Chapter 21

Practice Exam 3: Answers and Explanations

After taking the Practice Exam 3 in Chapter 20, use this chapter to check your answers and see how you did. Carefully review the explanations because doing so can help you understand why you missed the questions you did and also give you a better understanding of the thought process that helped you select the correct answers. If you’re in a hurry, flip to the end of the chapter for an abbreviated answer key.

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. D. An anachronism is a reference to something that couldn’t have existed in the time it’s referenced, like Brutus and Cassius discussing a mechanical clock (a clock that can strike a specific time) when no such clock existed. Archaic (out of date) also refers to time, but it doesn’t quite work as well as anachronism in this context. Relic refers to something really old, which the reference itself may be, but in the context of referring to a mechanical clock, it doesn’t fit either. Tropism refers to the orientation of an organism in response to a stimulus, such as a plant growing toward sunlight, so it obviously doesn’t work here. And a euphemism is a mild form of an expression that may be offensive or not politically correct.

2. A. Veracity means truth, accuracy, which is an essential quality of any story a journalist may report. The only other choice that comes close is plausibility, but that doesn’t necessarily mean the story is true, only believable. None of the remaining choices (tenacity, meaning persistence, originality, and righteousness) work here.

3. C, E. Geocentric means, as the phrase after it explains, that the earth is at the center of the universe. If Galileo was labeled as a heretic for questioning a belief, his ideas would be proscribed (prohibited).

4. C, D. Amalgam is a metal alloy (mixture) commonly used in dental fillings. Although amalgam is metal, it contains several metals, as explained in the second sentence, so amalgam is the better choice. Experts would question the supposition (speculation), because people who believe amalgam fillings pose a health risk are not only making the accusation or ­allegation but are basing their hypothesis on the reasoning that because the fillings contain mercury, the mercury must leach out in levels high enough to pose a threat.

5. B, E. Propensity means the inclination. Law students may also have an aptitude (skill) and desire, but propensity conveys a sense that they’re more likely than not to do it. As a result, law students would become entangled in recondite (obscure) language, not sophisticated (refined) or erudite (learned) language.

6. A, F, G. Phlegmatic (unflappable) teachers would be the opposite of choleric (irritable) and would perform better and last longer in junior high school, where classroom management can become onerous (burdensome), certainly not elementary, and not necessarily truculent (aggressive, hostile), although the students may be. Sanguine (confident, optimistic) could work for the first blank, but because the rest of the passage talks about oppositional students, phlegmatic is a better choice. Melancholic (sad) teachers would certainly not perform as well under such conditions. Over time, a choleric temperament would increase antipathy (aversion) not opposition (resistance) and usually not hostility (aggression), which is too strong a word.

7. A, F, H. Specious arguments are unsound, unsupported. In this case, arguments for increasing domestic oil production at the expense of developing renewable energy sources would be specious, because it’s manifestly (clearly) obvious that oil production can’t possibly keep pace with escalating (growing) demand. For the first blank, standard obviously doesn’t work. Surreptitious (sneaky, underhanded) may make a good second choice, but specious is a better fit. For the second blank, deliberately obviously doesn’t fit, and consummately means complete or perfect, which would also be a poor choice. For the third blank, nascent means emerging, as in being born, and doesn’t work because the demand already exists. Proliferating is sort of like escalating, but refers more to growing in number than amount.

8. A, B. Choices (A) and (B) are correct because they demonstrate specific areas of the brain that control specific functions. The third choice is wrong, because it describes a case in which almost an entire area of the brain must be non-functional for unconsciousness to occur.

9. D. Choice (D) is correct because it shows that facial recognition is not linked solely to the damaged area of the man’s brain.

10. C. The big clue here is the sentence that transitions from Dax’s to Broca’s research: “The notion that language was localized to the left side of the brain (the left hemisphere) developed momentum with new discoveries linking specific language functions to specific regions of the left hemisphere.”

11. B. The passage specifically states that the river bed cut deeper and the Nile narrowed (the opposite of becoming wider), and although the delta may have become more fertile over time, nothing supports the idea that the river itself became more fertile.

12. A. Aggraded in this context means to build up. If large amounts of detritus sank to the bottom, it would aggrade, not wash away, erode, level off, or cut through.

13. B. The second sentence explains that the word culture is derived from nature. The rest of the passage provides details supporting that statement.

14. E. Manurance (cultivation) appears in the passage but only as part of one of the examples showing that the word culture was first used to describe an activity. All of the other words in the answer choices are specifically cited as being derived from nature.

15. A, E. Dissonant (harsh sounding) and cacophonous (grating) are the two correct answers. Symphonic and mellifluous both mean the opposite of what’s needed here — harmonious. Disparate means dissimilar, and raucous means something more like loud and unruly, which is close but not quite the best match.

16. C, F. Impassive and stolid both mean unemotional, which would be the opposite of passionately mad. Dull means uninteresting and stygian means hellish, neither of which generally apply to scientists. Zealous (passionate, enthusiastic) doesn’t work, because it doesn’t ­contrast to the idea of a passionately mad scientist. Finally, although most scientists have profound thoughts, you wouldn’t describe someone as profound.

17. A, B. Refractory and recalcitrant, in this context, mean resistant to treatment. An acute wound would probably not require long-term treatment, and although the wounds may be severe or excruciating, neither of those qualities would necessarily make the wounds resistant to treatment. Perspicacious means wise, so it definitely doesn’t work here.

18. C, E. Indigence and penury both mean poverty. They’re the only two words in the list that match. Malnutrition and famine are close, but the second sentence, which describes how the prosperous view it, focuses the correct choices on poverty rather than starvation. Illiteracy has no match, and squalor means something more like filth or uncleanliness, which may accompany poverty but isn’t poverty.

19. A, C. Mitigate and assuage both mean to lessen or alleviate. Augment (amplify) and incite (provoke) obviously don’t work, and repress and subjugate, both of which mean to put down by force, are too strong.

20. C. “Nature can improve the healing process” is the best answer. The answer is in the third sentence of the second paragraph: “The idea that access to nature could assist in healing was all but lost.” All the other choices go too far and lack support in the passage.

Section 2: Quantitative Reasoning

1. B. Combine the to equal , and reduce to . Because is closer to than to , its value is closer to 3 than to 4.

2. C. For each quantity, count only the numbers that aren’t in the other quantity. Both quantities have the numbers 101 to 198, so those numbers won’t affect which is greater. Only Quantity A has 99 and 100 (which total 199), and only Quantity B has 199.

3. D. Because x is between 9 and 10, it could be equal to 9.001 or 9.999. Don’t square those — square the 9 and the 10 instead for 81 and 100.

4. C. To use the equation , substitute the numbers before and after

the triangle for a and b, respectively, in the equation. For Quantity A, becomes

then . For Quantity B, becomes (0 × 1) + 2(0 + 1) then 2. To the

power of –3, it becomes , same as Quantity A.

5. C. The side ratio of the 30-60-90 triangle is , with 2x being the hypotenuse. The only way that the perimeter could be is if x were 1, making the hypotenuse 2.

6. B. The formula for combinations is , with C being the number of possibilities,

n being the group of students, and r being the students attending the meeting. And reduces to 120.

7. C. The formula for probability is . The number of

desired possible outcomes is four (three odd numbers plus one even number), and the

number of total possible outcomes is six. So reduces to .

8. B. Let x represent the amount invested at 3% and set the equation up like this:

(x)(0.03) + (8,000 – x)(0.05) = 340

Solve for x, and Tom invested $3,000 at 3% and $5,000 at 5%.

9. C. Pick two consecutive even integers, such as 8 and 10, giving you a product of 80. Only one formula will return 80 if you plug in 8 for n.

10. E. This is basically a large circle around a small circle, and the task of finding the difference between the two. The large circle has a radius of 5 (the 3-foot-radius garden plus the 2-foot-wide sidewalk), giving it an area of 25π. Subtract from that the area of the small circle (the garden), 9π, for a difference of 16π.

11. E. Set this up as two different equations: b – 8 = j, and b – 2 = 2(j + 2). Solve for b by substituting b – 8 for j in the second equation: b – 2 = 2(b – 8 + 2). Solve for b as being equal to 10.

12. B. The number of mothers with children under the age of 18 in 2005 is about 90,000. A 10% increase in 2010 brings the number to about 100,000. The percentage of mothers in the workforce with youngest children ages 12 to 17 in 2005 is 80%. Because the percentage stays about the same in 2010, 80% of 100,000 is 80,000.

13. A. The first number is 20%, and the second number is 70%. This produces a ratio of 2 to 7.

14. A, C. Choice (A) is correct because more mothers are having children, so the population is increasing. Choice (B) is wrong because mothers in the workforce aren’t necessarily single. Choice (C) is correct because with more mothers working, and more babies in Country X, the demand for daycare increases.

15. 4. Use the equation to solve for a2. Substitute a1 for an and a2 for an + 1. Because a1 = 38, solve for a2, which equals 20. Now use the equation to solve for a3 by substituting 20 for a2 and a3 for an + 1. Thus, a3 equals 11. Do this process again for a4, which equals 6.5. This is the first non-integer value of an, so 4 is the lowest value for n that gives you an answer that isn’t an integer.

16. 126. Factor the numbers under the radical: becomes

. Find number pairs to remove from the radical: Two 7s

mean a 7 comes out; two 2s mean a 2 comes out; four 3s mean two 3s come out. Nothing is left under the radical. Multiply all the numbers that came out: 7 × 3 × 3 × 2 = 126.

17. 2. Because 120,248 is even, it can be divided by 2, which is the smallest prime factor.

18. B, E. Each engine lift uses three pulleys, and each box contains eight pulleys. To avoid having any pulleys left over, the number of pulleys used has to be a multiple of 24. The ratio of pulleys to levers is 3:7, so the ratio used in the manufacturing job has to be a multiple of 24:56. Any number of levers that isn’t a multiple of 56 can’t be the number used in the manufacturing job.

19. A, B, C, F. Because 396 = 2 × 2 × 3 × 3 × 11, any answer choice that cancels completely with those primes produces an integer. The remaining answer choices don’t work because 24 has too many 2s and 27 has too many 3s.

20. A, C. The units digit of any product depends on the units digit of the numbers multiplied, for any integer. For example, any number with the units digit of 7 times any number with the units digit of 3 produces a number ending with the units digit of 1 (7 × 3 = 21, so just use the units digit of 1). The units digit of any number to the fifth power is the same as the units digit of the original number. For example, 25 = 32, 35 = 243, and 45 = 1,024, making n5 one of the answers. And n10 = (n5)2, so if n were 2, 32 squared has a units digit of 4. However, n25 = (n5)5, preserving the n5 rule and making n25 the other answer.

Section 3: Verbal Reasoning

1. C. Tangential conveys a sense of not being essential or central to the play. Essential (necessary) is the opposite of what’s needed here, and neither incisive (perceptive) nor predominant (main, principal) fit the context. Scenes could be concurrent (happening at the same time), but this wouldn’t convey the sense that the scenes are of less importance.

2. E. Obviated means something along the lines of “made unnecessary.” Precluded (prevented) and prohibited (banned) are too strong, and although the speaker had anticipated the questions, that would not anticipate the need for discussion. Adjourned doesn’t work, because you adjourn a meeting, but you don’t adjourn a need.

3. B, D. A libertine (morally unrestrained) existence could conceivably lead to a loss of self-discipline, but a Spartan (simple) or ascetic (puritan) lifestyle would tend to make someone more disciplined. For the second blank, you’d expect something opposite to “hedonistic paradise,” making stygian (hellish) the only choice. Quixotic means idealistic, and utopian means perfect (in a good way).

4. C, F. This passage is all about two’s — the body and soul, so filling the first blank is relatively easy: Dichotomy is a separation into two. A paradox is an apparent contradiction that may be true, and irony is the use of words to express the opposite of what the words mean. Finding the right match for the second blank is more challenging because all the words have two or separation in their meaning. Bisected (divided in two) is the best choice. Bifurcated is divided but more like a fork in a road, while dissected is more along the lines of dividing into several parts.

5. C, E. Intransigence is inflexibility, and precipitate means to bring about. Tractability (compliance) is the opposite of what’s needed for the first blank, and indolence means laziness. For the second blank, expedite (hasten) would make a decent second choice, but precipitate is more fitting. Motivate (provide with a motive) doesn’t work, because you may motivate individuals but not actions, such as conflict.

6. B, D, I. During an interrogation, you want to elicit (extract) information, not dissemble ­(mislead) or disseminate (spread) it. To stop interrogations without giving in, suspects may prevaricate (mislead, lie), not prognosticate (predict) or adjudicate (mediate), which would call into question the efficacy (effectiveness) of such methods, not their efficiency (ability to accomplish something with minimal effort) or alacrity (speed).

7. B, D, G. High winds and large waves would occur if nothing was in their way to impede (slow), not debilitate (incapacitate), them. Disperse (scatter) would make a good second choice. These high winds and large waves would be endemic (characteristic of) instead of pandemic (epidemic) or intrinsic (fundamental). Plankton would gather in pools, which tend to be more quiescent (calm) than a wavy ocean, not dormant (sleeping), and definitely not truculent (hostile).

8. E. “What Rose calls a ‘state of welfare’ emerged to provide basic forms of social insurance, child welfare, health, mental hygiene, universal education, and similar services that both ‘civilized’ the working class and joined citizens to the State and to each other through formalized ‘solidarities and dependencies.’” Several other sentences explain the purpose of welfare, but this sentence does so in the greatest detail.

9. A. Compare and contrast, explain, and describe reflect the author’s purpose, but lament and argue imply more emotion on the part of the author than is displayed in the passage, so eliminate Choices (C) and (E). Worker productivity has nothing to do with showing how our ancestors perceived night differently, so you can eliminate Choice (B). Choice (D) is simply wrong; the author doesn’t maintain that the moon is actually getting darker, just that it’s become overshadowed by electric lights.

10. A, B. This specific information exception question asks you to refer to the text to eliminate answers that are ways in the passage that travelers can find a path at night. The second paragraph specifically mentions Choice (A), light-colored stones or trees with bark stripped off; and Choice (B), the moon or a torch. Railings aren’t mentioned anywhere in the passage.

11. A. Choice (B) is wrong because although the passage implies that brain cells shrivel and die when not in use, it provides no scientific evidence to support this claim. Choice (C) is wrong because the cause-effect is flipped; although a 10 to 20 percent loss of neurons may occur in Alzheimer’s, the passage doesn’t state that a 10 to 20 percent loss of neurons causes Alzheimer’s.

12. D. “Television’s drive to entertain is incompatible with serious discussion of complex issues.” The other choices go too far, saying that TV cannot instead of that it does not. The passage doesn’t criticize television itself but how it’s used.

13. D. To strengthen the argument, find an answer that promotes the lack of swimming as the primary cause of a lack of snakes. If snakes are absent from the other large islands, the reason would seem to be that they can’t swim.

14. D. “Several countries that provide universal healthcare and free college rank much lower in happiness than Denmark.” This would mean that something other than socialism is boosting Denmark to the number one position.

15. B. “Higher taxes are essential to providing for the needs of citizens.” The passage focuses on taxes and how Denmark uses them to provide for the needs of its citizens. Choice (C) is a reasonable candidate, but the phrase more to happiness extends its reach outside the scope of the passage.

16. A, D. Complaisant and conciliatory mean inclined to please. Incendiary (provocative) means the opposite, and beguiling means deceiving with trickery. Apprehensive means anxious, and complacent, which is included to trip you up with its similarity to complaisant, means satisfied, content.

17. D, F. Invective and diatribe refer to bitter, abusive language, something you’d want to avoid if your goal was to foster bipartisanship and cooperation. None of the other choices are good matches: Supplication (plea), vernacular (dialect), malapropism (confusion of words with similar sounds), and hyperbole (exaggeration).

18. A, D. Fawning and obsequious refer to brownnosing, which would incline people to act as cheerleaders instead of players. Assertive and aggressive mean the opposite of what’s required here. Timorous means shy, which would make a good second choice, but it has no match. Indignant is more along the lines of expressing anger over injustice.

19. B, D. Duplicitous and disingenuous mean deceitful. Erroneous means false. Mendacious is more along the lines of being a compulsive liar. Sagacious means wise, and pretentious describes someone who’s phony.

20. C, E. Salubrious and wholesome are both good for you. Salacious (scandalous), specious (unsupported), and pernicious (malicious) aren’t. Propitious (favorable) could be good for you, but doesn’t express the meaning of being healthy, which is what’s needed here.

Section 4: Quantitative Reasoning

1. B. Because the line passes through both the origin and point (2, 1), calculate the slope of

the line as 0.5: .

2. A. The degree measure of an arc is twice its inscribed angle. So minor arc AC, which originates from the angle of the equilateral triangle, is twice 60 degrees. Therefore, minor arc AC is 120 degrees, or one-third of the circle. Because the circle has a radius of 2, its circumference

is 4π. One-third of 4π is , which is greater than π.

3. C. The angle supplementary to y, inside the triangle, can be represented as (180 – y) degrees. Because the triangle’s angles total 180 degrees, add up the angles and set them equal to 180:

x + 90 + 180 – y = 180.

Solve for x, which equals y – 90.

4. C. The two numerators are equal: 220 = (24)5 = 165. The two denominators are also equal: 315 = (33)5 = 275. Therefore, the two quantities are equal.

5. A. Because no price is given, pick $100 as the starting point for the value of the car. So $100 marked up 20 percent is $120, and the 20 percent discount from $120 brings the price to $96.

6. A. From Quantity A, becomes , which reduces to 100 × 99 and is greater than 992.

7. C. The sum of all integers from 1 to 20 can be found using the formula , where n

represents the 20. And .

8. C. Don’t fall for the trap of multiplying all these numbers and looking for the square roots. Instead, solve for Quantity A by finding and multiplying the square roots of each of the numbers under the radical: . To compare this to Quantity B, consider that .

9. E. Set up the conversion steps as a series of fractions and cancel out as much as you can:

. The unit represents the

30-second interval that the question asks for. Avoid putting 30 sec as the unit, which will lead to a math mistake.

10. B. To find the volume of the remaining space, subtract the volume of the eraser, which is 1 × 2 × 6 = 12, from the volume of the tennis ball can, which is πr2h = π(1.5)2(10) = 22.5π.

11. A. Plug in each answer choice for x and see what works. The only number that doesn’t

work is –1: becomes then 1 > 1, which isn’t true.

12. E. Check both graphs at the 20–30 points. The first graph shows $600 per month. The second graph shows 25,000 homes. Multiply these together for a monthly expenditure of $15,000,000. Multiply this by 12 for an annual expenditure of $180,000,000.

13. A. The graph shows approximately 10,000 homes with household incomes between $5,000 and $10,000 and approximately 35,000 homes with household incomes between $30,000 and $40,000. The ratio of 10,000 to 35,000 reduces to 2 to 7.

14. A, B. This question asks you to choose the answer choices that cannot be inferred. For Choice (A), how many of those homes have incomes between $50,000 and $60,000 isn’t known. For Choice (B), how many homes are being built and for what demographic isn’t known. Finally, Choice (C), 75,000 homes have incomes lower than $30,000 to $40,000, and 70,000 homes have higher incomes. Because 35,000 homes are within the $30,000 to $40,000 bracket, the median income is also in that bracket.

15. 1,440. The formula for calculating the sum of angles of any polygon is (n – 2)180, where n represents the number of angles. Therefore, (10 – 2)180, or 8 × 180, is 1,440.

16. 42. Combine the ratios so that 3:4 glasses to utensils combined with 6:7 utensils to plates produces a combined ratio of glasses to utensils to plates of 9:12:14. To get 27 drinking glasses total, multiply the entire ratio by 3, for a proportion of 27:36:42.

17. 4. Because the average of x, y, and z is 1, write out the equation as an averages formula:

, which tells you that x + y + z = 3. From the question, simplify the 8x + 2z,

z – 2x + 3y, y – x + z, and 4 – x by adding them together, giving you 4x + 4y + 4x + 4. Divide this sum by 4 for the average of x + y + z + 1. Because x + y + z = 3, the answer is 4.

18. B, C, D. Try each answer choice: 33 = 27, 43 = 64, 53 = 125, 63 = 216, 73 = 343, and 83 = 512.

19. A, C. For any square root to be an integer, each factor under the radical has to be in a pair.

For example, is an integer because it equals , and the 2s are in a pair. For to

be an integer, all the factors of 60 have to be in pairs: . The 2s are in a pair, but the y has to complete the 3-pair and the 5-pair to make an integer. So y has to contain 3 and 5, making 15 one possible value. However, y could also be 15 times any other perfect square, such as 4. So 15 × 4 = 60, which is the other possible value of y in this list.

20. A, C. Factor x2 = 4x = 0 into x(x – 4) = 0, making both 0 and 4 possible answers for x.

Answer Key for Practice Exam 3