Chapter 19

Practice Exam 2: Answers and Explanations

Analytical Writing Sections

Give your essays to someone to read and evaluate for you. Refer that helpful person to Chapters 14 and 15 for scoring guidelines.

Section 1: Verbal Reasoning

1. B. A dirge is a funeral hymn. All the other choices refer to songs but are less descriptive of the type of song you’d hear at a funeral.

2. E. A tirade is a long, violent speech, something a person may deliver in the midst of perceived injustice. Speech and discussion are too neutral to be correct. Homily is more like a sermon you hear at a church service, and although Gwendolyn’s speech may have triggered an argument, nobody launches into an argument.

3. A, E. The gustatory system is responsible for the sense of taste, and a more discerning (perceptive) palate is able to distinguish subtle differences. The lymphatic system fights infection, while the digestive system breaks down food. For the second blank, discrete (distinct) doesn’t work, and distended (swollen) isn’t even in the ballpark.

4. A, F. A tsunami is a wave that would inundate (flood) the resort, causing a loss of property that would act as a catalyst (stimulus) for any renovation. Choice (C), drowned, fits the meaning but isn’t the proper word. Because the resort isn’t a living thing, it can’t drown. Dissembled (concealed) isn’t even close. Although a loss of property could be a symbol for something, it’s not a very good symbol for much needed renovation. A loss of property could result in many mendicants (vagrants), but the word just doesn’t make sense in ­context.

5. C, D. Castle walls that are impervious to attack cannot be penetrated, and after several attempts to break through the walls, an enemy’s energy and enthusiasm would begin to flag (weaken). Walls cannot be amenable (agreeable). The walls may be impeccable (flawless), but because they frustrated the enemy’s attempts to get inside, impervious is a better choice. As for the other choices for the second blank, the enemy’s enthusiasm wouldn’t rally (become stronger) as a result of failure, nor would it flee (run away), although the enemy certainly would.

6. C, D, G. Aware of the burgeoning (growing) debt, congress would impose an austerity (disciplined) program to curtail (reduce) spending. For the first blank, pervasive (widespread) would be a good second choice, but shrinking is the opposite of what’s needed here. For the second blank, spending would be a decent second choice, but not quite strong enough and a little redundant because it’s used at the end of the sentence. Defense definitely doesn’t fit. For the third blank, attenuate may be okay, but it means something more like to decrease in strength. Desiccate (dehydrate) doesn’t make the cut, either.

7. B, F, H. A discrepancy (difference) between a person’s demeanor and statement would make officers suspicious; a correlation or relationship, both meaning connected, would not. The word but provides a clue that although the officers were suspicious, they couldn’t do much, so you know that their evidence would be unsubstantiated (without support), not corroborated (confirmed) or vetted (examined closely). This means their case would be tenuous (shaky) at best, not compelling (convincing) or conclusive (certain).

8. C. The second paragraph, third sentence states that experts recommend profiling by behavior and intelligence.

9. A. If true, Choice (A) describes a solution that improves security without compromising civil liberties. Choice (B) may be true, but the passage cites profiling as a violation of civil liberties. Choice (C) also may be true, but precertification requires a background check, which some people may consider a violation of civil liberties. Choices (D) and (E) fail to address the question.

10. A, C. The third sentence states that the Cold War shaped international and domestic politics and cultures, and the fourth sentence states that war has influenced the development of new states. Choice (B) is wrong, because sentence six presents civil wars and conflicts as causes, not effects of war.

11. E. Terrorists and rogue states are mentioned only in respect to the possibility of them acquiring nuclear weapons, while nuclear proliferation is singled out as a threat in itself. According to the passage, the Cold War has ended, although nobody seems to have let the Russians know, and the proliferation of civil wars is mentioned not as a threat but only as an agent of change in the developing world.

12. D. The sixth sentence describes the goal stated in the first sentence — to position yourself as an expert with useful information, so the marketplace will always need what you have to offer.

13. B. The fourth sentence answers this question: “. . . [T]here is an important difference between somebody who is selling something and somebody who is an expert.” Most of the choices are differences mentioned in the passage but are not the difference between marketing and UnMarketing.

14. C. If the prices of health services are more than 50 percent higher in the United States, then this accounts for the fact that the United States spends more than 50 percent as much per capita on healthcare than most European countries, undermining the argument that poor diet is responsible for the difference.

15. B, D. Tacit and implicit both indicate that the coach approved without having to say so. Perhaps during practice the coach had expressed a desire that the team play with more heart and throw caution to the wind. Choices (C), cautious, and (E), enthusiastic, both are fitting words to describe approval but neither has a suitable match in the list. Ambiguous (unclear) and salubrious (healthy) obviously don’t fit.

16. E, F. As a sumo wrestler, Kazuki would need to be fairly robust so people may be surprised to see him so abstemious (moderate) or ascetic (prone to self-denial) when he was eating. Choice (D), courteous, doesn’t fit, and the other three choices all mean the opposite of moderate.

17. C, D. Embellishment and hyperbole both mean exaggeration and carry the positive connotation that the exaggeration is meant to make something better or more interesting. Choice (F), overemphasis, also means exaggeration, but in a negative way. None of the remaining choices even come close: sarcasm (irony), allegory (parable), and ennui (boredom).

18. A, D. Pugnacious means aggressive and truculent means defiantly aggressive. Irascible (irritable) is nearly a match, but the two correct choices are better. Choices (B) and (C), lackadaisical (easy-going) and quiescent (calm) are nearly identical in meaning, but they don’t fit the sentence; because the other puppies in the litter were gentle, this one would stand out as being the opposite. If the puppy were soporific, it would tend to calm those around it.

19. B, C. If Mary seemed to be up to something (in a bad way), then her offer to help would come across as disingenuous (think genuine with a dis in front of it) or duplicitous (think dupli as two or two-faced). Choices (A), sincere, and (F), authentic, are nearly the opposite of what’s needed here, both meaning genuine or real. Hypocritical is close but has more to do with pretending to hold a certain belief.

20. E. The passage identifies several features of the global environment that are sending out warning signs. All the other choices focus on each warning sign and aren’t broad enough to be summaries of this passage.

Section 2: Quantitative Reasoning

1. C. To get the area of triangle ABC, you need the base and the height. Because the radius of the circle is 1, side CB is 2. You already know AB = 1, making the right triangle a 30-60-90 triangle. Because the side ratio of this triangle is 1, 2, , the base is 1 and the height is .

And is the area of a triangle, making Quantity A equal to

Quantity B.

2. B. To get the weighted average, add the product of 10 and 120 to the product of 20 and 90. Divide by the total number of test scores (30), and the weighted average is 100.

3. D. If you assumed the highest possible value of n is 14, making , then you fell

for the trap and chose Choice (B). However, because n isn’t necessarily an integer, it could be equal to 14.999, which is greater than 0.72 when placed over 20. Because n could also

be 11, could be either less than or greater than 0.72.

4. A. If cups of lentils are required to make six servings, and servings, the

amount of lentils required to make 15 servings is

Because is more than 3, Choice (A) is the correct answer.

5. C. Remember how to find the area of a trapezoid? Average the two bases and multiply by the height. Because the bases are 9 and 11, the average is 10. Multiplying by the height gives you 50, which is the same as the area of the rectangle.

6. C. Call the interior angles of the triangle A, B, and C, according to the labels on the drawing. Because the angle supplementary to angle C is 2x, angle C equals 180 – 2x. The three angles of any triangle total 180, making angle B equal to 180 minus the other two angles, or 180 – x – (180 – 2x), which can also be written as 180 – x – 180 + 2x. The 180s cancel, and –x + 2x becomes x. Now you know two of the angles are equal, making the triangle isosceles and segments AC and BC equal.

7. A. The equation x2 – x – 6 = 0 becomes (x – 3)(x + 2) = 0, making the roots of the equation 3 and –2. (The roots are the two values for x, either of which makes the statement true.) The sum of these two numbers total 1, making Quantity A greater than Quantity B. If you thought the roots are –3 and 2 and chose Choice (C), then you fell for the trap by thinking that – 3 and + 2 in the equation are the roots.

8. B. The median is the middle number, but if you have two middle numbers, you average them. The two middle numbers are 5 and 6, which averages to 5.5. The range is the distance between the lowest and highest values. The range of this set, being 8 – 3, is 5.

9. A. The units digit of any product depends on the units digits of the two numbers being multiplied. To find the units digit of 219,473 × 162,597, just use the units digits of the two numbers: 3 and 7. Then, 3 × 7 = 21, so the units digit of 219,473 × 162,597 is 1.

10. E. To find the slope of the line, convert the equation to the slope-intercept formula, which is y = mx + b. Solve for y, and m is the slope.

11. A, B, C, and D. These four answer choices are correct because 15 to 30 percent of $50,000 is $7,500 to $15,000. In this type of question, you select all of the correct answer choices.

12. 61. Set the ratios up as baseballs:gloves = 2:9 and baseballs:bats = 5:3. Because baseballs are in both ratios, once as 2 and once as 5, the actual number of baseballs has to be a multiple of both 2 and 5. The question asks for the lowest number, so the lowest multiple of 2 and 5 is 10. If the ratio of baseballs to gloves is 2:9, and there are 10 baseballs, there must be 45 gloves (multiply both sides of the ratio by 5). Also, if the ratio of baseballs to bats is 5:3, and there are 10 baseballs, there must be 6 bats (multiply both sides of the ratio by 2). Add these up for the number of sporting items: 10 baseballs + 45 gloves + 6 bats = 61 items.

13. 24. If the average of x, y, and z is 5, then x + y + z = 15. To find the average of the expressions 4x + y, 2y – x, and 3z + 27, add them up and divide by 3. The equations 4x + y, 2y – x, and 3z + 27 simplify to 3x + 3y + 3z + 27. Because x + y + z = 15, 3x + 3y + 3z = 3(15), or 45. Add the 27 for a total of 72. And 72 ÷ 3 is 24.

14. D. If the central angle is 45 degrees, then the resulting arc is also 45 degrees, which is of

the circle. If the radius of the circle is 8, then the circumference is 16π. And of 16π is 2π.

15. D. On Test B, a score of 300 placed the examinee in the 94th percentile ranking. This means that the examinee scored higher than 94 percent of the other examinees. It also means that 5 percent of the examinees scored 300, which is 1 out of 20 examinees.

16. E. In the first graph, the line for Test A examinees crosses the 40,000 line at two points: 30 and 210. However, 30 isn’t an answer choice, so if you chose Choices (A) or (B), you fell for the trap of not looking far enough on the chart. This examinee could also have a score of 210, which is an answer choice and the correct answer. Choice (C), 90, is the group of 40,000 like scorers on Test B, another trap. Choice (D), 180, is the score at which the two testing trend lines cross, but has nothing to do with a cohort of 40,000.

17. C. Using the line chart, approximately 75,000 examinees scored 100 and 80,000 scored 110. By jumping from 100 to 120, the examinee surpasses about 155,000 examinees.

18. E. The area of any circle is πr2. Because the radius of the original circle increased by

50 percent, the new radius is . Plug the new radius into the area formula, or square it

and multiply by π for .

19. C. If the circle is inscribed within the square, then the diameter of the circle is equal to one side of the square, which is 6. This makes the radius of the circle 3 and the area 9π. The

circle occupies of the square, which reduces to .

20. 5. The volume of a cylinder can be found with πr2h. You’re given the volume and height, so back solve to find the radius. Begin with 50π = πr22. Eliminate the π and 2 from both sides for 25 = r2, making the radius 5.

Section 3: Verbal Reasoning

1. B. A tome is a large, scholarly book or a volume of such a book, so the volumes that comprise the Oxford English Dictionary definitely meet the criteria. Because the size and weight of the tomes is specified, none of the other answer choices comes close. For future reference, a novella is a short novel — longer than a short story, shorter than the average novel.

2. E. Officious means intrusive or meddlesome. Banal (dull) may be a good second choice if the couple moved anywhere else, but because they moved to a remote location, presumably where neighbors would be more distant, officious makes more sense. If the neighbors had been accommodating or sincere, the couple would have little reason to move. Nor would they likely move because the neighbors were ambivalent (wishy-washy).

3. A, E. People who are capricious tend to change their mind easily, so they have a penchant for or tendency to abandon their shopping carts before checking out. For the first blank, predictable doesn’t work, because it’s the opposite of capricious, and fatuous means silly or inane. For the second blank, neither inkling (hunch) nor passion (desire) make sense in this context.

4. C, D. Because the compensation was commensurate (proportional), Jerry wouldn’t quibble (argue) over the deadlines. For the first blank, discordant (conflicting) means nearly the opposite of commensurate, and pursuant means in agreement with (as in the terms of a ­contract). Acquiesce and concede both mean to go along with, neither of which fit the ­connotation of this sentence.

5. A, F. Because the audience was impatient, it was more likely intractable (difficult to control) than imperturbable (calm and cool) or indolent (lazy). If everything the speaker said to silence the rabble didn’t work, it must have exacerbated the situation (made it worse), not precipitated (triggered) or exonerated (forgave) it.

6. C, D, G. Reading the sentence from the end, you know that the teacher was concerned about student safety, so safety issues would have superseded (take precedence over) all other concerns, and not preceded (come earlier) or negated (canceled) them. If safety became a concern, the mixture must have become volatile (evaporating rapidly), definitely not piquant (spicy), but perhaps acidic, although that wouldn’t require an evacuation. Something changed the nature of the mixture, so that would be a catalyst (an agent of change), not just any old chemical, and certainly not a neutralizer, which would have made the mixture less volatile.

7. A, F, H. Pristine means perfect. Primordial is more along the lines of prehistoric, and rudimentary means basic. If the owner said that the vase certainly was, he averred (confirmed) that the vase was in pristine condition. Corroborated would have required someone else saying it before he did, and if he proved it, the vase really would have been in pristine condition. For the last blank, however is the key word; knowing that the owner claimed the vase was in pristine condition, however clues you in that it really wasn’t, in which case the buyer was duped (fooled), not sidetracked (diverted) or ostracized (excluded).

8. B, C. The second sentence names three factors that contributed to Great Britain’s ability to take an early lead in the Industrial Revolution: coal, waterways, and international trade. Choice (A), trade unions, is mentioned near the end but only as a reaction by the working class to the low pay and poor working conditions.

9. D. “Thus, employers had such a large labor pool to select from that they were able to dictate low wages and long hours, further suppressing the working poor.” The sentence clearly states that the reason wages were so low is because “employers had such a large labor pool to select from.”

10. E. “Great Britain’s Industrial Revolution: Natural Resources, Migration, and Unions.” The passage covers these three topics but isn’t entirely based on any one. Choice (A) is wrong because the passage never says Great Britain went bust. Choice (B) is wrong because it describes only half the passage. Choice (C) is wrong because unions are mentioned only in the final sentence and the passage doesn’t say that unions originated in Great Britain. Choice (D) is wrong because the perspective in the passage is one of historian, not one of the exploited poor.

11. A. If some teachers have a better track record than others in educating students at the same school, the difference in teacher expertise is probably the reason why. Choices (B), (C), and (E) would help point toward some other cause, while Choice (D) is off topic.

12. C. If population growth offsets any savings in resources from reducing consumption, then regardless of how much consumption is reduced, the population will eventually be too large for the planet to sustain it. Choice (A) is wrong because the fact that the population doubles every 40 years is not necessarily a problem in and of itself. Choice (B) is wrong because it doesn’t counter the argument. Choices (D) is off topic, and Choice (E) is more in support of the argument.

13. B. Even if you don’t know the meaning of rapprochement, the parenthetical that follows it, (rejection of), provides a clue that rapprochement means the opposite of rejection of, so it means something like acceptance of. Reconciliation is the closest in meaning to acceptance of.

14. C. The second sentence mentions the only answer choice that’s correct: “It can be a triumphant parade of ‘great men and women.’” Choice (A) is wrong because although the passage mentions psychoanalysis, it does so only as one of a sequence of paradigmatic shifts. Choice (B) is wrong because although the passage mentions film language, it does so only as an example of an orienting metaphor.

15. B, E. If Amanda was known as the life of the party and acted that way during a ceremony of any sort, her behavior would appear loutish or boorish, both of which mean rude. At a ceremony, people are expected to be courteous or decorous, both of which mean polite. Capricious means fickle, and contentious means quarrelsome, neither of which fits in this context.

16. D, F. Convoluted and tortuous both mean complex, full of twists and turns, which would make the manager’s plans difficult to follow and execute. Desultory means aimless or unfocused, making it a good word to describe the manager’s plans, but it doesn’t have a match in the answer choices. If the plans were methodical (systematic), they’d be easy to follow, and if they were proscribed (prohibited), nobody on his staff would be allowed to carry them out.

17. A, E. If the candidates weren’t strong and were pandering, they must have been pusillanimous or craven (cowardly). They certainly would not be impudent (bold, in a disrespectful way), audacious (daring), sanctimonious (self-righteous), or intransigent (stubborn).

18. B, E. When children misbehave, parents are expected to admonish (scold) or castigate (punish) them, but not vilify (slander) or disparage (ridicule) them. Of course, they should never sanction (approve of) such behavior or congratulate the child for it.

19. A, C. Obdurate and implacable both convey a sense of stubbornness; implacable is stubborn in a sense of not being satisfied with anything being offered. Recalcitrant and subversive are a little too strong, conveying a sense of rebellion. Assiduous means hardworking, which the couple may have been, but that wouldn’t necessarily make them reluctant to move. Fundamentalist (die-hard, or one who is unyielding) isn’t even in the ball park.

20. B. The answer is most clearly provided in the final sentence. Naturalism relied on accuracy of description, whereas symbolism requires vividness of expression. Choice (E) is tempting, but authenticity is used to describe both naturalism and symbolism. Choice (A) is also a little tempting, but the passage mentions two types of art — that which is rooted in the real world (such as nature) and that which originates in the artist’s soul (symbolism) — so it’s not exactly art versus nature. Neither of the remaining two choices comes close.

Section 4: Quantitative Reasoning

1. B. The percents profit and loss are based on the dealer’s purchase price, not the dealer’s selling price. If he sold a sofa for $400 at a 25 percent profit, then he sold it for 125 percent

or what he paid for it, which is x, so

The dealer sold the other sofa for $400 at a 20 percent loss, or for 100% – 20% = 80%, or

what he paid for it (call it y), so the dealer purchased it for

So just subtract 20% of $500 (or $100) from $500 to arrive at the price of $400. The net gain was $400 – $320 = $80 and the net loss was $500 – $400 = $100, so Quantity B is larger. If you chose Choice (A), then you calculated the profit and loss on the dealer’s sale prices of $400, not the dealer’s purchase prices.

2. B. The number of integers between 200 and 500 with a units digit of 5 is 30.

3. B. If ab < 0, then either a or b is negative, but not both. Making them both positive, as in Quantity B, and then adding them produces a higher number than adding them first (with one as a negative) and then making the result positive.

4. D. If you chose Choice (B), then you fell for the trap. Just because , doesn’t mean that

a = 2 or b­ = 3. They could be 20 and 30, for example. Or a and b could also be negative, such as –2 and –3.

5. A. Draw the xy-coordinate plane and place the points A and C as directed. These are two points of the square, and you know they’re the opposite corners because the question tells you the sides of the square are parallel to the axes. Measure the width and height and multiply for an area of 25.

6. C. Drawing a line from point A to point C splits the square into two 45-45-90 triangles. The side ratio of this triangle is , so if two of the sides are 5, then the hypotenuse is .

7. D. If n equals 2, then Quantity A is greater; if n equals , then Quantity B is greater. All you

know is that n is positive, but not whether it’s an integer or a fraction that’s less than 1.

8. B. Set up the conversions as fractions and do the math:

Note that the three zeros in the numerators cancel the three zeros in the denominator of the second fraction.

9. C, E. If (x – 5)2 = 900, then take the square root of both sides to get x – 5 = 30 or x – 5 = –30. Add 5s all around, and x = 35, –25.

10. B. If the radius of the pool is r, then the radius from the center of the pool to the outer circumference of the sidewalk is . First, calculate the area of the pool and sidewalk by

substituting () for r in the equation for the area of a circle:

Next, calculate the area of the pool alone, which is easy: A = πr2. Finally, subtract the area of the pool from the total area of the pool plus the sidewalk, remembering that you need a common denominator to subtract:

11. 120. The sum of angles for any shape (other than a circle) can be found with the formula (n – 2)(180°), making the sum of the hexagon’s angles 720 degrees. Because the hexagon is a regular hexagon, meaning all sides and angles are the same, each angle is 120 degrees.

12. 3. Pick a number that has a remainder of 3 when divided by 35, such as 38 or 73. Divide the number by 7, and it has the same remainder.

13. E. Pick simple numbers for the length and width of the rectangle, such as 5 and 5, for an area of 25. Increase one by 20 percent and decrease the other by 20 percent, for new sides of 6 and 4 and a new area of 24. Regardless of the numbers you pick for the original rectangle, the ratio of the area of that to the new rectangle is the same.

14. D. If you multiplied the Bachelor’s-degree holder’s median weekly earnings of $1,012 by 4

and chose Choice (C), you fell for the trap. An average month is weeks long:

Now multiply the median weekly earnings of $1,012 by the number of weeks per month: $1,012 × 4.3 = $4,351.60, which is closest to Choice (D), $4,350.

15. B. To count the unemployed Doctoral-degree holders, take 2 percent of 10,000, which is 200. To count the unemployed Master’s-degree holders, take 2.4 percent of 200,000, which is 4,800. Reduce the ratio of 200:4,800 to 1:24.

16. D. Good thing you can use a calculator. To find the annual earnings of the Associate-degree holder earning 20 percent less than the median, multiply the median amount of $757 by 0.8 and by 52, for an annual salary of $31,491. To find the annual earnings of the Bachelor’s-degree holder earning 25 percent above the median, multiply the median amount of $1,012 by 1.25 and by 52, for an annual salary of $65,780. The difference is $34,290, making the closest answer choice $34,300.

17. B. You can find the area of an equilateral triangle by using the formula , where s is

any of the sides, including the base. You can also consider the equilateral triangle to be

two 30-60-90 triangles, giving the triangle a height of , and use the formula.

18. B, C, D. Of the 49 houses, the median value will be of house number 25, in order of value. This places the median house in the third group, valued in thousands from $150 to $199. The median value can be any value in that range.

19. A. With the two equations, solve for x by eliminating y. Because y = x + 3 and y = 2x + 5, replace the y in one equation with its value from the other equation: x + 3 = 2x + 5. Solve for x as –2 then substitute x in either original equation to get the value of y as 1.

20. C. The idea is to simplify this fraction as quickly and easily as possible. Factor the

into . Cancel the (52 – 1) from the top and bottom, and reduce the to 5.

Answer Key for Practice Exam 2