah painted her bedroom red.

    However unlikely to work we may find Tyronicah’s plan, the best support for it would show that Sparky is apparently affected by the color of the bedroom. Choice (D) does that.

  100. B. It is evidence that supports the premise.

    The use of statistics is almost always a presentation of evidence. Here, the sentence in bold is a statistic that is used as evidence to support the premise that there has been a significant increase in accidents. Thus, Choice (B) is best.

  101. D. The lawmakers assume that the threat of jail time would be a deterrent for those who might have contemplated texting while driving.

    While Choice (E) is likely true, it’s not an inference drawn from this argument itself. The better answer is Choice (D), which looks at the specifics of this argument: Jail time is more likely to deter texting while driving than a fine.

  102. D. The first sentence presents a theory about a topic, while the second sentence introduces the a more recent theory about that topic.

    The connection between the two sentences is clear. The first explains what some scientists have put forward as a theory about PTSD, while the second seeks to replace that theory with a new idea. Choice (D) explains this well.

  103. D. An explanation of what the new theory about the link between the impact and the patient is.

    In a well written passage — which one must assume this is — the most logical next sentence would explain what the new theory is, exactly. That makes Choice (D) the best.

  104. B. They are interested in reading new theories about PTSD.

    In a question like this, the GMAT test-makers know that you’re being asked to speculate. The answer will therefore be simple. In this case, the best choice is Choice (B), which is indeed so obvious as to be almost overlooked. It is the best choice because it is the only assumption of those offered that can be very safely made.

  105. A. Bridget: But they also are able to set the price accurately. When you sell your home yourself, you run the risk of underpricing it. And keep in mind that you still have to pay for much of what the agency would cover, such as listing and closing costs.

    Luke’s concern is that using a real estate agent will be expensive because they take a big profit from the sale of a house. If Bridget responds with Choice (A), she is most directly speaking to that particular concern, so it’s the best choice.

  106. C. It is an assumption Luke has made to support his argument.

    The sentence Luke says isn’t detailed enough to be evidence: He doesn’t provide any supporting information. He is using it to support his argument, but it is an assumption he is making. Choice (C) is thus the best answer.

  107. C. Vlad has only walked around in neighborhoods that cater to the large number of American tourists who visit the city each year.

    If Vlad is making his argument based on insufficient or biased evidence, the argument cannot be valid. Choice (C) presents a situation in which that would be the case: He isn’t getting an accurate sampling of London’s restaurant scene, and he’s collecting evidence in an area that’s biased towards a certain kind of patron.

  108. D. A London daily newspaper recently polled its readers on their favorite cuisine when dining out. “American” won by 30 percent.

    Evidence is best presented in quantifiable form, so far as the GMAT is concerned. Choice (D) does so with a figure that supports the idea that American food is increasingly popular in London.

  109. B. He could argue that the practice of wearing glasses with non-prescription lenses is very common these days, citing a statistic that 25 percent of glasses-wearers do not actually need them.

    Nancy refuses to wear glasses because she does not need them, and feels doing so would mislead her viewers. The best counter-argument presented here is Choice (B), which effectively points out that viewers may not assume that Nancy needs the glasses.

  110. C. Studies show that when a news anchor feels she is lying, it is perceivable by viewers in her body language.

    Nancy’s argument is that wearing glasses would be a lie, which would affect her performance and/or her relationship with the audience of the show. Choice (C) most clearly speaks to that idea.

  111. C. The author’s novel will become a best-seller.

    The assumption least likely to be in use here is that the novel will become a best seller. We don’t know why the publisher wants to re-release this novel, and certainly have no reason to think he expects it to be a best seller. Thus, Choice (C) is the best bet.

  112. C. The author’s estate was recently taken over by a law firm capable of practicing much closer diligence.

    The publisher’s argument is based on the premise that the author’s estate is not paying attention to what happens to the author’s works. However, Choice (C) would indicate that the estate is now capable of paying far closer to attention, which would ruin the publisher’s plan. It’s the best answer.

  113. A. The margin of error for the poll is greater than the difference in support between the candidates.

    It’s good to remember that the question has asked for the “most likely” reason, not “a plausible” reason. There are several plausible reasons, but Choice (A) is the most likely reason: It is factual and would be an immediate disincentive to publish a prediction if true.

  114. B. Written proof that the fundraisers for this organization were paid for by generous donors so that the money raised could go to people in need.

    Because Ben’s specific concern seems to be that the organization is putting a great deal of money into lavish fundraisers instead of helping people in need, proof that the organization is not paying for those fundraisers would be most helpful in convincing him. Thus, Choice (B) is the right answer.

  115. A. Over 40 percent of the organization’s budget is dedicated to fundraising.

    To support Ben’s argument, it’s necessary to find a evidence that the organization bankrolls fundraising far more than helping people in need. Choice (A) would help with that. 40 percent is a significant portion of any size budget.

  116. D. The first sentence is evidence that Ben is using to support the argument he is making, and the second is the conclusion to his argument.

    In the first bolded sentence, Ben is sharing evidence to support his argument (that the organization spends too much on lavish fundraisers). The second sentence is his conclusion: He states what he will do instead of supporting the organization. Choice (D) is best.

  117. E. Scientific studies have conclusively proven that there’s no truth to this advice.

    Suzie’s argument is that her mother’s advice must be correct because she’s followed it and never had a cramp while swimming. The best argument against this is to show that the connection is coincidental, not casual. Thus, Choice (E) is best because it provides factual proof that Suzie’s argument does not make sense.

  118. B. “I asked my doctor, and she said that this was a good policy to follow. Cramps are often caused by eating followed by vigorous exercise.”

    Suzie’s argument is weak because it relies on what could be coincidence. It can be improved with some sort of evidence. The closest to doing that here is Choice (B), in which a scientist puts her weight behind Suzie’s argument.

  119. D… . students should be encouraged to think about whether spending time on social media is affecting their decision-making about bullying behaviors.

    Most of the choices here are too broad to have been derived from the study. Choice (A) is the sort of obvious response that is a societal goal, not the result of a study. Choice (D) gives the best take-away from the study, presenting a reasonable response not a broad statement.

  120. C. There is a direct link between the use of social media and the likelihood that the user is an online bully.

    Without the assumption in Choice (C) — that social media’s usage and bullying are interconnected — the argument does not make logical sense. Thus, it is the best choice.

  121. C. The loss of a major contract with a hotel corporation has also contributed to the manufacturer’s decline.

    The manufacturer’s argument is an attempt to show how that the factory can no longer be profitable. To do this, showing that business will not pick up is helpful. Choice (C) gives more evidence suggesting the factory’s decline.

  122. A. The manufacturer recently secured a large, multi-year contract with a restaurant chain.

    A contract with a lucrative customer would argue against ceasing production. That the contract is “multi-year” is particularly compelling. Choice (A) is the best choice.

  123. E. A beauty salon has decided to close. Few women need a weekly hairstyling session, and the products used in styling hair are very expensive. Thus, the salon is putting more money into products than its making back in sales.

    The connection between a hair salon and a raincoat manufacturer may be less obvious, but the argument — essentially that supply far outpaces demand — is essentially the same. Thus, Choice (E) is correct.

  124. E. “As you know, the Police Department is next door, and we’re going to offer a discounted admission to people who present a ticket from that auction.”

    This question is fairly easy; you just need to find the sentence that provides actual evidence. Choice (E) does that the best, if you recognize that Choice (A) would weaken the argument, not strengthen it.

  125. A. “The Police Department’s event has three times the number of items up for auction and admission is free!”

    Choice (A) provides a reasonable counter-argument: If the other event has more items and is free, people are indeed more likely to attend it. Notice that Choices (B) and (D) might provide counter-arguments if they were given more context, but without more information, Choice (A) is stronger.

  126. D. The prior eight years are incidental, not prophetic.

    The question is essentially asking you to find the biggest flaw in the argument. Here, the assumption that the rate of inflation follows a fixed pattern is the largest flaw, and Choice (D) points that out. Other choices point to flaws, but not as large as Choice (D).

  127. E. It is evidence that supports the argument being made.

    The bolded sentence presents evidence that supports the argument being made, so Choice (E) is best. Choice (C) would have been a good guess if it was about the argument, not the counter-argument.

  128. B. It is possible to produce food without preservatives that is safe to consume.

    For the passage to be true, it must also be true that Marr Foods is able to make products that are safe to consume and do not have chemicals. That makes Choice (B) the best.

  129. C. Several other scientific studies found that preservatives were in no way harmful to those who consumed food with them.

    The basic premise of the argument is preservatives are harmful to those who consume them. If that is not true, the rest of the argument falls apart. Choice (C) makes a strong argument that the scientific study presented by Marr Foods is not representative of the common consensus.

  130. C. Neighbor A is on a plan from the water authority that provides a lower rate on water in the morning hours.

    The key here it to identify the correct argument that you need to find support for. Neighbor A’s chief concern is the cost of watering his lawn later in the day. Choice (C) points to why that is: He is able to save money by watering the lawn earlier.

  131. D. That Neighbor A doesn’t have a good reason for watering his lawn in the morning.

    To choose the answer correctly, you need to be alert to the difference between facts and assumptions. Choices (C) and (E) are facts; Choice (D) is an assumption that Neighbor B is making about Neighbor A. Given the wording of the question, Choice (D) is thus best.

  132. A. The first sentence is a premise to an argument, and the second sentence is a response to a counter-argument.

    The first sentence presents Neighbor A’s argument, and the second sentence shows that Neighbor A is rejecting Neighbor B’s counter-argument. Choice (A) is correct.

  133. B. Customers have repeatedly asked the company to offer an unlimited usage plan, which many other cell service providers already offer.

    If customers do not like the new plan, it will not do well. If they do, it will do well and revenues will increase, regardless of any other detail. That makes Choice (B) the best offered.

  134. D. A mock trial team that often makes it to the final round of competition but rarely wins is frustrated. They’ve decided to interview the members of the 2002 team, which won the state competition. Using those techniques, they’re sure, will put them over the top to win.

    The logical structure in the original passage is a flawed plan to use the idiosyncratic success of a past group of people to improve the chances of another unique group of people in winning the same title. Choice (D) best follows that logical scale.

  135. A. It concludes the coach’s argument.

    The best answer is Choice (A). If the team follows the coach’s plan, it will conclude in making it to the final game. Remember that the merits of the argument are not the question here. You may find it flawed, and it is, but that’s not the point of the question. Avoid Choice (C).

  136. C… . look for opportunities to schedule events before or after typical working hours and on weekends.

    All of the choices here are possible, so you need to focus on choosing the one that best completes the passage. The need for further information, as in Choices (B) and (D) seems unnecessary. Choice (A) doesn’t address the problem, and Choice (E) addressed the problem with the wrong people. That leaves Choice (C), the most direct response to the problem, and the best choice.

  137. D. There’s no “build up” in playing the slot machines. Each game is new and not tied to the game before it.

    Sheila’s theory is based on the idea that slot machines must be primed to cash out, and thus watching someone else lose repeatedly is priming the machine for her take-over and win. If Choice (D) is true, it means that her plan is meritless: Slot machines are not primed.

  138. B. A scientific study, based on the observation of 500 slot machines at a Las Vegas casino, showed that machines that are played repeatedly are three times more likely to cash out.

    The best evidence would show help to prove Sheila’s theory that slot machines that have been played frequently are primed to cash out. Choice (B) provides scientific evidence that proves that, in at least one case, Sheila’s theory is true.

  139. D. When Jane says that she prefers to go to the beach when it is less crowded, she may not mean that there are actually fewer people on the beach than at any other time of the day.

    The trick with this question is to understand that the logic it is seeking is not Jane’s internal logic, but rather, how Jane’s choice can be justified logically. Choice (D) does that best because it explains what Jane is most likely thinking.

  140. B. An explanation of an apparent discrepancy in her argument.

    Jake is presenting a discrepancy between what Jane says she prefers and what she actually does. He’s found an error and wants her to explain it. Choice (B) is correct.

  141. E. Reducing an avalanche’s impact by 50 percent is not the same as reducing the likelihood of an avalanche by 50 percent.

    The answer here is obvious if you take the time to read through everything presented to find it. Any reduction in an avalanche’s impact is not the same as being less likely to have an avalanche. Thus, Choice (E) is the best answer.

  142. C. When the impact of an avalanche is reduced, the avalanche is less likely to travel further down the mountain and affect skiers.

    The main problem with the argument made by the marketing company is that it conflates the impact of an avalanche with having an avalanche at all. Choice (C) provides further evidence to solve the problem, making it the right choice.

  143. D. Company L’s speed at producing widgets has repeatedly caused accidents that ultimately cost the company more money than producing at a lower rate.

    Here, you’re looking for a reason why the owner of Company K would not fully embrace Company L’s methods. Choice (D) provides the best evidence why this would be true: Company L’s methods are both dangerous and costly.

  144. A. Because Company K’s production line was already more efficient than Company L’s, a few more small changes should allow Company K to produce widgets at a rate of 150 a minute.

    In order to attack the argument presented, you need to find a reason why Company K shouldn’t stop at just two improvements. Choice (A), which reveals that the Company could soon be producing 150 widgets a minute, is the best choice.

  145. B. The first sentence is evidence used in building the argument, and the second sentence is the conclusion of the argument.

    Choice (B) is best here. The first sentence presents evidence that helps to build the argument (even if it seems to be countering the main argument), while the second sentence presents the conclusion of the argument, using the evidence from the first sentence.

  146. B. In a poll of recent law school graduates, “job fluidity” — that is, the ability to change positions and firms — was one of the top three qualities new lawyers wanted in their first jobs.

    To argue against the board’s idea, you need to find reasons to show that the potential pool of applicants would not like having to sign a five-year contract. Choice (B) provides evidence that this would be disliked.

  147. D. Poll data collected from current first-year associates about whether they would have taken the job if such a clause was included in their contracts.

    The best answer here is Choice (D). First-year associates at the firm are in the best position to evaluate whether the contract — which they have recently signed themselves — would be as sought-after if they had to commit themselves to five years at the firm.

  148. B. It’s possible to correctly bake a cake at a higher temperature so long as the time the cake is in the oven is reduced.

    The cake baker in the argument is making an (incorrect) assumption that baking a cake at a higher temperature will work out find so long as the time the cake is in the oven is reduced. That makes Choice (B) the best answer.

  149. E. Baking is a chemical reaction dictated by the recipe that cannot be sped up by setting the oven temperature higher.

    This is the kind of argument that is so clearly flawed that it can be difficult to figure out exactly what the flaw is. Choice (E), which points out that the argument has no scientific merit, is the best bet.

  150. D. The majority of volunteers who staff the clinic are doctors and nurses with full-time jobs, and they are often scheduled for hospital rounds and surgery in the morning hours.

    The argument here is not about whether the clinic is a good idea, or even if it is needed. Instead, the question is asking you why the supervisors would decline to open the clinic in the morning. Choice (D) provides the best answer. Choice (C) has some merit but is really making a separate argument for evening hours, not arguing against opening the clinic during morning hours.

  151. C. Morning hours would allow the clinic to see, on average, 20 additional patients per day.

    Don’t get confused by the question. The Davis County supervisor wants to extend hours into the morning at the clinic. Choices (A), (B) and (D) support the existence of a clinic more broadly and do not offer any particular support for morning hours. Only Choice (C) does that, making it the correct answer.

  152. E. CheapDeals won’t build in a town where they have been clearly told they are not welcome.

    The argument is to support the idea of protesting the arrival of CheapDeals. The assumption presented in Choice (E) — that CheapDeals won’t build where they’re not welcome — is the assumption behind the protest.

  153. C. CheapDeals tries to keep a low-profile; the publicity from a protest has kept the company from setting up shop in other towns.

    To support the argument that they should protest, the store owner needs to show that a protest could be effective. Choice (C) best shows how that could be true by offering evidence that protests against this company have worked before.

  154. B. If the jewels were to be stolen, thieves might target the smaller items, which will be displayed less securely, rather than the larger items.

    The director’s argument is flawed, but the key to this question is figuring out where the greatest flaw is. Choice (B) points out one of the problems with his logic: He’s assuming that thieves would choose to take the larger jewels, but there’s actually no reason to think that is likely.

  155. D. “I put on sunscreen before leaving the house, but I didn't bother with insect repellent. The sunblock should be strong enough to keep away any mosquitos that show up.”

    The best answer here is Choice (D). While the topic here is different from the original argument, the logic is the same. By buying one kind of protection, the speaker hopes that other protections will fall into place even though steps have not been taken to secure them.

  156. E. “I put on sunscreen before leaving the house, but I didn't bother with insect repellent. The sunblock should be strong enough to keep away any mosquitos that show up.”

    Remember, the conclusion of an argument doesn’t always have to arrive at the end of the passage. Here, Principal Lavine proposes his solution before presenting evidence that explains why the solution must be what it is. That’s Choice (E).

  157. B. The parking for visitors and parents is rarely used, so 30 empty spaces are often next to the school but forbidden to the students.

    Choice (B) is best because it argues against the premise the principal puts forward in his argument: There is no alternative for expanding student parking except to convert a field into a parking lot. Choice (B) implies that, in fact, the visitor and parent parking could be converted without much difficulty.

  158. D. A historical map showing the growth of neighborhoods in New Winchester.

    It’s probably possible to rank these from most to least helpful, but surely Choice (D) would prove to be of little help. It’s not clear how understanding the past growth of neighborhoods in the city would shed any light on the paradox Julian has noted.

  159. B. The grocery stores are located on the outskirts of town, whereas the corner stores are in residential areas.

    The discrepancy must be addressed here: What would cause people to routinely pay more for an item that they could get less at a grocery store? Choice (B) provides the best answer: The corner stores are geographically more convenient than the grocery stores.

  160. A. There must be something appealing about the corner stores that make people willing to spend slightly more money there than at the grocery store.

    Choice (A) seems so simple as to be obvious, but it’s really the only choice one can logically conclude from the passage. Notice that the question asks for a “logical conclusion” — that’s the key that Choice (A) must be right.

  161. B. How does lettuce production from Mapple’s government-owned farmland compared to production from farmland owned by private industries?

    In order to evaluate this argument, you must look for a question that gets to the heart of it: Why is private industry’s farmland more productive than farmland owned by the government? Choice (B) is the best evaluation question here because it would allow for the collection of data comparing the two types of farmland.

  162. C. There’s no discernable difference in the amount of lettuce produced per acre by the government’s farmland and by farmland owned by private industry.

    The basic premise of the argument is that there is a significant difference between the amount of lettuce produced on government farmland and the amount produced on farmland owned by private industry. If this is not true, as in Choice (C), the argument is severely weakened.

  163. B. The bridge is only open from 6:00 to 8:00 a.m. on weekdays.

    If Choice (B) is true, it implies that the problem with the bridge is not that it should be closed down, but rather, that it is not open enough.

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