Part IV. Answers and Explanations

VERBAL DRILL 1

  1. D The clue in the sentence is “Children … have become ‘hasty viewers.’ ” The trigger punctuation is a “same-direction” semicolon. So a good word for the blank would be “wanders.” In any case, it has to be a negative word. The words in answer choices (A), (B), and (E) are positive, and answer choice (C) isn’t really negative. That leaves (D).

  2. C Find the story. This architect doesn’t promote himself, therefore his fame can’t be a result of self promotion. Try a word like fame for the blank. Neither proficiency nor temperament mean fame so cross off choices (A) and (B). Prominence could work, so give (C) a maybe and move on. There is nothing in the sentence to indicate that the architect is superior, so eliminate choice (D). While the architect may have been reticent, we are looking for fame. Cross off choice (E). The best answer is (D).

  3. virtuosic, mellifluous

The clue “roused the audience to a standing ovation” indicates that both blanks need a positive word. The toughest part about filling either blank is the difficult vocab in the two columns. Use positive/negative to eliminate unlikely choices. Hackneyed sounds negative, while virtuosic looks a lot like virtue, a positive word. In the second column, mellifluous looks a bit like mellow, which is usually a good thing, but insipid has the prefix in, which means against. That may give it a negative connotation. All told, virtuosic and mellifluous both have positive meanings and suit the sentence best.

  4. ambiguous, dissuade

The clue for the first blank, “such unproven programs,” comes at the end of the sentence. You need a word meaning inconclusive to describe the results. Conclusive is clearly the opposite of what you want, but ambiguouslooks good, especially given its prefix ambi, which means “going in both directions.” Auspicious, in contrast, may sound like suspicious, but if you’ve been studying your Hit Parade, you’ll know that it has a positive meaning. Hang onto ambiguous and work the second blank. You already know that the program’s results have not been proven, but the reverse-direction trigger however indicates that those findings are having an unexpected or contradictory effect on parents’ desire to enroll their children. Since the phrase “have failed to” comes right before the blank, you need a word meaning discourage. Keep disabuse and dissuade if you’re not sure of their meanings, but get rid of distinguish. Meanwhile, notice that dissuade shares the same word root as persuade, but has the prefix dis, which means not. That makes it a likely choice, leaving ambiguous and dissuade as the two best answers.

  5. bliss, irrational, scant

The reverse-direction trigger nonetheless tells you that the first blank needs a word meaning the opposite of either “rational” or “pragmatic”. Since there’s no synonym for irrational in the first column, try not practical and use POE. While an impractical person might make his own suffering a priority—via melancholy or discord—bliss makes more sense, especially given that “regard for their own happiness” is mentioned later in the sentence. Another reverse-direction trigger, in contrast, is also used to reverse either rational or pragmatic for the second blank. Choose irrational from the second column and work the third blank. The first part of the sentence tells you that classical economics sees humans as trying to maximize their own happiness, and then the reverse-direction trigger in contrast gives us Veblen’s view. As such, the third blank needs a word that means the opposite of maximizing happiness. Scant is the closest match from the third column, making it, bliss, and irrational the best answers.

  6. plagiarism, proliferate, ensure

The clue at the end of the sentence, “copying from a website,” gives us plagiarism for the first blank. Use the second part of the sentence and the reverse trigger “however” for the second blank; since their fears were not realized, we know we need a word like increase. If you don’t know the word proliferate, studying your Greek roots can make it a great bet. For the last blank, we know that the educators are checking their students’ work, so a good word for the last blank would be prove. Rebut is tempting, but doesn’t quite fit, and neglect isn’t even close, so we’re left with ensure, the correct answer.

  7. E The conclusion of the argument is the first sentence—medieval stoneworkers are more skilled than modern ones—and the results of the survey provide the premise on which this conclusion is based. The argument assumes, though, that cathedrals are typical of medieval stonework; if not, the medieval masons are being evaluated on an atypical sample of their work. Thus, choice (E) most weakens the argument: If lower quality stonework is more likely to be destroyed, then medieval masons are being judged on their best work—their worst work likely having been destroyed long ago. Choices (A) and (B) would both strengthen the argument: choice (A), by removing a possible distinction between medieval and modern masons that might otherwise account for the difference in quality; choice (B), by directly supporting the above assumption. Without further information relating building size or apprenticeship length to skill in stonework, finally, both choices (C) and (D) are beyond the scope of the argument.

  8. C This is a main idea question about the passage as a whole. Your “treasure hunt” should have revealed that the passage is basically discussing the way in which Strachey interprets the English women’s movement. Eliminate (B) right away because it’s not about a “literary” work. Eliminate (D) because it’s not a “novel analysis.” Eliminate (A) and (E) because they are too specific. That leaves (C).

  9. C For line reference questions, go back to the lines cited, and read about five lines before and after those lines. You can find the answer in either place for this question. The first sentence of the paragraph tells us Strachey is writing about “the historical connections between the women’s movement and other social and political developments.” Choice (C) is just a paraphrase of this.

10. B Look back in the passage for the place where the author “faults” Strachey. It’s in the last paragraph, in lines 42-45. The author states, “Where Strachey pictured a relatively fixed image of domestic women throughout the first half of the nineteenth century, recent historical and literary works suggest that this image was both complex and unstable.” Sounds like (B).

11. D First, go back to the passage to find out what the author said about “the similarity between the English and American women’s movements.” It’s at the end of the first paragraph. The author says that “like its American counterpart, the English women’s movement had a powerful sense of its own historic importance and of its relationship to wider social and political change.” So you’re looking for an answer choice that would indicate that was not true. Choice (D) directly contradicts the author’s assertion.

12. unrecognizable, reworked 

The best word for the blank here is something like “new” since we know that it is very different and we have the change direction trigger “though.” The best two answers, therefore, are choices (B) and (E). None of the other choices really match each other or the meaning of the blank.

13. furtive, surreptitious

The clue for the blank is “he had ulterior motives.” Think sneaky or secretive and use POE. Inconspicuous is out, since it’s the opposite of the clue, but hang onto furtive (even if you don’t know its meaning). Overt is also the opposite of sneaky; get rid of it. Unorthodox and predictable, meanwhile, don’t match the clue, but surreptitious does. That leaves furtive and surreptitious, the two best answers.

14. urbane, cosmopolitan

Since the hotel had both “refined interiors” and an “amply stocked reading room”, it would appeal to guests who were well-read and liked refinement. Think sophisticated or worldly and use POE. Philistine is the opposite of refined or worldly, but both urbane and cosmopolitan are solid matches. In contrast, uncouth’s meaning is very similar to that of philistine, so cross out that choice. Grandiloquent and pretentious, meanwhile, don’t match the clue, leaving you with urbane and cosmopolitan.

15. amiable, affable

“His inherent irascibility” is reversed by the change-direction trigger not, which comes before the blank describing Wilbert. You need a word that means the opposite of irascible. Think friendly or good-tempered and use POE. Neither loquacious nor pedantic means friendly, but amiable matches. Garrulous, meanwhile, has the same meaning as loquacious, so cross it out. Finally, affable is a good match but stentorian doesn’t work. Amiableand affable suit the sentence best.

16. It is hard from our modern perspective to imagine that theatre has the power to influence politics, yet the plays of pre-republican Ireland did just that.

The passage starts out with its conclusion that, in the case of Ireland, theater influenced politics. The rest of the paragraph tells how this occurred.

17. C Go back to the first paragraph. In lines 6–7 the passage states, “In some localities the mosquito was abundant but malaria rare or absent.”

18. C Try putting your own word in the passage to replace host. The trigger but indicates that the reference to distinct biological traits should contrast with the statement that the mosquitoes seem almost identical, so you need a word that means something like large number. Of the choices, multitude is the best match. Beware of choice (A), which, though tempting, refers specifically to people. Likewise, be careful with choice (E): while the mosquitoes in question do, in fact, support parasites, that usage wouldn’t make sense in this context.

19. A Reread the second sentence of the second paragraph. It says that the mosquito becomes a carrier when it feeds on human blood.

20. E Choice (E) is best supported in the passage. The first paragraph discusses a seemingly inconsistent relationship between the presence of the mosquitoes and the prevalence of malaria, a paradox resolved by the discovery of multiple species among the insects; the boldface text suggests why this multiplicity of species wasn’t immediately apparent. Choices (C) and (D), while appropriately referring to the paradox, incorrectly describe the value of the bolded text: it neither resolves nor clarifies the importance of that paradox. Choices (A) and (B), finally, are not supported because the boldface text doesn’t directly weaken or strengthen the author’s main point, which is the discussion of one important step in the effort to eradicate malaria.

VERBAL DRILL #2

  1. C That semicolon is a trigger punctuation. It tells you that the first part of the sentence agrees with the second part. The second part contains the clue “what one group sees as peacekeeping, another group might see as subjugation.” How can we describe that—it sounds like a contradiction. How about “contradictory” for the blank? Time to go to the answers. You can eliminate (A) academic, because it doesn’t mean contradictory. Choice (B) portentous means predicting the future, which might be true of historical events, but has nothing to do with this sentence. Choice (C) paradoxical means seemingly contradictory, so keep it (if you weren’t sure, you’d keep it in anyway). Choice (D) trifling means frivolous or of little value, so eliminate it. Choice (E) bellicose means warlike, which might be true of some historical events, but has nothing to do with this sentence. The best answer is (C).

  2. B The clue for the blank after the trigger word “however” is “daily routines,” so the word in the blank can be “routine.” That definitely eliminates (A), (D), and (E). If you know what quotidian or recalcitrant means, you know the answer is (B). If you don’t, (C) is a good guess (although it’s wrong).

  3. fledgling, precipitously

The only thing that we really know about the store is that it is pretty new, so that would be a good word for the first blank. While urbane and ostentatious could both apply to a clothing store, they do not match the meaning of the clue. Since we know that the situation is a crisis, a good word for the second blank would be something like a lot. The best answer, then, is precipitously while none of the other choices match the direction of the clue.

  4. abstruse, lucid

What would earn Reagan the distinction of “The Great Communicator,” other than an ability to make difficult or complicated topics easy to understand? Hang onto abstruse, but don’t fall for the trap of obtuse. You can also cross out mundane, as it means common or ordinary—not complicated. Moving to the second blank, think clear or understandable, given the first part of the sentence. Palatable is close, but lucid is a much more precise match. Munificent, meanwhile, doesn’t mean understandable, making abstruse and lucid the best choices.

  5. arduous, transient, static

“Is made even more difficult” is the clue for the first blank. Recycle difficult and use POE. Only arduous matches. Regarding the second blank, the clue “people seldom reside in any one place for very long” suggests a word meaning moving around or mobile. Inert is the opposite of the clue, and aesthetic doesn’t match, so choose transient and work the third blank. The change-direction trigger however, which comes right after the blank, calls for a word meaning the opposite of mobile. Static is a strong match, making it, arduous, and transient the best choices.

  6. bedlam, epithets, neophyte

The second and third blanks might be a little easier on this one. A good word for the third blank would be something like inexperienced since we are told that a person with “more experience” would have handled things better. The best choice, then, is answer neophyte. For the second blank, a good word would be something like insults since we are told that things were getting personal. The best answer here is epithets. For the first blank a good word would be something like chaos since the meeting started out well but resulted in disarray. The best answer here is bedlam.

  7. B The examples of how different terminology can determine who benefits is an example of the issues that make selling naming rights so legally complicated, choice (B). The naming rights may be complicated, but they are not described as confusing, choice (A). Answer choice (C) draws too large a conclusion from a specific example. Answer choice (D) is too extreme for the situation described. The differences in benefits are between facility owners and teams; the terminology does not affect the community’s benefits (E). Therefore, the best answer is (B).

  8. B In the credited response, the author suggests that the naming rights may seem like a win-win proposition. However, the rest of the sentence—and the rest of the paragraph—is devoted to enumerating some of the difficulties and concerns that such deals often raise.

  9. D Try putting your own word in the passage to replace practice. The trigger though indicates that the first part of the sentence will contrast with the current proliferation of sponsorships, so a word like activity or deed might make sense—anything that conveys the meaning that it was once unheard of for something to happen. Of the choices, action is the best fit.

10. C Choice (A) is not supported, as the passage makes no mention of other playwrights to whom a comparison can be made. Choice (B) is also not supported: the focus here is on a wartime comedy with a serious message, but the author doesn’t comment on the propriety of studying this or any other play. Choice (C) is supported by the main idea of the passage, that Lysistrata has an oft-overlooked meaning that depends on the political situation in Greece at the time of its composition.

11. B Choice (B) is best supported by the passage: the oracle is brought up in a list of examples supporting the importance of the idea of Greek unity in the play. Choices (A) and (C) can be eliminated because the passage doesn’t directly relate the oracle to Lampito or the origin of the conspiracy. Choice (D) is also not supported: although a superficial interpretation of Lysistrata is being questioned, the passage doesn’t provide enough information to characterize either interpretation as earlier. Choice (E), finally, is backwards, as the oracle supports the author’s emphasis on cohesion in the play.

12. A The conclusion of the argument is at the end: “Significant progress is being made toward the extending the lives of cancer patients.” The premise on which the argument is based is that patients are living longer after their initial diagnosis. For this argument to be valid, though, you need to assume that length of life is the same thing as time after initial diagnosis. Hence, choice (A) is the best response: if cancer is being diagnosed progressively earlier, then people could be aware of their condition longer without living any longer. Keep a close eye on the scope of the argument to help you eliminate the incorrect choices. The argument isn’t about a comparison among types of cancer, or between cancer and other diseases, so eliminate choices (B) and (E). Likewise, the argument isn’t about the number of either cancer diagnoses or people who make full recoveries, so eliminate choices (C) and (D).

13. congruence, concurrence

“Fervent schisms … were largely overplayed” is the clue indicating that the blank needs a word meaning the opposite of disagreement. Think agreement and use POE. Congruence matches, but asperity and contradiction go in the opposite direction of agreement. Concurrence, like congruence, matches the clue, but impassivity and truculence, like the second and third choices, go in the opposite direction of the clue. That leaves congruence and concurrence as the two best answers.

14. mettle, tenacity

The blank needs a word meaning perseverance or determination, given the semicolon, which acts as a same-direction trigger, followed by the rest of the sentence, which discusses all that Johnson achieved “though he never attended school.” Mettle works, but timidity does not. Tenacity, like mettle, is a good match for perseverance, but tenuousness goes in the opposite direction. Apply your clue word to the two remaining choices. Does candormean perseverance? What about alacrity? Neither one matches, leaving you with mettle and tenacity, the two best answers.

15. officious, meddlesome

What does the sentence tell you about the sales clerk? From the clue “drove many a potential customer away with her pushy, overeager manner,” you can recycle pushy or overeager for the blank and use POE. Eliminate loquacious and irreverent if you know what they mean (here’s where knowing your vocab comes in handy). Officious, on the other hand, could work, but innocuous doesn’t mean anything close to pushy, so cross it out. Meddlesome, like officious, matches the clue, but vigilant doesn’t mean pushy or overeager. That leaves you with officious and meddlesome, which are the two best choices.

16. complaisance, deference

The clue for the blank is “even the most compliant of employees.” Recycle part of the clue word and apply compliancy to the answer choices. Effrontery and truculence go in the opposite direction of compliancy, so toss those two. Deference makes sense (think defer), but cross out both prevarication and chicanery, since they have to do with dishonesty (don’t let the phrase “motivated by a hidden agenda” shift your focus away from the clue for the blank, which describes compliant employees). Complaisance, in contrast, agrees with the clue, making it and deference the two best choices.

17. C The first sentence of the passage says that dopamine is recycled to prevent overstimulation. This clue tells you that released dopamine must have a stimulating effect, so pique means stimulate. Neither choice (A) nor (D) has this meaning. Choice (E) specifies a negative stimulation, which is not supported by the text. Choice (B) is also not supported by context. Excite is a good synonym for stimulate and is the correct choice.

18. D Choice (A) is not supported by the text because the discovery of a different process does not necessarily make the old one incorrect. The same logic applies when considering choice (B); that one method is traditional does not make a different one incorrect. The passage never gives any indication of preferences or personal beliefs, so choice (C) is also incorrect. Choice (E) goes too far in saying that many people cannot overcome addiction; the passage does not offer statistics on recovery. Choice (D) is correct because the first sentence indicates a long standing belief in DAT blockage as the primary problem.

19. C Choice (A) is not supported: the passage suggests that the manageable distance for oxen was less than that for horses, but no specifics are provided for either animal. Choice (B) is also not supported, as the passage focuses on agricultural developments; the military preeminence of mounted cavalry is only mentioned as inspiring early selective breeding. Choice (C), finally, is supported by the passage: the first paragraph indicates that the neck strap of the older harnesses inhibited the flow of both air and blood to the horse’s brain.

20. B Choice (B) is best supported: the passage discusses the move to horses as primary draft animals, and the boldface text gives factors that hindered that transition. Choices (A) and (C), then, both contradict the passage and can be eliminated. Choices (D) and (E) are also not supported by the passage. Although the factors in boldface might be considered part of a paradox—how horses overtook oxen despite significant disadvantages—the information presented neither solves nor further explores the ramifications of any such paradox.

MATH DRILL #1

  1. A In a parallelogram, opposite angles are equal, and the big angle plus the small angle adds up to 180 degrees. So x + 120 = 180. That makes Quantity A 60, which is bigger than the 45 in Quantity B. The answer is (A).

  2. A To find the amount Mr. Jones paid in addition to the regular price of the bedroom set, multiply $69 by the 9 months and get $621. Then add the $300 payment. 621 + 300 = 921. So Mr. Jones paid an additional $21. The $23 in Quantity A is larger than the $21 in Quantity B. The answer is (A).

  3. B To find the perimeter of triangle BCD, first, find the length of BD using the Pythagorean theorem. 5² + BD² = 13². Or you may remember that 5² + 12² = 13². So BD = 12. Then, you can find the third side of triangle BCD. 12² + DC² = 15². Notice that this is a 3:4:5 right triangle. So DC is 9. Next, add up the sides of triangle BCD. 9 + 12 + 15 = 36. So, Quantity A is 36. Because Quantity B is 42, (B) is the answer.

  4. B Draw yourself a picture! The formula for circumference is C = πd, also known as 2πr. Because r = , C = (2)π (), or π. So you have π in Quantity A and 4 in Quantity B. Remember that π is equal to a little more than 3. That means the answer is (B).

  5. D First, Plug In an easy number. How about x = 2? That gives us 3 as the quantity in Quantity A and −1 as the quantity in Quantity B. We know that 3 is greater than −1; so far the answer is (A). Eliminate (B) and (C) on your scratch paper. For our second round of Plugging In, try x = 0. That gives us 1 in Quantity A and 1 in Quantity B—now the two columns are equal. You Plugged In different numbers, you got different answers. Therefore, the answer is (D).

  6. B When you see the word “average,” make your pie. In this case, you have the average, 17, and the number, 2. That makes the total 34. In other words, the two numbers have to add up to 34, but neither of them can be 12 or less. Because Quantity A is asking for twice the larger of the two integers, figure out what the largest integer could be by pairing it with the smallest integer we can use, or 13. If the total is 34, and one number is 13, that means the other number is 21 because 21 + 13 = 34. So, in Quantity A, we get 42, which is twice 21. We have 44 in Quantity B, so (B) is the answer.

  7. D First, Plug In a pair of easy numbers. Try 3 for x and 4 for y. (4 is a good plug-in for y, because  is an integer.) This gives 12 for Quantity A and 6 for Quantity B. With these plug-ins, choice (A) works, which means you can eliminate choices (B) and (C). But you have to plug in again, because you still have choice (D) to contend with. Plug In some weird numbers. How about 0 for x and 0 for y? (There’s no rule that says x and y have to be different.) That gives 0 for Quantity A and 0 for Quantity B. Because these numbers make the two columns equal, this proves that Quantity A is not always the answer, and the correct answer is (D).

  8. B First, there were no variables in this problem, so the answer can’t be (D). The word “inclusive” in Quantity B is the key. “Inclusive” means including 15 and −15 and 0, which must be more than 30 (in Quantity A). You’ll prove it by listing them: −15, −14, −13, −12, −11, −10, −9, −8, −7, −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. That’s 31, and that’s (B).

  9. D Which costs more, the car or the paint job? The car. What do the answer choices represent? The cost of the car. Ballpark first. If the combined cost was $4,800, and the biggest chunk of that is the cost of the car, choices (A) and (B), are ridiculously low. A $4,000 paint job for an $800 car? No way. Eliminate those choices. What choices are left? (C), (D), and (E). Start plugging in the middle of those values, (D), $4,000. Hey, it’s also the easiest number to work with, so why not? You’re told that the cost of the paint job was  the cost of the car. One-fifth of $4,000 is $800 (now you see where that trap answer choice came from). Is $4,000 plus $800 equal to $4,800? Yes. You’re done—the answer is (D).

10. B To find the perimeter of the figure, you need to add up all the sides. To find the missing side of the rectangle, solve for the opposite side of the rectangle, using the Pythagorean theorem: a² + b² = c². You may remember that 5²+ 12² =13². So the missing sides of the rectangle are each 13. Now, add up the sides of the figure: 5 + 12 + 17 + 13 + 17 = 64. That’s (B).

11. A Plug In 2 for x and 3 for y—that makes xy an even integer.
(A)    (2)(3) + 5 = 11. That’s odd, so leave it in.
(B)    2 + 3 = 5. That’s odd, so leave it in.
(C)    . That’s not an integer, so eliminate it.
(D)    4(2) = 8. That’s even, so eliminate it.
(E)    7(2)(3) = 42. That’s even, so eliminate it.
So, you got rid of choices (C), (D), and (E). But standard operating procedure on a “must be” question says we need to Plug In twice; otherwise, how would we choose between (A) and (B)? At first, you made x even and yodd. Make them both even and just change y to 4. Is xy even, using these numbers? Yes, it’s 8. Go back to the two remaining choices.
(A)    (2)(3) + 5 = 13. That’s still odd, so leave it in.
(B)    2 + 4 = 6. That’s even, so eliminate it. The answer is (A).

12. 25 Don’t solve for x: you’re told that 3x = −2, so substitute −2 for 3x in the problem to yield (−2 − 3)², or (−5)², which equals 25.

13. A A line has 180 degrees, so a + 20 + b = 180. That means that a + b = 160. You’re also told that a = 3b. So, plug in those answer choices for b: (C) b = 25, so a = 75. Does 25 + 75 = 160? Nope, it’s 100, too small. (B) b = 30, so a = 90. Does 30 + 90 = 160? Nope, it’s 120, too small. Bet the answer’s (A). Double-check to make sure. (A) b = 40, so a = 120. Does 40 + 120 = 160? Yes. That’s the answer.

14. 8,230 First, add the total number of male and female voters to get the overall total of 9,053. Don’t subtract 10% from that, though—that’s a 10% decrease, and the big trap in the problem. Instead, find the number that gives 9,053 when increased by 10%. Increasing something by 10% makes it 110% of its original value, so translate the question “9,053 is 110% of what?” into the equation 9,053 = x. Solve for x, and x = 8,230.

15. D Take advantage of the work that’s already done for you—the total number of females—and add the males who were less than 48 years old: 4,671 + 1,030 + 1,114 = 6,815.

16. C You can compare the ratio of the actual numbers of people, or the ratio of the percentages. Either way the ratios will be the same. Since we already know the percentage of Democrats and the percentages are smaller numbers, let’s stay with percentages. To find out the percentage of male voters age 48 to 62, write “1,291 is what percent of 9,053?” as an equation on your scratch paper: 1,291 = x/100(9,053). The answer is 14.2%. The ratio of 43% to 14% is closest to 3 to 1. The correct answer is (C).

17. C Use those answer choices! Because the question is asking for the least number, start by Plugging In (A), the least number in the answer choices.
(A)   Does {3(−3) + 2} {−3 − 3} = 0? (−7) (−6) = −42, which isn’t 0.
(B)   Does {3(−2) + 2} {−2 − 2} = 0? (−4) (−4) = −16, which isn’t 0.
(C)   Does {3(−) + 2} {− − 3} = 0? (0) (−3 ) = 0. Bingo!

18. 236 Draw yourself a picture! To find the perimeter of a rectangle, you need to know the length and the width. If the newspaper ad with a width of 14 has the same area as another ad 52 long and 28 wide, that means that 14(length) = 52(28). Divide both sides by 14, and you get length = 52(2) = 104. So, the perimeter of the mystery ad is 104 + 104 +14 + 14, which equals 236.

19. C With all of these percents, wouldn’t it be nice to have a total number? Just Plug In one. Make the total number of voters 100 (the best number to plug in when you’re dealing with percents). 60 percent of the voters are women, so that’s 60 women, and the remaining voters are men, so that’s 40 (we made the total 100, remember?) men. 30 percent of the women would be 30 percent of 60, which is  (60), or 18 women, who voted for candidate X. 20 percent of the men would be 20 percent of 40, which is (40), or 8 men, who voted for candidate X. So, the total number of people voting for candidate X is 18 + 8, or 26. Because your total is 100, 26 is equal to 26 percent. That’s (C).

20. B, C, and E

Use your on-screen calculator to find 21 × 54 × 22, and Plug In The Answers to see which ones divide into integers. Alternately, you could work with the factors: 21 = 7 × 3, 54 = 3 × 3 × 3 × 2, and 22 = 2 × 11, so you can divide their product by any number that contains only the factors in 22 × 34 × 7 × 11. The denominators in choices (A) and (F) both have 5 as factors, and choice (D) has too many 2’s; the rest of the choices all yield integers.

MATH DRILL #2

  1. A When in doubt, expand it out, and don’t calculate, because this is quant comp and you only have to compare. In Quantity A, there is (4)(2)(2)(2)(2)(2)(2). In Quantity B, there is (6)(4)(4). Break it down even further: Quantity A is (2)(2)(2)(2)(2)(2)(2) (2), and Quantity B is (3)(2)(2)(2)(2)(2). Now, get rid of anything both columns have in common. Each column has five 2’s, so cross them out. What’s left? (2)(2)(2) in Quantity A and (3) in Quantity B. In other words, Quantity A has an 8, and Quantity B has a 3. The answer is (A).

  2. A First of all, there are only numbers in this problem, so the answer cannot be (D). Now, the formula for percent increase is the difference divided by the original, multiplied by 100. In Quantity A, the difference (between 4 and 5) is 1, and the original number is 4, so that’s . Multiply that by 100 and you get 25%. In Quantity B, the difference (between 4 and 5) is 1, but the original number is 5, so that’s . Multiply that by 100 and you get 20%. 25% is bigger than 20%, so the answer is (A).

  3. A Draw yourself a picture! Plug In some numbers and see what happens. To start with, make r = 2. Then, you get πr = 4π (which is about 12-ish) in Quantity A and 4(2) = 8 in Quantity B. So Quantity A is greater if r = 2. Eliminate choices (B) and (C). Now Plug In a weird number; make r = . Then you get π in Quantity A and 2 in Quantity B. Quantity A wins again. You can’t Plug In 0 or a negative number because r is the radius of the circle and the side of the square. The answer is (A).

  4. C When you see the word “average,” draw a pie. In Quantity A, the average is 7 + 3 + 4 + 2, or 16, divided by 4, which is 4. In Quantity B, you have to find the average of 2a + 5, 4a, and 7 − 6a. Why not Plug In something for ato make this easier? How about 2? Now you’re finding the average of 9, 8, and −5. 9 + 8 − 5 = 12, divided by the number of numbers, which is 3, gives 4. So far the answer is (C). Plug In again—something weird this time, just to be sure. How about 0? Now you’re finding the average of 5, 0, and 7. 12 divided by the number of numbers, which is 3, gives 4. Again, you get (C). By the way, you could also have solved Quantity B by adding everything up as is: 2a + 5 + 4a + 7 − 6a = 12. 12 divided by the number of numbers, which is 3, gives 4.

  5. C Triangle ABC is isosceles. That means that the base and the height are each equal to 4. So the base of the unshaded region is 3, because the base of the shaded region is 1. The area of triangle ABC is (4)(4), or 8. The area of triangle ABD is (4)(3), or 6. Subtract the area of ABD from the area of ABC to get the area of the shaded region, BCD. That’s 8 − 6, which is 2. So, in Quantity A, the area of the shaded region, 2, divided by the area of the unshaded region, 6, is , or . The answer is (C).

  6. C Looks ugly, doesn’t it? This is a tough one, but don’t worry; you’d never be expected to calculate these. All you need to do is compare. Start by doing a little factoring to change the look of these numbers. In Quantity A, what’s the biggest thing that we can “pull out” of 3¹⁷ and 3¹⁸? You can divide the whole thing, or “pull out” 3¹⁷, so you end up with 3¹⁷ (1 + 3¹), or 3¹⁷ (4). Looks like Quantity B, doesn’t it? The answer is (C).

  7. C Don’t forget to Plug In on geometry problems with variables. Plugging In according to the rule of 180, You can make a = 50, and make the other two angles inside the triangle 60 and 70. Because b and c are vertical to the other angles in the triangle, b + c = 130 in Quantity A. 180 − 50 = 130 in Quantity B. The answer is (C).

  8. D First of all, do a little Ballparking. If a one-hour call costs $7.20, a ten-minute call must cost much less. Eliminate (A). Now, make a proportion, but first, change “one hour” into “60 minutes,” because you’re comparing it to ten minutes. So, you have: . A little cross-multiplying gets you 60x = (7.20) (10), or 60x = 72. Divide both sides by 60 and you get x = 1.20. That’s (D).

  9. C To find the value of n, start with the right triangle for which you’re given two of the three sides. Use the Pythagorean theorem: 15² + b² = 25². Notice that this is a 3:4:5 right triangle; 15 = 3(5) and 25 = 5(5). So b = 20 or 4(5). Now you have two of the three sides of the triangle: 12² + n² = 20. Notice that you’ve got another 3:4:5 right triangle. 12 = 3(4) and 20 = 5(4). So n = 4(4) or 16. That’s (C).

10. A, B, C, and D

The minute you see the phrase “must be” you know you need to Plug In more than once and you are going to use your “must be” set-up. On your scratch paper, list your answer choices down the left, and x =, y =, and z = three times across the top. Now Plug In according to the rules you’ve been given. If x = 2 then y = 2 and z must equal 4. Check your answer choices. For (A), 4 + 4 = 8. This works, give it a check. For (B), 2 − 2=0, this works, give it a check. For (C), 2 − 4 = 2 − 4, this works, give it a check. For (D), 2 = , this works, give it a check. And for (E), 2 − 2 = 8. This does not work, so cross off answer choice (E). You are going to have to Plug In more than once, but that is what your set-up is for. Make sure you try all of the weird numbers, so plug in fractions, negative numbers, and zero. You will find that (A), (B), (C), and (D) will work all of the time. Since this is an All That Apply question, the correct answer is (A), (B), (C), and (D).

11. D Remember, if you don’t get a diagram, draw one yourself. Your little map should form a 3:4:5 right triangle, so the street from the supermarket to the beauty parlor is 5 blocks long. Drawing your own diagram makes this problem so much easier!

12. B Plug In those answer choices! There are two conditions on the answer. First, its second digit must be 3 times the first digit. Because ETS’s answer must satisfy both conditions, you can eliminate any choice that fails to satisfy either of them. Therefore, you tackle one condition at a time. Choice (C): Is 6 three times 3? No. Eliminate. Choice (B): Is 6 three times 2? Yes. A possibility. Choice (D): Is 2 three times 6? No. Eliminate. Choice (A): Is 3 three times 1? Yes. A possibility. Choice (E): Is 3 three times 9? No. Eliminate. You’ve already narrowed it down to two possibilities, choices (A) and (B). Now you apply the second condition, that the reversed form of the number must be 36 more than the original number. Check the remaining choices: Choice (A): Is 31 equal to 36 more than 13? No. Eliminate. That’s it, the answer must be (B). Check it to make sure: 62 is exactly 36 more than 26.

13. 20 The information about tips is the catch. Its only purpose is to cause careless errors. Confront this trap by reducing the day’s total by $20—to $160. Now you’re left with a very straightforward problem. If each customer bought two $4 dishes, then each customer spent $8 total, and $160 ÷ $8 = 20.

14. C Go to the graph and find January 1971 to April 1978. Use Process of Elimination. The greatest amount of private donations to charitable causes for that period was to the category of Child Safety. Eliminate (D). The second greatest was Other. Eliminate choice (E). The third greatest was Environmental Protection. That’s (C).

15. D This question requires you to find the amount of money received by Child Safety organizations in September 1989 from the left-hand chart. It was $9.4 million. Then, divide that amount by the number of Child Safety organizations—38 (from the right-hand chart). It’s time to Ballpark! To make it as easy as possible, round both of those figures up. Pretend it’s $10 million divided by 40. That’s $250,000. That’s (D).

16. C Go to the graph and find September 1985 to December 1989. The amount donated to Homeless Aid causes for that period was about $300 million. The amount donated to Animal Rights causes for that period was about $225 million. You can reduce ratios! The ratio of 300:225 reduces to 12:9, or 4:3. That’s (C).

17. E Plug In a number for a. How about 10? So, Alex gave Jonathan 10 dollars. She gave Gina two dollars more than she gave Jonathan, so she gave Gina 12 dollars. She gave Louanne three dollars less than she gave Gina, so she gave Louanne 9 dollars. So altogether, Alex gave Gina, Jonathan, and Louanne 10 + 12 + 9, or 31 dollars. (By the way, just ignore that “in terms of a.” Because you Plugged In, you’re not answering the question in terms of aanymore.) Now check the answers, Plugging In 10 for a, and looking for the target answer, 31.
(A)    Does  = 31? Nope.
(B)    Does 10 − 1 = 31? Nope.
(C)    Does 3(10) = 31? Nope.
(D)    Does 3(10) − 1 = 31? Nope.
(E)    Does 3(10) + 1 = 31? Yes. The answer is (E).

18. C Remember those quadratic equations? Doesn’t m² + 2mn + n² look exactly like x² + 2xy + y², which equals (x + y)²? That means you could rewrite m² + 2mn + n² as (m + n)². Now, you’re also told that m + n = p, which means that p and m + n are interchangeable. If you replace the m + n in the (m + n)² with the p, you get p².
So, m² + 2mn + n² = (m + n)² = p². That’s (C). Whew! But hey—you can also plug in on this one: 2 for m, 3 for n, and 5 for p—we get 2² + (2)(2)(3) + 3², which equals 25. That’s our target answer. Now, to the answers.
(A)    (4)(5) = 20. Eliminate.
(B)    15 − 2 = 13. Eliminate.
(C)    (5)² = 25. Bingo!
(D)    (5)² + 4(2 + 5) = 25 + 28 = 53. Eliminate.
(E)    (5)² + (3)(5) + (2)² = 25 + 15 + 4 = 44. Eliminate.
It’s (C)!

19. E Don’t worry, there’s no such thing as a “*.” This is one of those funny-symboled function problems. This time, you don’t have numbers to use. Sounds like a plug in! Plug In x = 3 and y = 2. First, you’ll do the x ≈ y in the parentheses. You know that x * y = x(x − y), so 3(3 − 2) = 3(1) = 3. So, x * (x * y) can be rewritten as x * 3. Now, remembering that you made x = 3, the question really is 3 * 3 = 3(3 − 3) = 3(0) = 0. That’s the target you’re looking for in the answer choices: 0. So, Plug In x = 3 and y = 2 in the answer choices, and look for 0.
(A)    Does x² − xy = 0? (3)² − (3)(2) = 9 − 6 = 3. Nope.
(B)    Does x² − 2xy = 0? (3)² − 2(3)(2) = 9 − 12 = −3. Nope.
(C)    Does x³ − x² − xy = 0? (3)³ − (3)² − (3)(2) = 27 − 9 − 6 = 12. Nope.
(D)    Does x³ − (xy)² = 0? (3)³ − {(3)(2)}² = 27 − 36 = − 9. Nope.
(E)    Does x² − x³ + x²y = 0? (3)² − (3)³ + {(3)²(2)} = 9 − 27 + 18 = 0. Bingo!

20. A, B, C, and E

Just start dividing and find your remainders. 117 ÷ 2 = 58 with a remainder of 1, so select choice (A). 117 is divisible by 3, so 3 doesn’t give you a new remainder. 117 ÷ 4 = 29 with a remainder of 1, but you already have 1. 117 ÷ 5 = 23 with a remainder of 2, so select choice (B). 117 ÷ 6 = 19 with a remainder of 3, so select choice (C). 117 ÷ 7 = 16 with a remainder of 5, so select choice (E). 117 ÷ 8 = 14 with a remainder of 5, but you already have 5. 117 is divisible by 9, so 9 doesn’t give you a new remainder. The correct choices are (A), (B), (C), and (E).