Chapter 22
Practice Test Answers and Explanations
You’ve finished the test, but you’re not done yet. Reading through the following explanations may be the most important part of taking the practice exam. Examine the information for the questions you missed as well as those you answered correctly. You may find tips and techniques you haven’t thought of before in one of the answer explanations. If you’re short on time or just want to quickly check your answers, head to the end of this chapter for an abbreviated answer key.
Section 1: Analytical Writing Assessment
Scoring the practice analytical writing task is a little different than scoring the other sections. Your job is to honestly analyze the essay you’ve written and assign yourself a score. You can also ask a friend or composition teacher to look over your essay and give you an opinion. Refer to the scoring considerations in Chapters 7 and 9 for guidance on what readers are looking for. To help you determine your score for this section, we’ve included a sample essay and an explanation of its strengths and weaknesses. Use these tools to identify your own essay’s strengths and weaknesses and improve your essay response before you take the actual test.
Here’s a sample response to the essay prompt:
- The author of the prompt is making the argument that American charter schools have failed to “live up to the hype,” so to speak, and he or she makes some sound arguments in doing so. The argument is well-organized in that the author first discusses what charter schools are supposed to accomplish (more options as far as school choice and more opportunities for teachers) before discussing some of the ways in which they have failed to accomplish what was intended, such as the fact that many teachers leave within the first year.
- While the argument is well-organized, the author falters somewhat in his or her explanation of why charter schools are failing. In addition to the goal of increasing opportunities for teachers, the author notes that charter schools seek to give students and families alternatives to traditional, public schools. While the author provides an explanation for why these schools aren’t achieving their goals as far as teachers (again, teachers are leaving), he or she does not address how they fail in terms of giving students and families more options as far as school choice, and the overall strength of the argument suffers because of this obvious omission.
- It might make for a stronger argument if, instead of referencing school choice in the beginning, the author just cut straight to the chase and referenced teachers and accountability. He or she does discuss how charter schools are failing in terms of accountability later in the argument (when he or she notes that many are getting taken over by private companies without local interests), so it might strengthen the argument to only call out points that can be successfully refuted later on.
- It also seems a little odd that the entire argument focuses on how charter schools are failing, but yet it fails to address — at all — the academic performance of charter school students. One could argue that academic performance should be the single-biggest indicator of whether a school is succeeding, and the author’s failure to even touch upon that diminishes the strength of the points he or she does make.
Here is a quick analysis of the sample essay:
The essay author carefully considered the strengths and weaknesses of the arguments made about charter schools before crafting the response. The essay also identifies two clear omissions that probably should have made it into the original argument — the prompt author’s failure to address how charter schools are “failing” in how they offer alternative environments to traditional public school settings, and the fact that she never touched upon the academic performance of students in charter schools when arguing against them.
While the argument would benefit from these additions, it might also benefit from more clarity about the areas in which the essay author thought the original argument was strong. While the essay notes that the author of the prompt made “sound arguments” for why charter schools have failed to live up to the hype while using the plural form “arguments,” the only sound argument actually referenced is the fact that many teachers leave within the first year. The essay in its entirety may have proved more convincing if its author had called out other sound arguments.
Nonetheless, the author did provide a thoughtful analysis of the argument made in the prompt, and she was largely articulate and grammatically correct in doing so. The essay is also free from spelling errors and flows well. Because the author carefully considered the subject matter and poked some valid holes in the initial argument, and because she wrote a clear, concise response that was virtually free from spelling or grammar issues, it is unlikely this essay would score below a 4. However, the author’s failure to clarify her comments about sound arguments might keep it from scoring higher.
Section 2: Integrated Reasoning
Refer to “Section 2: Integrated Reasoning” of Practice Exam 1 online to check your answers for the 12 questions in this section. (Note: You can find instructions for accessing the online practice in the Introduction.)
Section 3: Quantitative
E. Statements (1) and (2) together are not sufficient to answer the question asked.
Look at the information the question provides, and evaluate whether more is needed for a solution.
Find out what to solve for.
This question is asking you how many cases of doughnuts a machine will be able to produce in a three-hour period of time. You could find the answer to the question if you knew the number of doughnuts the machine produces per hour and the number of doughnuts in a case. Rewrite the question as an equation where the solution (x) is the number of cases produced in three hours.
At this point, you have two unknowns on the right side of your equation. You don’t know how many doughnuts the machine can produce in each hour, and you don’t know how many doughnuts are needed to fill a case.
Examine Statement (1).
Statement (1) tells you that the machine produces 5 doughnuts per minute (which is 300 per hour). This eliminates one of the unknowns in your equation, but still doesn’t give you enough information to solve the question. Write down
. You can eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) says that the company sells cases of doughnuts in two sizes: 80 doughnuts and 240 doughnuts. This statement doesn’t provide you with the information needed to solve the problem. Write down
and eliminate Choice (B).Check out what you’ve written.
You have double nos, so look at all of the information provided by both statements.
Evaluate the two statements together.
Statement (2) told you that the doughnuts may be packaged in cases of either 80 or 240 doughnuts. While this may seem to be helpful in solving the question, it actually means that you need more information to solve the problem. You would need to know which size of case is being filled. Because this information isn’t provided in either statement, you won’t be able to solve this question.
D. Each statement alone is sufficient to answer the question asked.
Analyze all of the information given in the problem before looking at each statement.
Find out what to solve for.
The problem provides you with a figure showing an overlapping rectangle and circle and asks you for the area of the circle. You can convert the question into an equation, solving for the circle’s area (A). Using the standard formula, the area is equal to
multiplied by the circle’s radius (r) squared. So 
.From the information the question provides, you know that you need to figure out either the value of x or the value of y to solve the problem. Looking first at x, you know one figure is a rectangle, so the height on both sides is the same. This means the height on both sides equals x. From the information provided in the problem, you also know the center of the circle is at the same point as the corner of the rectangle. So, you can solve the problem if you can solve for x. In terms of x, then, the area of the circle is
.From the information in the question, you can also write your equation in terms of y. The question tells you that Point B bisects the length of the rectangle, so
, and therefore 
.Examine Statement (1).
Statement (1) tells you that
. You can use this value for y to solve the above equation for the area of the circle, 
. Statement (1) is sufficient. Write yes next to (1) on your noteboard and eliminate Choices (B), (C), and (E).Evaluate Statement (2).
Statement (2) tells you that the area of the rectangle is 18. This gives you
. You previously determined from the problem statement that the radius of the circle is equal to x, and also equal to half of y. So knowing 
and 
, you can substitute in values for x and y in terms of r: 
, so 
, and therefore 
. This allows you to solve for the area of the circle. Statement (2) is also sufficient. Write yes next to (2) and pick Choice (D).
A.
This question gives you an equation with variables of x and y, and asks you to solve for the value of y. It gives you a value of x, and says that
. Looking at the first part of the expression, you may notice that you are able to factor the numerator. Factor out the common factor of 5x: 
Since you know that
, you know that the denominator is not equal to 0, so you are able to cancel out the common factor of 
. Now you have 
.Rearranging the equation to solve for y:
When you insert 4 for x, you arrive at the conclusion that
.D. $21.60
In this price discount problem, you will need to apply multiple price discounts to the original price of the peaches in order to calculate the final price. The problem tells you that each peach costs $1, so a carton of 30 peaches would therefore cost $30. But the problem says that the price is discounted by 10 percent when the peaches are bought in a carton of 30. If the discount is 10 percent, then the price of the peaches will be
, which is 90 percent. So, two cartons of peaches would be 60 peaches, and the price would be 
.The problem tells you that there is an additional discount of 60 percent. To apply the additional discount, simply multiply $54 by 40 percent, and you get $21.60.
D. Each statement alone is sufficient to answer the question asked.
Be sure to evaluate each statement individually.
Find out what to solve for.
The question is asking for the value of
. So, it’s asking you to solve the equation
. But, the question already provides you with the value of y. So you just need to figure out the value of x.Examine Statement (1).
Statement (1) tells you that
. Since you already know 
, you can use this equation to solve for x. Going back to the question, you can plug in your values for x and y and determine the solution. Statement (1) is sufficient. Write yes next to (1) on your noteboard. You can eliminate Choices (B), (C), and (E).Evaluate Statement (2).
Statement (2) tells you that
. Again, since you know the value of 
from the question, you can use this equation to solve for x. Then you can insert your values for x and y and come up with the solution. Statement (2) is also sufficient. Write yes next to (2), and pick Choice (D).
D. AWL
This data-interpretation question presents you with a table showing peak prices of various stocks over the course of five years. The question is asking you to find which stock had the greatest increase in peak price from Year 1 to Year 3. Looking at the peak prices for OMK, you can see that they were $5.12 in Year 1 and $9.12 in Year 3. This is an increase of $4. Use estimation to evaluate the rest of the table.
Continuing down the table, you can see that the peak price of RRW increased by about
, and the peak price of LKP increased by about 
.If you don’t find an answer with a greater increase, you’ll have to evaluate these two options more carefully later. But there are still two more stocks to evaluate. Looking at AWL, its peak price increased by about
. AWL is now the highest increase in peak price you’ve seen and is definitely higher than TCK, which increased from around $62.00 to $74.00, an increase of only about $12.00.Of all the stocks, the peak price of AWL, Choice (D), increased the most from Year 1 to Year 3.
C. Both statements together are sufficient, but neither statement alone is sufficient to answer the question asked.
Be sure to separate out the facts of each statements:
Find out what to solve for.
The question is asking for the distance that a bullet train will travel to get from Tokyo to Kyoto. This is a rate question. So, to find the distance travelled (d), you will need to multiply the rate of travel (r) by the time spent travelling (t). In other words, you need to solve
.Examine Statement (1).
Statement (1) provides the time required for the bullet train to get from Tokyo to Kyoto. This gives you
. While this gets you one step closer to a solution, you still don’t know the rate at which the train travels. Statement (1) isn’t sufficient. Write down 
. Eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) says that the bullet train travels at a speed of 250 kilometers per hour from Tokyo to Kyoto. This gives you the rate of travel of the train. But, as it turns out, knowing the rate of travel alone is not enough to solve for the distance travelled. Statement (2) alone isn’t sufficient. Write down
. Eliminate Choice (B).Check out what you’ve written.
You have two nos. Since each statement alone is insufficient, you need to consider both statements together.
Evaluate the two statements together.
Statement (1) gives you the time travelled
, and Statement (2) tells you that the rate of travel is 
. Because you have the necessary pieces of the equation, you’re able to solve for the distance that the bullet train travels. The two statements together provide you with enough information to solve the question.
C. 64
This question concerns exponents. You are given an expression and asked for the value of the expression if
. Look for a way to make the bases of the terms the same. Because 
, you can rewrite the expression as: 
Since exponents with the same base can be added together, you can simplify the expression to:
The z terms cancel out and you are left with
. You know that 
, so the expression becomes 
, or 64. The answer is Choice (C).A.
The first fraction involves addition, so you’ll need to find a common denominator. The easiest common denominator to find for 3 and x would be 3x. So, multiply the first fraction by
and the second fraction by 
to create the common denominator. Then add: 
Multiply this new fraction by
:
Simplify:
And you’re done!
C. Both statements together are sufficient, but neither statement alone is sufficient to answer the question asked.
Don’t get too concerned about performing calculations or attempting to completely solve the problem. Just focus on whether the statements provide enough information to reach a solution.
Find out what to solve for.
The question is asking for the original price of a phone charger. The statement tells you that the total discounted price (t) is $630. You don’t know enough about the details of the discount yet to start solving the problem, so it’s time to look at each statement.
Examine Statement (1).
Statement (1) gives you the details of the sale that the store is offering. Since you know that the discount is going to be applied to the total purchase price, you can write an equation to help determine the original price of the phone charger alone. Use d to represent the discount percentage. The discounted price will be the original price multiplied by
.The total discounted price (t) is equal to
multiplied by the sum of the original prices of the smartphone (s) and the phone charger (c). So 
. You know that 
, and you can figure out whether d is 15 percent or 20 percent, but you don’t know the original prices for the smartphone or the phone charger. Therefore, you still have two unknowns in your equation: s and c.With a single equation and two unknowns, you don’t have enough information to solve the problem. Statement (1) is insufficient. Write down
. You can eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) tells you that the original price of the smartphone alone was $720. Since this doesn’t give you any information about the details of the sale that the store is offering, Statement (2) is not sufficient. Write down
and eliminate Choice (B).Check out what you’ve written.
You have nos for each statement, so now you need to look at both of them together.
Evaluate the two statements together.
Using Statement (1), you know that the total purchase must have been at least $500 to end up with a final price of $630, so you know there is a discount of at least 15 percent. To figure out if the customer is receiving a discount of 20 percent, multiply $800 by 0.8, which equals $640. Since the final price is less than $640, you know that the total price was not high enough to get the 20 percent discount. So, the discount was 15 percent, and
.You can substitute in values for t and d:
Statement (2) provided you with the final piece of information that you were missing after evaluating Statement (1). Now that you have this, you can plug in $720 for s in your equation and solve for the original price of the phone charger. The combination of the two statements provides enough information to answer the question.
B.
This is a coordinate geometry question, so you’ll need to work with equations of lines and slope to determine where the lines intersect.
While drawing out a sketch of the points and lines will help to visualize the problem, you shouldn’t rely on your artistic skills to find the correct answer; some of the points may be close together, and graphing by hand isn’t 100 percent accurate.
You know that the first line passes through the points (–2, 2) and (–1, –3). To find the equation of this line, first you’ll need to find the slope, m. To find m, figure out rise over run by dividing the difference in y values by the difference in x values:
Once you know the slope is –5, you can substitute the value for m in the equation of the line:
.You know the point (–2, 2) is on the line, so substitute these coordinates for x and y to find the value for b:
Now you know the equation for the first line:
.The equation for the second line is
. To find where the two lines intersect, set them equal to each other and solve for x:
When you know that
, you can tell the correct answer is Choice (B); it’s the only answer with an x value of 0.You don’t have to solve for y to solve this problem, but you can if you want by substituting x into either equation:
B.
This problem deals you an algebraic expression with two unknowns: x and y. The problem tells you that
, so you can insert that value for y in the equation to get the expression solely in terms of x. Solve by performing division in the first fraction: 
, which simplifies to 
when you cancel x from the numerator and denominator.Then add to find the correct answer:
.D. Each statement alone is sufficient to answer the question asked.
For this problem, drawing a Venn diagram may help you visualize the relationships in the data.
Find out what to solve for.
The question is asking you to determine how many families have shopped at both Fresh Food Mart as well as Sally’s Market.
You are determining the number of families that have shopped at both stores (b). Based on the diagram, you know that
. The problem statement tells you that 17 of the families have shopped at Fresh Food Mart, so 
. It also tells you that 12 of the families have shopped at Sally’s Market, so 
. At this point, you have three equations with four unknowns. Statements that supply a value for at least one of the unknowns will allow you to solve for any of the others.Examine Statement (1).
Statement (1) tells you that 15 percent of the families haven’t shopped at either store. Therefore,
, so 
. You can substitute n into your first equation to give you 
. You now have three equations with three unknowns, so you can solve for each of the variables.You could stop here, but if you want to be completely sure of your answer, you can solve for b: Substituting
into your first equation, you get 
. This gives you 
. When you substitute s into your final equation, you get 
, therefore 
. Statement (1) is sufficient. Write 
on your noteboard. You’ve eliminated Choices (B), (C), and (E).Evaluate Statement (2).
Statement (2) says that all the families who have shopped at Sally’s Market have also shopped at Fresh Food Mart. This tells you that no families have shopped at only Sally’s Market, so
, and therefore 
. Statement (2) is also sufficient. Write 
. Both statements are sufficient.
D. 96,800
This is a percent change problem dealing with the number of parts produced in different years. Knowing that Anthony’s business made 80,000 parts last year and 88,000 parts this year, you can calculate the percent growth using the percent change formula, which is the difference between the two values divided by the original value:
To maintain 10 percent growth next year, the business will need to produce the same number of parts as last year + 10 percent more, which you can express as 110 percent or 1.1 of 88,000:
, which is Choice (D).Make sure you use the new year’s value when calculating the percentage increase for the upcoming year. Choice (C) reflects an increase of 8,000 parts, but that amount is 10 percent of the parts made last year and only about 9.1 percent of the parts made this year. To maintain 10 percent growth, the number of additional parts made next year must be greater than this year’s.
A.
To find the surface area of a cylinder, you need to add up the areas of each of its components. The area of each circular base is
. Multiply this formula by 2 to account for both circular ends of the cylinder: 
.You have the formula for the area of both ends, but you still have to consider the area of the curved side of the cylinder. That dimension is the circumference of the circular base
multiplied by the height (h) of the cylinder: 
.Find the total surface area by adding the two dimensions:
.Now plug in the values. The diameter of the cylinder is 1, and the radius is half the diameter, or 0.5. The height of the cylinder is 3. Insert 0.5 for r and 3 for h, and find the sum:
A. Statement (1) alone is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Be careful not to jump ahead, even if you are able to figure out the solution with the first statement.
Find out what to solve for.
The question is asking whether
. Since y is a positive integer, you can multiply both sides of the equation by y. So now you just need to figure out whether 
.Examine Statement (1).
Statement (1) says that
, so 
. Clearly, 
. Therefore, x is not greater than y, and the inequality given in the question is false. Statement (1) is sufficient. Write down 
and eliminate Choices (B), (C), and (E).Evaluate Statement (2).
Statement (2) tells you that
.Multiply both sides of the equation by y to get
, which you can also present as 
. While you can come up with some values for x and y that would satisfy both this equation and the equation given in the problem statement, Statement (2) really doesn’t give you enough information to determine whether the statement 
is true or false in every case. Statement (2) is not sufficient. Write down 
on your noteboard. The answer must be Choice (A).
C. $64.00
This a profit question dealing with two different merchants each selling the same product.
You can eliminate Choice (A) right away. If Patrick makes more profit than Mel, he must be charging more than $60, the price Mel charges for her shirts.
A general equation for the profit of each merchant is that profit (p) is equal to selling price (s) minus cost (c). So,
. You can write a profit equation for each merchant to make solving the question easier. For Mel (M), 
. Because Mel is selling her shirts for $60, 
and 
.For Patrick (P),
. You know that Patrick’s profit is $24, so 
.If Patrick makes 20 percent more profit than Mel, then
. Find Mel’s profit by substituting $24 for 
in the equation: 
Once you know Mel’s profit is $20 per shirt, you can find the cost of her shirt:
Because you know Patrick and Mel have the same shirt cost, you can now find out how much Patrick sells his shirt for:
Patrick sells his shirt for $64.00, Choice (C).
B.
To solve this algebra question with one unknown, begin by dividing both sides by 7:
Next, determine a common denominator for the fractions on the left side and find their sum:
Set that sum equal to
and solve for x:
B. Statement (2) alone is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
You may be tempted to start this problem by solving for variables, but wait until you’re sure this activity actually helps you answer the question:
Find out what to solve for.
The question is asking for the value of a function of x and y. The problem statement tells you that y is 1, so you just need the value of x to determine the value of the function.
Examine Statement (1).
Statement (1) gives you the equation
. You already know the value of y, so solving this equation isn’t going to get you any closer to the solution. Statement (1) is not sufficient. Write no next to (1) on your noteboard and eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) tells you that
. Substituting in 
, you can solve for x and determine that x is also equal to 1. Going back to the function, you can plug in values of 1 for x and y and determine the value of the function. Statement (2) is sufficient. Write yes next to (2) and pick Choice (B).
E. Statements (1) and (2) together are not sufficient to answer the question asked.
As you answer the questions, rely only on the given information and not assumptions about the properties of geometric figures.
Find out what to solve for.
The question is asking for the length of side m of a triangle. The figure alone doesn’t really give you many clues about the angles or lengths of any of the sides of the triangle, so there’s not much you can figure out up front.
Examine Statement (1).
Statement (1) tells you that side p has a length of 4. This alone really isn’t useful. Since you don’t know the angles, you can’t figure anything else out. Although it may be tempting to assume that sides p and n are the same length since they look similar, resist the urge! Statement (1) is not sufficient. Write
on your noteboard and eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) tells you that angle A is 90 degrees, meaning that this is a right triangle. This also means that m is the hypotenuse of the triangle and can be solved for using the equation
. However, you still don’t know what the lengths of sides n and p are, so you can’t yet solve the problem. Statement (2) is also not sufficient. Write 
. You’ve eliminated Choice (B).Check out what you’ve written.
You have two nos, so you need to look at the information in both statements together.
Evaluate the two statements together.
Using the length of p from Statement (1) and the fact that the triangle is a right triangle from Statement (2), you can write the equation
. While each statement provides some information about the properties of the triangle, you are still missing the length of side n, so you can’t quite solve for the length of side m. Even with the information from both statements combined, there is not enough to solve the problem.
D.
This question presents you with an inequality and asks for the possible values of x to solve the inequality. The fastest way to solve this problem is to get x by itself on one side of the inequality. An easy way of getting rid of the denominators is by multiplying the entire inequality by 6.
Then, you can more simply solve the inequality for x:
Remember, when dividing an inequality by a negative number, the inequality sign flips from greater than to less than or vice versa.
A. Statement (1) alone is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Rewriting the word problems as equations can help you determine whether you have enough information to solve the problem.
Find out what to solve for.
This is a work-rate problem dealing with the rates at which Roland and Felicia can perform testing of circuit boards. The question is asking how many circuit boards Felicia can test in an hour. Let f be the number of minutes it takes for Felicia to test a circuit board alone. To find the number of circuit boards Felicia can test in an hour, you divide 60 minutes by f.
The problem statement tells you that Roland and Felicia together can test a circuit board in eight minutes. This can be rewritten as an equation, with r being the number of minutes it takes for Roland to test a circuit board on his own:
.Examine Statement (1).
Statement (1) tells you that Felicia can test circuit boards twice as fast as Roland. This means Felicia can test a circuit board in half the time that it takes Roland. From this you can write the equation
. Using this equation in combination with the equation you wrote above, you have two equations with two variables, and can solve for f. This will allow you to find the number of circuit boards Felicia can test in an hour. Statement (1) is sufficient, so write 
on your noteboard. You’ve eliminated Choices (B), (C), and (E).Evaluate Statement (2).
Statement (2) throws an extra person into the mix, and tells you that with their friend Cory helping them, the three can test a circuit board in seven minutes. From this, you can write the equation
. Looking at the equation and the one you developed from the problem statement, you can see that you have two equations with three unknowns. You won’t be able to solve the question with just this information. Statement (2) on its own is not sufficient, so write 
.
D. 16
This question deals with the average age of cars in a parking lot. It tells you that the average age of the ten cars is seven years. The equation for averages can help for this problem:
.You know that the average age is seven years, and the quantity of cars is ten, so the sum of the ages is 70 years:
.The problem then tells you that the average age of nine of the cars is six years. Using the same average equation, you can find that the sum of the ages of those cars is 54 years:
.The difference in the sums is the age of the remaining car:
. The age of the tenth car is 16 years.C. 3
This is a rate problem dealing with the speed and distance of a runner, Cindy. In rate problems, rate multiplied by time equals distance.
First, Cindy runs for 16 minutes at 7.5 miles per hour. Multiplying the rate by the time will get you the distance traveled. However, you need to convert the units so that you’re only dealing with minutes.
So, for the first portion of her run, Cindy traveled a distance of two miles. For the second portion, Cindy runs at six miles per hour for ten minutes.
Therefore, Cindy ran for two miles at 7.5 miles per hour and then for one mile at 6 miles per hour, which results in a total of three miles.
B. Statement (2) alone is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
Don’t get tripped up dealing with decimals!
Find out what to solve for.
The question is asking for the value of a. Since you are given an equation with two variables, a and b, you know you need to find b to solve for a. Rewriting the equation to not use scientific notation may also make it easier to handle:
.Examine Statement (1).
Statement (1) gives you an additional equation, also with unknown variables of a and b. At first glance, it seems like you should be able to use this equation to solve the problem, since you have two equations and two unknowns. Solving this new equation for b gives you
.Substituting this expression back into the original equation gives you
. When you simplify, you get 
. Trying to solve for a, you realize that the equation given to you in Statement (1) is just the same equation given in the problem statement, and it doesn’t help you to find the value of a. Statement (1) is not sufficient, so write 
on your noteboard. You can eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) also provides you an additional equation with unknown variables a and b. Using the same process as before, you can rearrange the equation in terms of b to get
. Substituting this expression back into the original equation, you get 
. At this point, it’s obvious you can solve for a, so Statement (2) is sufficient. Write yes next to (2) on your noteboard. The correct answer is Choice (B).
E. Statements (1) and (2) together are not sufficient to answer the question asked.
Use only the information the problem gives you.
Find out what to solve for.
The question is asking you for the value of the perimeter of a four-sided shape. Since the problem statement doesn’t say anything about the lengths of the sides or the angles, don’t assume the shape is a square or a rectangle even if it appears so. At this point, you know that you need to add up
to calculate the perimeter.Examine Statement (1).
Statement (1) says that all the angles in the figure are right angles. This tells you that the shape is a rectangle. This doesn’t really get you any closer to solving the problem, because you’re still stuck at
. Statement (1) is not sufficient, so write 
on your noteboard. You can eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) gives you a value of 2 for t. If you knew that the shape was a square, that would be enough to calculate the perimeter. But the problem statement doesn’t tell you that, so Statement (2) is also not sufficient. Write
and eliminate Choice (B).Check out what you’ve written.
You have two nos on your noteboard, so you need to see if you can solve the problem with both statements together.
Evaluate the two statements together.
Using both statements together, you know that the shape is a rectangle where one side has a length of 2. Since it’s a rectangle, you know that the opposite side has the same value, so v is also 2. However, you don’t have enough information to figure out the length of u and w, so you can’t solve the problem. The statements together are insufficient.
D. $1,500
This problem can be translated to math equations to help visualize the information in the problem. The total amount spent is equal to the sum of buying supplies (s) plus hiring labor (l) plus truck rental (t). The equation is
.You know that Jerry spent 10 percent on supplies:
.So,
.You also know that the truck rental cost five times as much as hiring labor:
.Substitute the values for s and t into your first equation:
When you know Jerry spent $300 on hiring labor, you know that he spent five times as much, or $1,500, on his truck rental.
B. 50 percent
This geometry problem deals with a right triangle. The question asks you to find what x would have to be if the area of the triangle were tripled and if y were doubled. Problems that concern primarily variables may be easier to solve when you give those variables simple values. For example, you could treat the triangle in the figure as a 3:4:5 right triangle. Its base and height would therefore be 3 and 4, so the area would be
, which is 6. If you triple the area to 18 and double y to 8, the resulting value for x in the larger triangle would be 
: 
Because
is 50 percent greater than 3, the answer is Choice (B).You can also solve by creating equations for the area of each triangle. You can use subscripts of 1 to denote the original triangle and 2 to denote the new, larger triangle:
Based on information in the question, you also know that
and 
.Plug the value into the area expression for the larger triangle:
Simplify the equation by dividing
from both sides of the equation:
This tells you that the larger triangle has a side length x that is 1.5 times the length of the original side x. This is an increase of 50 percent.
C. Both statements together are sufficient, but neither statement alone is sufficient to answer the question asked.
Using a chart can help you get the question information organized.
Find out what to solve for.
The question provides some information about the types of bikes sold at a bike shop. You can tell that the shop sells mountain bikes and road bikes. The question is asking you what percentage of bikes sold are mountain bikes for kids. Since you don’t have any information yet about what percentage of bikes are for kids, you need more information.
Examine Statement (1).
Statement (1) tells you that 20 percent of the bikes sold are for kids and 80 percent are for adults. This is a key piece of information missing from the problem statement. With this new data, you can draw a table to organize the information:
At this point, still too many different possibilities exist for how the types of bikes could be distributed. You need more information to determine what percent of bikes sold are mountain bikes for kids. Statement (1) is not sufficient, so write
on your noteboard. You can eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) tells you that 20 percent of the bikes sold are road bikes for adults. You can create another table, this time filling it in with the information from the question and Statement (2):
You can determine that 5 percent of the bikes sold are road bikes for kids because you know that 25 percent of all bikes sold are road bikes and 20 percent are road bikes for adults. But once again, you don’t have enough information to solve the problem. Statement (2) is not sufficient. Write
on your noteboard and eliminate Choice (B).Check out what you’ve written.
You’ve found that each statement on its own isn’t sufficient, so now it’s time to evaluate whether they give you enough information combined.
Evaluate the two statements together.
You can finally fill in the table using all the information provided in both statements:
Both statements combined give you what you need to determine the percentage of bikes sold that are mountain bikes for kids.
D. Each statement alone is sufficient to answer the question asked.
Don’t underestimate simple-looking questions. Be diligent and work through the steps.
Find out what to solve for.
The question is asking for the value of x, and gives you the expression
. At this point, all you can do is rearrange the equation to put x on one side: 
This information doesn’t get you any closer to solving for x.
Examine Statement (1).
Statement (1) tells you that x, y, and z are all equal. Substitute x for y and z in the expression, and you get
, which you can surely solve for x. Statement (1) is sufficient. Write 
on your noteboard. You can eliminate Choices (B), (C), and (E).Evaluate Statement (2).
Statement (2) gives you the equation
. At first glance, this may not seem too helpful, since you only have two equations and three unknowns. But when you substitute the equation into the original expression in place of z, you get 
. The y terms end up cancelling each other, so you’re left with 
, which you can also clearly solve for x. Solution (2) is also sufficient.
A. Statement (1) alone is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Converting word problems into equations may help you solve them.
Find out what to solve for.
This is a mixture problem, so you know you’ll need to use a mixture equation. You only know that George has 1,000 gallons of fuel in his supply tank at 11 percent ethanol, but you don’t know the percentages of ethanol in the suppliers’ fuel. Write the problem in equation form:
With b designating the percent of ethanol in Brian’s Biofuels and g the number of gallons of Brian’s Biofuel needed to add, substitute the information you know already into the equation:
You need to determine g, so you can see that what you really need is the percent of ethanol in Brian’s Biofuels, or b.
Examine Statement (1).
Statement (1) tells you that Brian’s Biofuels provides fuel with 80 percent ethanol. This is the value for b you were previously missing. All you have to do is plug in 80 percent for b in the equation you wrote above, and solve for g. Statement (1) is sufficient. Write
on your noteboard and eliminate Choices (B), (C), and (E).Evaluate Statement (2).
Statement (2) gives you information about the mixture currently in George’s supply tank. It has 10 gallons of fuel from Brian’s Biofuels and 990 gallons of fuel from Dyon. Writing this as an equation where d is the percent of ethanol in Dyon fuel, you have
.Using this equation along with the one you developed form the problem statement, you have two equations with three unknowns, so you aren’t able to reach a solution. Statement (2) is not sufficient. Write
on your noteboard and pick Choice (A).
C.
This problem shows you an isosceles right triangle and tells you that the hypotenuse has a length of 9. For a right triangle, apply the Pythagorean theorem: the sum of the legs squared equals the hypotenuse squared.
You can also solve this problem by observing the side ratios of isosceles right triangles:
. Because the hypotenuse is 9, the side length of each leg is 
.
But that answer isn’t available. Clearly, though, Choices (A) and (B) are wrong. To convert your answer to one that expresses the entire value as a square root, square 4.5 to get 20.25. Then take 20.25 times the 2 under the root sign to get 40.5. The answer that is the same as
is Choice (C).C. 10
This problem is asking how many of the 60 guests at Taco Fusion restaurant ordered both tacos and sushi for lunch. You may find it helpful to draw a diagram:
In the diagram, t is the number of guests that ordered only tacos, s is the number that ordered only sushi, b is the number that ordered both, and n is the number that ordered neither.
The problem tells you that there were 60 guests, so
.You know 20 guests ordered sushi, so
. In terms of b, 
.You also know 45 of the guests ordered tacos, so
. In terms of b, 
.Finally, five of the guests ordered neither item, so
.When you substitute these expressions for s, t, and n into your first equation, you get this:
B. Statement (2) alone is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
Even if a piece of information seems helpful, don’t count it as sufficient if it isn’t necessary.
Find out what to solve for.
The question is asking for the population of Greenvale at the end of this year. The problem statement tells you that the population grows by 10 percent each year, but doesn’t give you any idea what the population is. To solve the question, you need to know the population of Greenvale.
Examine Statement (1).
Statement (1) tells you that the population of Greenvale grows by 21 percent over a two-year period. While this tidbit may seem useful at first, it’s really just a restatement of information you already have. You know that the population grows by 10 percent each year, so this statement just tells you that over a two-year period
. Statement (1) is not sufficient. Write 
on your noteboard and eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) says that there were 10,000 people living in Greenvale at the beginning of last year. This data gives you a starting point to calculate the population at the end of this year. If the population grew by 10 percent last year, then the population at the end of last year was
. So the population at the end of this year will be 
. Statement (2) is sufficient. Write 
on your noteboard, and pick Choice (B).
A. Statement (1) alone is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Make sure you know your basic geometric formulas for area.
Find out what to solve for.
The question is asking for the area of the triangle. You know the formula for the area of a triangle is one-half the base times the height. In this case, the base of the triangle is x, and the height of the triangle is y, so
.Examine Statement (1).
Statement (1) tells you that
. This is very helpful for finding the area, because you can plug it directly into your area formula. Substituting in 100 for xy, you know you can solve for A: 
. Statement (1) is sufficient. Write 
on your noteboard and eliminate Choices (B), (C), and (D).Evaluate Statement (2).
Statement (2) says that
. You can substitute this data into your area formula to get 
, but you still need to know the value of x to solve the problem, so Statement (2) is insufficient. Write 
on your noteboard, and pick Choice (A).
C. $1.60
This question asks you to figure out the cost of production when given a profit percentage.
Be sure to set up your profit equation correctly. You can’t just multiply $2.00 by 75 percent to figure out the cost. In this case, the profit percentage is based on the cost, not on the price the company charges.
Write an equation using p as the price the company is selling each gallon of liquid nitrogen for and c as the cost of production of one gallon of liquid nitrogen when it wants a profit to be 25 percent of its cost:
.So
. Because you know the price is $2.00, you can solve for the cost:
The cost of production is $1.60.
C. Both statements together are sufficient, but neither statement alone is sufficient to answer the question asked.
Apply the steps:
Find out what to solve for.
The question tells you that Jack has three activities that make up his morning routine. Assign a variable to each one to represent the amount of time it takes him to complete that activity. That way, you can rewrite the problem as an equation. The total time taken, 45 minutes, is equal to the time spent taking a shower (s) plus the time spent drinking coffee (c) plus the time spent walking to work (w). So, your equation is
. The question is asking you how long it takes for Jack to drink coffee, so you’re solving for c.Examine Statement (1).
Statement (1) says that it takes Jack four times as long to walk to work as it takes him to drink coffee. In equation form, this is
. Substitute this value for w in the equation: 
. You still have two unknown variables; you would need to know how long it takes Jack to take a shower to solve the question. Statement (1) is not sufficient. Write 
on your noteboard and eliminate Choices (A) and (D).Evaluate Statement (2).
Statement (2) tells you that showering and drinking coffee take Jack a total of 25 minutes. You can write this out in equation form:
. You can then substitute this value into the original equation: 
. You know 
, but you can’t solve for c. Statement (2) is also not sufficient. Write 
on your noteboard. You’ve eliminated Choice (B).Check out what you’ve written.
You have doubles nos, so you need to look at both statements together.
Evaluate the two statements together.
When you combine the equation from Statement (1),
, with the knowledge from the second statement that 
, you know 
, which clearly allows you to solve for c. The two statements together provide enough information to solve the problem.
Section 4: Verbal
A. The factors that make an area desirable are also those that can pose the most risk.
The substantiating details in the paragraph describe situations where those factors that create desirable areas such as the Toboku coast, Florida, Hawaii, and productive farmlands are the same factors that create great destruction, so Choice (A) is the best answer. Choice (B) is too specific. Choice (C) mentions the destructive forces in the paragraph but not the concomitant desirability of the environments they also cause. Choice (D) requires too much speculation. The paragraph states that humans pay a price for living on Earth, but it doesn’t state the requirement that they learn to live with the risks. The paragraph is less about humans and more about the kinds of natural risks on Earth. Choice (E) doesn’t address all of the risks provided in the paragraph and is therefore too specific to be its main idea.
C. Loss of retail clothing sales due to a mall flood
In the final paragraph of the passage, the author discusses what he calls direct and indirect losses. Direct losses, he notes, are those that involve the destruction of physical assets; indirect losses are those that arise as a result of the direct ones. Choices (A), (B), (D) and (E) all involve the actual destruction of physical assets: a library, school building, livestock, and a pavilion, respectively. Choice (C), on the other hand, reports the loss of income due to a direct loss — a mall flood. Thus, only Choice (C) denotes an indirect loss because loss in sales isn’t tangible and therefore isn’t a physical asset.
D. hazards are not under human control, while risks usually are
Skim the answer choices to determine whether any of them can be easily eliminated. Choice (B) isn’t a true statement according to the information contained in the passage. The passage notes that “… risk is the product of hazard,” which is the opposite of stating that hazards result from risks. You can also eliminate Choice (A) because it claims that risks occur naturally while hazards result from human interaction; the passage states that the opposite is true. So, you’ve narrowed options down to Choices (C), (D), or (E). Choice (C) makes another false statement — nowhere in the passage does the author report that hazards, and not risks, can lead to disasters. Rather, he implies that the two together increase the risk of a disaster. Choice (D) sounds like a serious contender, and the first two lines of the third paragraph back it up. Just to be sure, however, take a look at Choice (E). The words “harder to quantify” may jump out at you because you find them in the final paragraph, but upon more scrutiny, you can determine that the author claims that “economic impacts,” not risks, are hard to quantify. Choice (D) is the best answer.
A. describing the causes and impacts of natural disasters
Eliminate answers that contain information that appears in just a part of the passage rather than the whole. The author doesn’t discuss economic impacts until the final paragraph, so Choice (B) isn’t a strong contender for the passage’s primary concern. The role of human beings in risk is covered early in the passage, but the passage also discusses that some hazards are simply beyond human control, so Choice (C) isn’t the best expression of the primary purpose. Choice (D), too, only tells part of the story; in addition to loss of human life, the passage discusses financial costs. Choice (E) is also inaccurate; the author notes that hazards aren’t under human control, but risks, at least to some degree, are. By process of elimination, Choice (A) is the best answer. This general summary statement incorporates information discussed in the entire passage.
E. It applies statistical data to emphasize the magnitude of damage created by natural disasters.
Choice (A) is incorrect because the numerical information in the fourth paragraph relates to human lives lost rather than economic impacts. Choice (B) mentions a specific detail in the fourth paragraph, but the detail provides supporting evidence rather than the primary purpose of the paragraph. Choice (C) provides a better description of the function of the third paragraph than the fourth. And you can eliminate Choice (D) because its statement isn’t true; the paragraph gives numerical data about one event rather than sensory detail about several. Only Choice (E) offers a plausible explanation for the function of the fourth paragraph in relation to the rest of the passage. The paragraph provides statistics regarding a specific event that provides an example of the colossal destruction a natural disaster can cause.
E. Areas of high hazard, such as Japan’s Tohoku coast, may have a lower risk of natural disaster costs than areas where hazard incidents are lower.
The third paragraph clarifies that the highest cost risk isn’t always associated with the greatest hazard. Places with less hazard risk may experience greater costs because the hazard affects more people or the area is less prepared to withstand damage. Therefore, Choice (E) is correct.
The passage doesn’t provide clear data regarding the number of reported and unreported deaths in the tsunami and earthquake disaster, so you can’t definitively compare number of deaths in Choice (A). The passage says that the tsunami in 2004 caused many more deaths than average, but it doesn’t say the same for the 2010 Haiti disaster, so Choice (B) is wrong. Because you don’t have actual data for deaths due to natural disaster in Japan, Hawaii, and Haiti, you also can’t pick Choice (C). The passage suggests that both economic costs and death totals are unreported for natural disasters, but it doesn’t compare the two, so you can’t justify Choice (D).
D. must finish constructing, cleaning, and safety-proofing its interior
Two primary problems exist in this sentence. The easiest to spot is likely the use of it’s (the contraction of it is) instead of the possessive form its. Eliminate Choices (A) and (C). Then check parallel structure in the underlined list. All projects must share the same grammatical form. Choices (B) and (E) improperly mix the noun construction with the gerund forms of cleaning and safety-proofing, and Choice (E) improperly defines construction as cleaning and safety-proofing the interior. The only answer choice that corrects both issues is Choice (D).
B. continent’s past begin with Europeans striding ashore, claiming this “newfound land” and its human inhabitants for their respective empires
As you compare answer choices, note that some present the plural form continents’ and others make it singular. Because it’s preceded by the singular this instead of the plural these, you know there is just one continent and Choices (A) and (C) are out of contention. Another discrepancy is whether the verb should be the plural begin or the singular begins. The subject is plural — accounts — so the answer needs to contain the plural form begin to agree with the subject. Choices (D) and (E) are wrong. Yet another issue is whether the last pronoun should be the plural their or the singular its. The respective empires belong to the Europeans, which is plural, so their is proper, verifying that Choice (B) is correct.
D. is still used today by many Ethiopians to feed themselves
Because the subject of the sentence (injera) is singular, the proper verb is the singular is rather than are. Eliminate Choices (A) and (B). Choice (C) introduces an unnecessary pronoun, it, that also causes the sentence to be improperly punctuated. The addition of it creates another independent clause, and independent clauses linked by a conjunction such as and must also be separated by a comma. Between Choice (D) and Choice (E), (D) is the better-constructed option. The adverb today describes when the bread is used and therefore should occupy a position close to the verb used, as presented in Choice (D). Choice (D) also eliminates the redundant inclusion of a second use. You already know that Ethiopians use the bread; you don’t need to state the action again. Choice (D) is the properly worded answer.
A. The degree of erosion to which a coastline is subject is related to the shape of the sea bottom.
Choice (A) makes sense because the impact of waves is related to the shape of the sea bottom, and the coast’s erosion is related to the impact of waves. Choice (B) is wrong because the statements only state the factors (wind velocity and fetch) that influence wave size; there’s nothing to suggest that wave size stays close to an average. Choice (C) doesn’t work; if fetch is the length of the surface of the water, it shouldn’t be related to the shape of the sea bottom. Choice (D) is wrong because the size of waves comes from wind and fetch, not the shape of the bottom. Choice (E) looks wrong, too. Wind velocity creates size of waves, size of waves affects impact, and impact affects erosion, so average velocity of wind playing no role in erosion doesn’t make sense. Choice (A) is the best answer.
A. It is a specific example of a general condition described in the course of the argument.
The argument is that because patients need medical care and hospitals, regardless of what those services cost, hospitals and doctors rather than insurers bear the brunt of cost-containment measures; the MRI statement provides an example. Choice (A) is a good answer; the statement is a specific example of capital demands (MRIs and buildings) of the general condition of fiscal discipline described in the argument. Choice (B) doesn’t work because the MRI statement doesn’t counter an attack. Choice (C) isn’t as good an answer as Choice (A). The author’s claim or conclusion is that health insurers are still profiting from healthcare while doctors, hospitals, and patients are being increasingly squeezed, but the MRI statement doesn’t indirectly support that claim. Choice (D) doesn’t work. Patients’ needing treatment isn’t a social side effect but a normal event that remains consistent, regardless of changing circumstances. Choice (E) is wrong; the MRI statement doesn’t introduce the conclusion about the immunity of health insurers. Choice (A) is correct.
C. among them, the 20 players were only able to raise about 70 percent of the cost
Use between when discussing two entities, and use among when referring to groups of more than two. Therefore, you can easily eliminate Choices (A) and (B). Choice (D) has a verb tense problem; the present perfect tense have raised suggests that fundraising efforts are ongoing. Choice (E) changes to the passive voice “cost was raised by 20 players” for no apparent reason. Active voice is generally a better construction than passive voice. Choice (C) correctly changes between to among without creating new errors.
E. Allowing employees to take leave for family matters reduces absenteeism, improves morale, and surprisingly increases productivity because the employees who are granted leave tend to work much harder and more efficiently when they come back to work.
To weaken the argument, look for an answer showing that allowing family leave doesn’t hurt productivity or perhaps even helps it. Choice (A) doesn’t affect the argument because standard of living isn’t an issue, and it doesn’t mention workplace productivity. Choice (B) could arguably weaken the argument because it provides evidence that workers may not abuse the privilege of leave — fathers aren’t taking family leave at all, which weakens the conclusion that workers would work less if they had leave. On the other hand, if taking paternity leave angers co-workers, that strengthens the conclusion that family leave hurts workplace morale, so this isn’t the best answer. Choice (C) strengthens the argument by showing that FMLA leave costs the employer money. Choice (D) also strengthens the argument by illustrating the destruction caused by one employee leaving for a while. Choice (E) weakens the argument. If employers are worried about productivity and morale, this choice says that allowing leave actually increases productivity and morale. Choice (E) is the right answer.
D. were on board with the new uniforms for the girls’ basketball team, but the team had made its choice
First, eliminate Choices (A) and (B) because they pair the singular verb was with the plural subject all. Then eliminate Choice (C) because it uses the plural pronoun their to refer to the singular noun team. Between Choices (D) and (E), (D) is the better option. Choice (E) contains the present perfect tense “has made,” but the events take place in the past as indicated by the initial past-tense verb. Choice (D) is the winner.
B. forcing many families to make the unfortunate choice between having a roof over their heads and receiving healthcare
The proper conjunction is and for linking two elements one is choosing between. So Choices (A) and (C) are wrong because they include the conjunction or. Making a choice between one element or the other is incorrect. Choice (D) replaces “to make” with “with making,” but the proper preposition to pair with force is to; one is forced to take action rather than forced with taking action. Choice (E) incorrectly swaps between for among, which doesn’t work for a two-item choice.
A. Operating systems with generous amounts of memory are less susceptible to crashing, even when applications are poorly written.
Okay, you want to find the four answers indicating that operating systems are responsible for the smooth functioning of applications and are able to somehow manage their memory problems. The best way to do this is by process of elimination. If you can find four answers that show the operating system handling applications’ memory issues, then the answer that’s left over should be correct. Choice (B) helps the conclusion because it shows that operating systems are responsible for handling the memory used by individual applications. Choice (C) helps because it shows that operating systems can spot overuse of memory and stop it. Choice (D) helps because it tells you that programmers should know how to program an operating system that can prevent memory errors, which means all operating systems should be able to do this. Choice (E) helps the conclusion because it describes what an efficient operating system should be able to do. Choice (A) is the only answer that doesn’t put responsibility for memory management on the operating system; adding memory to the computer evidently can let the operating system off the hook. Choice (A) is the right answer.
E. If people see online images of items in the museum’s collection, they will no longer be interested in seeing the collection with their own eyes.
The argument seems to assume that if people see the images online, they won’t have any interest in visiting in person. Choice (A) isn’t the point because the author of the argument isn’t worried about damaging the images. Choice (B) doesn’t work because the author doesn’t mention a concern for decreased revenue. Choice (C) likely isn’t the author’s concern. He isn’t specifically worried about the extent of online distribution but rather its effect. Check the remaining answers to see whether you have a better option. Choice (D) isn’t his concern, either, because he doesn’t mention quality issues. Choice (E) is the best answer. The author is worried that online publication of the images will remove the incentive to visit the actual museum in person.
C. the number of residents has increased so considerably
Eliminate Choices (B) and (D) because they pluralize numbers. There is a number of residents rather than numbers of them. Choice (A) has the singular form number, but incorrectly pairs it with the plural verb have. That leaves you with Choices (C) and (E), and Choice (E) unnecessarily adds been to the verb and creates an awkward construction by moving so after considerably. Choice (C) is the best answer.
D. Risks are affected by human actions that increase or decrease vulnerability, such as where people live and how they build.
This sentence requires you to choose between affect and effect. The sentence uses the word as a verb, so you need to pick an option with affect rather than effect. Choices (A) and (C) can’t be right. You can also eliminate Choice (B) because it uses like to mean “for example.” The better option is “such as,” which leaves you with Choices (D) and (E). Choice (E) switches that to which, but which introduces nonessential clauses and therefore should be preceded by a comma. The descriptive clause is essential, so that is the proper pronoun and Choice (D) is the answer.
B. executive functioning
Answering this question is pretty cut and dried. The second paragraph indicates that learning how to resist distraction is part of what it takes for a child to recognize and work toward a goal, which is defined as — you guessed it — executive functioning. Choices (A), (C), (D), and (E) are all touched upon to some extent in the passage, but the definitive answer is Choice (B).
A. emphasize that school readiness regards the process as much as the results
The author’s key point is that school readiness is about assessing a child’s ability to learn rather than relying on test results and the like to determine knowledge. When they’re in a K–12 school setting, kids have to demonstrate “school readiness” through the results of academic testing and grades. Choice (A) expresses this point best. Choice (B) is wrong because although the author notes the difference between the guiding principles of school readiness and those used by K–12 school systems, nothing in the passage suggests that she considers those of the latter “failings.” Choice (C) essentially makes the same argument as Choice (B), so you can knock that option from contention, too. Eliminate Choice (D); no evidence exists that this passage is about the author’s opinion. Choice (E) is out, too. Although the author deals with cognition in the second paragraph, this factor isn’t the primary reason for making the more general distinction between school readiness and K–12 guidelines. Stick with Choice (A).
D. paying attention to the teacher
In the second paragraph, the author mentions a growing emphasis on executive functioning skills in the concept of school readiness. She then defines executive functions as those pertaining to working memory, attention control, attention shifting, and response inhibition. She gives the example of paying attention to the teacher as an indication of ability to resist distractions. Because paying attention to the teacher is an indication of executive functioning, this skill has likely been one of those on which there has been a “growing emphasis,” and Choice (D) is best.
Choice (A) is easy to eliminate; performance on achievement tests is associated with the K–12 system. The other answers relate to school readiness factors mentioned in the last paragraph and aren’t included as part of executive functioning. Choice (B) is associated with language skills, Choice (C) is defined as a socioemotional skill, and Choice (E) is part of the physical health domain.
E. socioemotional skills
In the final paragraph of the passage, the author mentions cooperation with teachers and peers and developing social relationships as examples of socioemotional skills, which is Choice (E). Motor skills pertain to the physical health domain. As for Choices (B) and (C), the author places them into the language skills category. Strong executive functioning skills are discussed in detail in the second paragraph, where the author notes that these skills help kids work toward achieving specific goals. Choice (E) is the best bet.
A. Spousal and marital difficulties were formerly responsible for many premature returns from foreign assignments.
If helping spouses has improved expatriate retention by such a huge amount, then unhappy spouses must have previously been responsible for lots of premature returns. Choice (A) looks like a good answer. If unhappy spouses contributed to employees’ leaving international assignments, helping spouses adjust would improve the situation. Choice (B) is wrong. If spouses are already thrilled with the international experience, their dissatisfaction is unlikely to contribute to employees’ leaving their overseas posts. Choice (C) would support the argument, but it's too specific to be a necessary assumption on which the conclusion depends (there could well be other reasons why spouses are dissatisfied). Choice (D) doesn’t explain why helping spouses has improved retention. Choice (E) provides an example of what companies are doing to help spouses but isn’t the assumption that links the argument’s premises to the conclusion. Choice (A) is the best answer.
E. after another, nor does it make its predecessor obsolete
The conjunction nor should be preceded by a comma when it joins two independent clauses, so Choices (A) and (C) improperly punctuate independent clauses joined by a conjunction. Choice (B) doesn’t help; it changes the last part of the sentence to an independent clause and therefore creates a comma splice. It also uses neither incorrectly. The conjunction neither has to be followed by its partner nor. Choice (D) creates the same conjunction error, and it also has a punctuation problem. Joining independent clauses in the same sentence with no punctuation creates a fused sentence. Choice (E) is the only answer that uses conjunctions properly.
A. resenting all their advances, refusing to let them lay hands on him, menacing them with bared fangs and bristling hair
Check the answers for parallel structure. The list of the dog’s unsociable traits is presented in –ing form, so eliminate Choices (C) and (D) because they break the structure with the past-tense form menaced. Pay attention as you examine Choice (B); it can’t be correct. Bristling is used as an adjective to describe the dog’s hair rather than a noun to end the list of traits. So the comma before the and is incorrect. The options are down to Choices (A) and (E). Choice (E) contains unnecessary words. The use of their advances is more succinct than the advances that they made, so Choice (A) is a better answer. Don’t get caught up with the lack of a comma and conjunction before the last element of the list. The sentence takes a bit of poetic license with standard list form, and no option exists to change the format.
E. The meadow voles that had the prairie vole gene implanted in them were released into and observed in the same habitat in which they had previously lived.
Look for information that supports the assumption that the meadow voles’ change in behavior was caused by the implanted gene. Choice (A) is wrong. The choice doesn’t relate the effects of the hormone to the gene that makes meadow voles monogamous. Choice (B) explains what’s up with prairie voles but not with meadow voles, and neither’s genes are mentioned. Choice (C) explains why meadow voles are typically promiscuous but says nothing about whether a gene plays a part in that. Choice (D) says nothing about whether the transferred gene is the cause of the monogamous behavior. Choice (E) provides the most support for the assertion that the scientists’ work with genes was the factor that turned the formerly promiscuous meadow voles into models of monogamy because it rules out a possible other important factor that may have explained the change (different surroundings). Choice (E) is the correct answer.
C. Women who want to have children increasingly seek to delay doing so for many varied reasons.
The conclusion is that predicting when menopause will occur will make a difference to women planning when to have children, which must mean that not knowing when menopause will occur makes it difficult to plan. Choice (A) is wrong because it doesn’t explain why predicting menopause will help anyone. Choice (B) just provides general information about menopause. Choice (C) may be right — it provides a reason that women would benefit from knowing when they will experience menopause (they’re delaying longer, so they need to know how long is too long to delay). Choice (D) isn’t relevant because the argument is about how accurately predicting the onset of menopause affects childbearing decisions, not how likely a woman is to conceive in the years immediately prior to menopause. Choice (E) is just information about ovaries, not an explanation of how this test will help make family planning decisions. Choice (C) is the best answer.
E. excelled not only academically but also athletically
To maintain parallel structure, the two elements joined by the conjunction but must share the same grammatical form. So athletically is a better choice to pair with academically than is “in athletics.” Eliminate Choices (A) and (D). The conjunction not only must be paired with either but also or but, so Choice (B) is out. Choice (C) contains the awkward phrasing “engaged in excellence,” which is less precise than simply excelled. Choice (E) is the best answer.
D. Employers assume that high-school graduates generally have a much higher level of mastery of academic subjects than those who earn GEDs.
The argument suggests that a GED is just as good as a high-school education; look for an answer that contradicts that. Choice (A) doesn’t work. You don’t want evidence showing the benefits of earning GEDs. Choice (B) doesn’t pose a problem. If universities accept GEDs, that’s more evidence that they’re as good as diplomas. Choice (C) actually strengthens the argument. Choice (D) does weaken it. If a GED might put one at a disadvantage in the job market, that’s a reason to stay in school. Choice (E) doesn’t strengthen or weaken the argument. Choice (D) is correct.
D. explain how attention to cybersecurity impacts companies’ technological innovation
Perform a quick scan through the answer choices and see if any catch your eye. Of those available, only Choice (D) specifically references the relationship between cyber-attacks and technological innovation, which was a major part of the subject matter. Choices (A), (B), and (E) similarly suggest that the main idea regards the hackers’ success, but the passage is less about hackers and more about how companies react to hacking. And Choice (E) even suggests that hacking is heroic. Choice (C) presents the primary purpose of the first paragraph but not the entire passage. Choice (D) is the only option that incorporates ideas that appear throughout the passage.
C. weighing business outcomes and risks
The third paragraph clearly states that indirect losses and the cost of defending against cyber-threats reduce the benefits of technology investments, so you can eliminate Choices (B) and (D). Likewise, in the second paragraph, you find evidence to support that theft of intellectual property is a risk of increased global connectivity created by technology investment, so Choice (A) is out. The last sentence of the second paragraph also suggests that the way that companies approach cyber-threats — reacting to them only when they occur — is costly and will likely result in more cyber-attacks. Therefore, Choice (E) likely decreases the benefit of investing in technology. The passage doesn’t indicate that the mere act of weighing risk and reward in itself incurs cost, so Choice (C) is the answer that has the least chance of decreasing the potential gains of investing in technology.
B. combat problems after they have occurred
When the author references companies’ “siloed and reactive approach” to cybersecurity, he does so after his discussion about how investing in technology comes with inherent cybersecurity risks. The implication is that companies take on these risks without a clear plan for protecting against them, and therefore, the hackers seem to be winning the battle against business security systems. Choice (A) incorrectly asserts that companies are performing their due diligence when it comes to trying to prevent cybersecurity, so you can likely count this one out. Choice (C) mistakenly gives the credit to companies, so you can eliminate that one for the same reason you knocked out Choice (A). The passage doesn’t quantify what constitutes “too much” investment, and regardless of whether Choice (D) is true, the passage infers that this “siloed and reactive approach” is not so much about spending money but about waiting for issues to develop rather than attempting to prepare for them. Finally, Choice (E) suggests that companies are moving full speed ahead with unnecessary technological innovations and advancements, which is contradictory to the information in the rest of the passage that suggests companies are becoming slower to innovate because of cybersecurity concerns. Choice (B) correctly indicates that companies’ reactive approach waits for problems to happen before considering the potential risks of technological investment. It’s the best answer.
E. an outline of a streamlined manufacturing process
The second paragraph specifically links intellectual property to a new product life-cycle management system. The answer that relates most directly to proprietary product information is Choice (E), information regarding a proprietary product producing process. Choice (A) describes intellectual property but not that which would likely be leaked in a new product life-cycle management system. The other choices aren’t examples of intellectual property.
A. Increased global communications mean more risk for security breaches.
The passage reveals that increased global connectivity created rewards as well as risks; Choice (C) overstates its risks and Choice (D) understates the rewards, so eliminate Choices (C) and (D). Choice (B) is incorrect. According to the passage, global connectivity makes companies more vulnerable to hackers, but dealing with the attacks is the primary reason for delayed technological innovation, not general connectivity. The second paragraph links tight connections to greater vulnerability rather than to greater power over hackers, so Choice (E) is wrong. The best answer is Choice (A). The author mentions global connectivity to set up the paragraph about the risks associated with increased access.
D. jumps to the conclusion that the defect in the glasses must be due to the optometrist’s lack of skill
The conclusion is that the optometrist is incompetent; the evidence is that one lens pops out regularly. But there’s no evidence that that’s because of the optometrist’s lack of skill. Choice (A) is wrong. Although giving the optometrist a chance to defend himself would be nice, it’s not a fault of the argument that the speaker doesn’t provide one. Choice (B) is wrong because other potentially unskilled optometrists have no bearing on the skills of the one in question here. Choice (C) doesn’t work. The author doesn’t mention any particular techniques. Choice (D) may be the answer. The author does jump to a conclusion here without making a connection between the glasses and the optometrist’s skill. Choice (E) is wrong because the author doesn’t suggest that sabotage played a role in the bad glasses. Choice (D) is the best answer.
C. The statement highlights the importance of this discovery because it disproves a long-held theory about hibernation.
This discovery of an animal that hibernates in hot weather may be groundbreaking, especially if previous scientific wisdom held that hibernation only happens in cold weather. Choice (A) is wrong because the belief being challenged isn’t that primates never hibernate but that animals never hibernate in the heat. Choice (B) isn’t right because the assertion isn’t an accusation of any kind. Choice (C) makes the most sense because it’s an important discovery. Choice (D) is wrong. The argument never disputes the conclusion that the behavior is in fact hibernation. Choice (E) doesn’t work because the argument doesn’t set up a rival theory in a deliberate ploy to attack it. Choice (C) is right.
B. we intuitively try to imagine what they would have looked like in real life and to visualize their physical features
The easiest issue to spot is the improper use of “he or she” to refer to the plural noun peoples. The proper plural pronoun is they, so Choices (A) and (C) are out. Choice (D) corrects the pronoun problem, but it replaces “their physical features” with the wordy “what their physical features were like,” a phrasing that is not only awkward but also constructed differently from the rest of the nouns in the series. Choice (E) improperly changes the verb from the conditional perfect tense “would have looked” to the conditional present tense “would look,” a construction that projects the appearance of past peoples in the yet-to-be-realized future rather than from a place in the past. Choice (B) applies the proper pronoun without creating additional errors, so it’s the best answer.
A. My European client calls once a week, always in the evening, after everyone has left the office. I’ll be sure to get his messages if I turn on my telephone’s answering machine once a week.
The flaw in the argument is the mistaken belief that the odds of an event occurring can tell you how often you need to do a certain act. Odds of 1 in 1,000 don’t mean that every 1,000th trip will realize a certain event. It means that an accident could happen in any trip out of 1,000, and you can’t predict which one. The flawed reasoning in Choice (A) is similar; turning on the answering machine on just one particular day won’t necessarily catch a weekly phone call because the call could come on any day of the week. Choice (B) is wrong. The conclusion is mistaken but in a different way from the original argument. It’s about proportionality, not probability. Choice (C) isn’t the same as the original argument because you’re not trying to guess which one of the 1,000 games will result in the jackpot; instead you’re covering them all. That’s closer to wearing the helmet for all 1,000 rides on the assumption that one of them will involve a wreck. Choice (D) is totally wrong because the second sentence is nothing like the original argument’s conclusion; it doesn’t state how many times people in cars should wear seat belts based on seat-belt statistics. Choice (E) is flawed but not in the same way as the original argument. The flaw would be more similar to the original argument if the MBA student applied to only one of 20 business schools because the odds are 1 in 20 of being chosen. Choice (A) is the closest and is correct.
A. Even though Carter had fewer quarters in his piggybank than did his brother Clark, Clark had less money overall.
This question requires you to access your knowledge of the correct usage of fewer and less. Use fewer when referring to plural entities, such as M&Ms, students, sunflowers, and quarters. Use less to reference singular entities, such as water, damage, appreciation, and money. So the proper construction in this sentence is “fewer quarters” and “less money”; eliminate Choices (B), (C), and (D). The language in Choice (E) is potentially confusing. The descriptive phrase “in his piggybank” seems to refer to Clark rather than the quarters. Choice (A) presents clearer construction.
C. Rugby is somewhat like American football in that both involve downs, tackles, and touchdowns, but it also combines elements from other sports, such as soccer and hurling.
Because the sentence makes a comparison between only two sports, both is proper and all is improper. Eliminate Choices (B) and (D). Choice (E) contains a subject/verb agreement problem: the plural noun both shouldn’t be paired with the singular verb involves. The difference between Choices (A) and (C) is the use of “like” or “such as.” Generally, you use like to compare nouns rather than to introduce examples. So the comma before like in Choice (A) is a big clue that it’s used incorrectly. The comma sets up examples. Therefore, Choice (C) is a better option than Choice (A).
Answers at a Glance
Section 3: Quantitative
- E
- D
- A
- D
- D
- D
- C
- C
- A
- C
- B
- B
- D
- D
- A
- A
- C
- B
- B
- E
- D
- A
- D
- C
- B
- E
- D
- B
- C
- D
- A
- C
- C
- B
- A
- C
- C
Section 4: Verbal
- A
- C
- D
- A
- E
- E
- D
- B
- D
- A
- A
- C
- E
- D
- B
- A
- E
- C
- D
- B
- A
- D
- E
- A
- E
- A
- E
- C
- E
- D
- D
- C
- B
- E
- A
- D
- C
- B
- A
- A
- C