Full-Length Practice Test

Answer: C

1. C

The regime is described as “oppressive” and has been consolidating power by taking over the military and the press. You can predict that an oppressive regime would want to “stop” a group that wished to promote individual freedoms. Choice (C) stymie, which means “to hinder,” correctly matches this prediction. Eliminate (A) produce, which means “to make happen,” and (B) facilitate, which means “to enable,” since each is the opposite of the prediction. (D) elucidate, which means “to clarify,” and (E) redress, which means “to make right,” do not make sense in context.

Answer: B

2. B

Since this sentence does not contain any detour road signs, you can expect that the meaning of the missing word will align with the context clues given in the sentence. The Norse god Loki is described as “mischievous” and as one who “interferes” by changing his form. You can predict that the missing word means something like “trickery.” There is a match for this prediction in (B) chicanery, which means “deceptive behavior.” Eliminate (A) avarice (“greed”), (C) pragmatism (“practicality”), (D) diffidence (“shyness”), and (E) apathy (“indifference”) because they do not fit the sentence’s context clues.

Answer: B, F

3. B, F

The detour road sign “but” in the first sentence indicates that there is a contrast between how the Dewey Decimal System is perceived in light of new technology and the fact that it “continues to be a valuable organizational tool.” You can predict that the Dewey Decimal System may seem “outdated.” This prediction matches (B) archaic, which means “old-fashioned.” Eliminate (A) abstruse, which means “difficult to understand,” and (C) misguided, which means “foolish,” as neither is supported by the context clues.

For the second blank, the context clues “continue” and “in perpetuity” (meaning “forever”) indicate that the accumulation of knowledge is a pursuit that never ends. You can predict the phrase “an infinite” to complete the sentence. Choice (F) an inexhaustible means “an endless” and is correct. Eliminate (D) a vacuous, as vacuous means “foolish,” and (E) an illuminating, as illuminating means “enlightening,” since neither meaning is supported by the context clues.

Answer: C, D

4. C, D

The detour road sign “while” indicates that the situation described in the first half of this sentence will contrast with the situation described in the second half. The context clues “intrepid” and “notoriously” in the first half of the sentence imply that the path chosen by the veteran hikers was difficult. Predict “dangerous” for the first blank. Choice (C) treacherous, which means “hazardous,” matches this prediction and is correct. Eliminate (A) facile, which means “easy,” since this is the opposite of the prediction, and (B) scenic, which means “pretty,” since this meaning is not supported by any context clues.

The second blank describes the other group of hikers. These hikers were “inexperienced” and opted to take a “less challenging” trail. You can predict that this group is “cautious.” Choice (D) circumspect, which means “careful,” is a match and is correct. Eliminate (E) bewildered, which means “confused,” as this is not supported by the context, and (F) reckless, which means “careless,” as this is the opposite of what the sentence calls for.

Answer: C, E, I

5. C, E, I

The key to this question is the detour road sign “yet.” Without that road sign and the rest of the sentence, one could predict a number of words for the first two blanks, even some that are opposite others. Was there little attention because of few fatalities? Was there a great deal of attention due to a large number of fatalities? “Yet, there were warnings” provides the answer. “Yet” hints that the warnings were not heeded. So predict that the pandemic initially drew “little” attention (for the first blank) due to the fact that even though many people were infected, there was a “lack” of deaths (for the second blank). This reasoning leads to (C) scant, or “having a small or insufficient supply,” as the correct answer for the first blank, and (E) infrequent, or “rare,” for the second blank. (A) widespread is the opposite of what is needed for the first blank, while (D) myriad and (F) innumerable, both of which mean “very many,” are the opposite of what is needed for the second blank. Additionally, (D) and (F) are close in meaning to each other, which is a sign that neither is correct. Note that (B) adverse, which means “hostile,” “harmful,” or “acting in a contrary direction,” doesn’t fit here, as there is nothing in the sentence that suggests the type of attention the pandemic received, just the amount it received.

For the third blank, if the young adults who died had been in poor health to begin with, their deaths wouldn’t have raised warning flags. It must be, then, that they were young adults of otherwise “good” or “stable” health. This prediction leads to (I) sound, or “free from injury or disease,” as the correct answer for the third blank. Similarly, if the young adults’ health had been (G) unpredictable, their deaths wouldn’t be expected to attract attention or serve as a warning. (H) vulnerable, or “capable of being attacked or wounded,” is the opposite of what this sentence requires.

Answer: B, F

6. B, F

Replacing human workers with robots could be considered a good thing or a bad thing, depending on whom you ask. The second part of the sentence mentions an “ability” of the robots. That’s a positive statement about the robots, so predict that the second blank will describe how the robots have “improved” production quality. (F) enhanced is a great match for the prediction and is the correct answer for the second blank. (D) hampered, or “created difficulties for,” is the opposite of what is needed here. (E) sterilized can mean “made incapable of reproducing,” “made free of living microorganisms,” or even “made powerless or useless,” none of which makes sense in this sentence.

For the first blank, note the straight-ahead road sign “not only . . . but . . . also” in the sentence. This phrase means that the first part of the sentence should mention something positive about using robots just as the second part of the sentence did. Additionally, note that the production process involves molten metal. Distancing humans from very hot, liquid metal sounds like a safety improvement, so predict that the change has made steel production less “dangerous.” (B) perilous, or “hazardous,” is a perfect match. (A) humane and (C) compassionate, both of which basically mean “sympathetic,” are tempting traps for those who miss the sentence’s clues and focus on how human workers might be losing their jobs rather than on the benefits of using robots.

Answer: C, E

7. C, E

Note the contrast between the first part of the sentence and the second. According to the second part of the sentence, scholars don’t view Johnson’s ideas favorably. They reject them without much consideration. Yet, as the first part of the sentence says, Johnson was awarded tenure. Based on the second part of the sentence, you can predict that Johnson’s colleagues—that is, other scholars—would be “surprised” or “puzzled” by the fact that he was awarded tenure. (C) perplexed and (E) bewildered, both of which mean “confused,” match the prediction and are correct. The sentence does not imply that Johnson’s colleagues were (A) irate, which means “angry,” at his being granted tenure; and even if they were, there is no second choice to give the sentence the same meaning. (D) envious, or “jealous,” can be eliminated for the same reason. (F) gratified, or “pleased,” doesn’t make sense in light of the fact that Johnson’s colleagues reject his ideas. Finally, (B) unsurprised is the opposite of what the sentence calls for.

Answer: C, E

8. C, E

The phrase “collided with” serves as a detour road sign in this sentence. The “promise” that mobile communication is supposed to improve “peace of mind” contrasts with the fact that it allows the professionals’ supervisors to reach them when they are trying to spend time with their families. Thus, the word in the blank should contrast with “peace of mind.” “Stress” or “anxiety” would be fine predictions. (C) perturbation, which means “agitation,” and (E) vexation, which means “frustration,” are great matches and are correct. (B) serenity and (F) tranquility both mean “calmness” and are the opposite of what is needed. Be careful: you might think that the ability to be reached by superiors at any time would lead to (A) flexibility or (D) productivity, but neither of these contrasts with the promised “peace of mind.”

Answer: B, D

9. B, D

The structure of this sentence is challenging: the blank is part of an example, so you should use the content of the example to predict. One type of food is “potatoes,” while the other is “chocolate.” Predict the answer: “specimens as ‘different’ as potatoes and chocolate.” (B) and (D) match that prediction nicely and create sentences with equivalent meanings. (A) distributed does not work well with the syntax of the sentence and does not have a match among the answer choices. (C) regarded and (E) unexpected are wrong for a similar reason: they have no synonyms among the other answer choices. Finally, (F) reviled has a strongly negative connotation that the sentence does not support.

Answer: A, D

10. A, D

Perhaps you weren’t expecting a chemistry lesson, but this question provides it. Don’t let the unfamiliar content distract you; instead, focus on the clues. You need a verb in the blank: what have people historically done to soap? The best clues are “treating” and “to create.” These words indicate that people made soap with this process. Both (A) manufactured and (D) produced match this meaning and are the correct answers. (B) enhanced and (C) improved are synonyms but do not match the clues in the sentence: there is nothing to indicate that soap was once an inferior product and needed improving. (E) ameliorated means “to make a bad situation more tolerable” and is not supported by the clues in the sentence. Finally, there’s no suggestion in this sentence that people (F) undermined soap; instead, they used this process to create it.

Answer: A, C

11. A, C

The passage defines ergodic literature as works that present the text, pages, or chapters without a prescribed order. Both (A) and (C) fit this definition, as Calligrammes presents the text such that it is not to be read “left to right and top to bottom,” and Composition No. 1 does not have a prescribed order to its pages. If matching these answer choices to the definition alone is difficult, compare them to the texts mentioned in the passage; Calligrammes is similar to House of Leaves in its arrangement of text on the page, and Composition No. 1 is similar to the I Ching in the randomness involved in determining its order of reading.

(B) does not match this definition. While Finnegans Wake might be difficult to understand or interpret, there is nothing in the description of the novel that suggests that determining the order of reading requires effort on the part of the reader.

Answer: E

12. E

Hieroglyphics are described in the passage as having a prescribed order of reading that is different from that of many modern forms of writing, and the passage states that this order was “understood” by ancient readers. By contrast, modern readers might find them difficult to understand or excessively complicated, and this is exactly what “involved” means in this context. (E) complex is a close match for this definition and is the correct answer.

(A) participatory is a common definition of “involved,” but the sentence does not specify anything that the hieroglyphics are participating in. There is nothing in the passage to suggest that hieroglyphics are (B) troubling, and (C) intelligible or “easily read or understood” is the opposite of the meaning expressed in the sentence. Finally, hieroglyphics are described as (D) archaic or “ancient,” but this answer choice misses the contrast between the difficulty modern readers may have in reading hieroglyphics and the ease with which contemporary readers understood their arrangement.

Answer: C

13. C

In this Logic question, you have to characterize the relationship between the two highlighted phrases. One of the difficulties in doing so is that the author’s thesis is not stated outright but merely implied: though Hannibal made a mistake in marching elephants across the Alps, it would be incorrect to consider only this incident when evaluating Hannibal’s military prowess. As a result, the first highlighted sentence is a position that the author believes is an accurate evaluation of Hannibal but isn’t the only thing we should remember about him. The second highlighted sentence provides evidence for the idea that Hannibal was actually a better general than many believe him to be based on the single story discussed in the first paragraph. The only answer choice that correctly matches both of these roles is (C).

(A) is incorrect because it misrepresents the author’s position; the author argues that this blunder isn’t the whole story, so the first highlighted sentence cannot be the author’s main point. (B) might seem tempting, but recall that the author agrees in the second paragraph that Hannibal “did incorrectly believe that the elephants would be hardier” than they were. Since the author concedes that this was a blunder, the author is not attempting to refute the first highlighted statement. (D) is a reasonable interpretation of the first highlighted statement, but since the second highlighted statement is evidence for a position rather than the position itself, this choice can be eliminated. Finally, (E) distorts the author’s tone; while the author concedes that Hannibal made a mistake, there is no language to suggest that this concession is difficult for the author.

Answer: E

14. E

This Global question asks for a summary of the author’s purpose. The passage focuses on the ways in which the geography of the Mesopotamian and Egyptian civilizations influenced their religious beliefs. The author’s tone is one of explanation rather than argument, so (B) “arguing that . . .” and (D) “persuading readers . . .” can be immediately eliminated. Looking at the remaining choices, (E) is a match. (A) is too broad; the author is interested in more than just a general explanation of the origin of the two religions, so this choice misses the major role of geography in the author’s explanation. (C) distorts the point of the passage, as the author does not drill all the way down to what “individual gods” in each pantheon represent, nor does the author use “different natural phenomena,” as both of the examined religions were influenced by the same phenomenon, flooding rivers.

Answer: B

15. B

The author claims that the cause for the specific features of the Mesopotamian religious beliefs is the “violent and unpredictable” nature of the region’s natural disasters. While the typhoons described in (A) are certainly violent, they are predictable, occurring once during a specific week of the year. This means that (A) can be eliminated. (B) describes a phenomenon that has both of these qualities: the tornadoes are highly destructive and occur “without warning,” so (B) is a correct answer. Finally, (C) misses the mark because while the tremors are unpredictable, they are described as “mild.” Eliminate (C).

Answer: Different circumstances existed in Egypt: The Egyptians lived along the Nile...

16. Different circumstances existed in Egypt: The Egyptians lived along the Nile, a river that, prior to the completion of the Aswan High Dam in 1970, would flood gently every four months, depositing silt that provided nutrients vital to agriculture in the region.

The question stem references a civilization that sees itself as favored by the gods, so the correct answer should be a sentence that can be associated with the Egyptians. Specifically, the question is asking for a cause for this view. Since the author’s position in the passage is that geography influenced the religious beliefs of the Mesopotamian and Egyptian cultures, look for the sentence that describes the environmental feature that led to this belief for the Egyptians. The second-to-last sentence is the one that describes the flooding of the Nile as gentle, predictable, and beneficial for the Egyptians, and the final sentence says that this results in the attitude described in the question stem. The second-to-last sentence, “Different circumstances existed in Egypt . . . ,” is the correct answer.

Answer: E

17. E

This question asks for a situation analogous to the first sentence of the second paragraph, which contains the aphorism “a little knowledge is a dangerous thing.” The passage provides some context for this idea, saying that someone who has a cursory understanding of the basic scientific principles discussed in the first paragraph might be led to incorrect and harmful conclusions about the ideas discussed in the second paragraph. The correct answer will share this structure.

(A) describes a situation in which restricting knowledge actually produces a desired effect, since this person is attempting to limit exposure to musical ideas that might influence his or her own writing, so this choice can be eliminated. (B) can likewise be eliminated since this person presumably has a great deal of knowledge but is not using it, instead benefiting from skills and intuition. Eliminate (C) because it describes someone who gains too much information rather than too little. Eliminate (D) because, while it describes an example of too little knowledge, there is no indication that this lack of knowledge will lead the student to come to an incorrect conclusion.

This leaves (E), which is correct. The individual described, similar to the critics described in the passage, has a little bit of knowledge about these two chemicals, but lacks an understanding about their reaction when mixed, and expects that their mixture would likewise be harmless. It turns out that the opposite is true, just as the critics in the passage expect the sea level to stay the same, when in reality it would rise.

Answer: A, B

18. A, B

Because there is no research clue given in the question stem, the best strategy for this all-that-apply Inference question is to check each choice against the information presented in the passage. (A) is supported by the first two sentences; ice floats on water because it is less dense than water, which results from the property that water expands when it freezes. The first sentence describes water as being “among the few substances” that do this, so it can be reasonably inferred that most substances do not. (B) is also supported by the second sentence; the lower density of ice directly causes it to float, so anything with a lower density can likewise be expected to float. (C), on the other hand, is contradicted by the second paragraph. The passage cites two reasons why the melting of ice caps would cause sea level rise: the land mass described in (C) and the difference in density between sea water and fresh water. Even if the Antarctic ice were not supported by land, the difference in density would still be sufficient to cause a rise in sea level. (C), therefore, is incorrect.

Answer: C

19. C

The passage provides four facts to fully explain the phenomenon in question, each of which corresponds to one of the four incorrect answers. The fact that water is rare among compounds in that it expands when it freezes corresponds to choice (A). The notion that the southern ice cap rests on a land mass, indicating that the scientific principles mentioned in the first paragraph do not apply in this case, matches up with (B). (C) is not present in the passage, as there is no mention of a specific event in the passage. Thus, it is the correct answer. The difference between salty ocean water and fresh water causing greater buoyancy allows elimination of (D). Finally, the description of differences in density causing the buoyant force is represented by (E).

Answer: D

20. D

The author begins by describing the Arnolfini Portrait and discusses some evidence for a common interpretation: The painting is a “marriage contract of sorts.” The author goes on to say that other art historians have reasons to doubt this interpretation. As a result, (D) is the best description of the author’s purpose.

Both (A) and (E) are too specific; the author does describe the painting and makes mention of marriage customs as evidence, but neither of these is the focus of the passage. (B) and (C) are extreme; the author doesn’t go as far as to condemn the interpretation or say that it is faulty, nor is the author interested in presenting her own interpretation of the painting.

Answer: C

1. C

The question shows a figure with an equilateral triangle that shares a side with the hypotenuse of a 30°-60°-90° triangle. You are asked to compare the height of the equilateral triangle to . Because triangle ABD is a 30°-60°-90° triangle, the length of the hypotenuse is twice that of the shortest side. Given that AB = 1, it follows that BD = 2. Since triangle BCD is equilateral, sides BC and CD are also 2 units long, and all three of its angles are 60°. A perpendicular line dropped from a vertex of an equilateral triangle to the opposite side bisects both the angle at the vertex and the opposite side. So, angle ECD is 30°, side DE is 1, and side CD is 2. You can use the Pythagorean theorem to calculate the length of CE: 1² + CE² = 2², so CE² = 4 − 1 = 3 and CE = . Alternatively, you could have used the ratios of the sides of the 30°-60°-90° triangle CED to get the same result. Since Quantity A and B are both , (C) is correct.

Answer: A

2. A

If you tried to solve the system of equations by substitution, because of the coefficients of a and b, you would wind up with fractions, so use combination instead. Start by rearranging the second equation to get 5a + 3b = 34. Make the coefficients of b the same in both equations by multiplying the first equation by 3 to get 9a − 6b = 27 and the second equation by 2 to yield 10a + 6b = 68. Now, add the two equations to eliminate b:

So a = 5. Plug this into the first equation to get 3(5) − 2b = 9, so 15 − 9 = 2b and b = 3. Thus a > b, so (A) is correct.

Answer: C

3. C

The centered information provides information about percents and fractions of different-colored marbles in a box. Since the problem involves percents of unknown values, pick 100 as the total number of marbles.

If 20% of the marbles are blue, then 20 out of the 100 are blue, and 80 are either red or white. Since one-quarter of those 80 are red, there are 80 × 0.25 = 20 red marbles; the other 80 − 20 = 60 are white. Thus, Quantity A is 20 and Quantity B is one-third of 60, which is also 20. Therefore, (C) is correct.

Answer: D

4. D

To make the quantities easier to compare, make them look more alike. Use FOIL to multiply out Quantity A: (r + 3)(s + 2) = rs + 2r + 3s + 6. Now, both quantities have terms rs and a number, so you can subtract Quantity B, rs + 12, from both quantities to make Quantity A 2r + 3s − 6. After the subtraction, Quantity B is zero. If 2r + 3s − 6 is positive, Quantity A is greater than Quantity B; if 2r + 3s − 6 is negative, Quantity B is greater than Quantity A. Since there are no restrictions on the values of r and s, either case could be true and (D) is correct.

You could also use Picking Numbers. For example, let r = 2 and s = 3. Then Quantity A is (2 + 3)(3 + 2) = 25 and Quantity B is (2 × 3) + 12 = 18. In this case, Quantity A is greater. But if you let r = −3 and s = −2, Quantity A will be 0 while Quantity B will still be 18, making Quantity B greater. Once again, you have demonstrated that a definite relationship cannot be determined.

Answer: B

5. B

The units digit (or ones digit) is the last digit before the decimal point; in this case, it will be the right-most digit. To compare the units digit of X to 5, you don’t actually need to do the entire multiplication; you need to pay attention only to the last digit. So, multiply the last digit in each of the individual numbers and drop the tens digit if applicable. The first two numbers, 86 and 47, become 6× 7 = 42; and then, 42 × 94 becomes 2 × 4 = 8; and so on: 8 × 3 = 24; 4 × 4 = 16; 6 × 6 = 36; and 6 × 2 = 12. Thus, the last digit is 2, which is less than 5. Choice (B) is correct.

Answer: B

6. B

First express the relationships described in the centered information algebraically. Diego drinks 50% more coffee than Pablo drinks. That means Diego drinks 150% of whatever amount Pablo drinks. Using P for the amount of coffee Pablo drinks in a year and D for the amount of coffee Diego drinks in a year, this relationship can be expressed as D = 1.5P. Lilly is also compared to Pablo. She, however, drinks twice as much in half a year as Pablo does in a whole year. So in one year, Lilly drinks four times as much as Pablo does. That equation can be written as L = 4P. Now consider Quantity A. If Diego drinks 1.5P in one year, then in 5 years, he drinks 5(1.5P) = 7.5P. For Quantity B, the amount of coffee Lilly and Pablo combined drink in 2 years would be 2(L + P) = 2(4P + P) = 2(5P) = 10P. Thus, Quantity B is greater than Quantity A, regardless of the value of P (i.e., how much coffee Pablo drinks per year), and the answer is (B).

You could also have picked numbers. Say Pablo drinks 100 ounces of coffee per year. Then, Diego drinks 150 ounces per year and Lilly drinks 400 ounces per year. Using these numbers, Quantity A is 150(5) = 750, while Quantity B is 2(400 + 100) = 1,000. Again, (B) is correct.

Answer: B

7. B

The figure shows a square with a perimeter of 20 units. Since all four sides of a square have the same length, each side of this square has a length of 20 ÷ 4 = 5 units; this is Quantity A. The area of a square is equal to the square of one of its sides, so the area of the square is (5 units)² = 25 units². Since each side of a square is the same length, the four triangles created by the two diagonals in the figure have the same area, which means that Quantity B, the area of the shaded region, is one-fourth the area of the square, or 25 units² ÷ 4. This is clearly greater than Quantity A, which is 20 units ÷ 4, so there is no need to do any further calculation. (B) is the correct answer.

Answer: D

8. D

Since a and b are integers, the sum of a and b will be an integer. The only way that sum can be greater than 4 and less than 6 is if it is equal to 5. Thus a + b = 5. Think of the possible integer values for a and b that would make this true. One of them could be 1 and the other 4, or one could be 2 and the other 3. However, the centered information also says that the absolute value of a − b is 1. This means a and b are one apart. Thus, either a = 2 and b = 3 or a = 3 and b = 2. Both Quantity A and Quantity B deal with the volume of a cylinder, which can be found by squaring the radius and multiplying by π and the height of the cylinder. Thus, Quantity A is a²(π)(b), while Quantity B is b²(π)(a). Since a, b, and π are all positive, both Quantities can be divided by all three of those values to end up with a for Quantity A and b for Quantity B. Since it’s impossible to know which of a or b is 2 and which is 3, the correct answer is (D).

Answer: B

9. B

Start with the most concrete information given. The angle to the right of the 115^o angle is supplementary to it and therefore measures 180 − 115 = 65. Since QR is parallel to ST, SP and TP are transversals, and therefore angle PST is 65^o, and the angle to the left of the y + 25 angle is equal to x. Finally, angle SPT is supplementary to y, and therefore measures 180 − y. At this point, the figure with information added looks like this:

The angles of triangle SPT add up to 180, so (180 − y) + 65 + x = 180. This simplifies to x − y = −65. (Note that the same equation could have been set up for the small triangle at the top of the figure with the portion of QR that crosses triangle SPT as its base.) Now make use of the y + 25 angle. Since it is supplementary to x, (y + 25) + x = 180. This simplifies to x + y = 155. At this point, you have two equations involving x and y: x − y = −65 and x + y = 155. Add the two equations together to get 2x = 90, which means x = 45 and the correct answer is (B).

Answer: 504

10. 504

This is a permutation problem because the order in which the fossils are chosen matters; each room is a slot that will be filled with one fossilized dinosaur skeleton. For the first room, there are 9 skeletons to choose from. Because one of the nine has already been chosen, for the second room there will be 8 possible skeletons, leaving 7 possibilities for the third room. Thus, the number of possible displays is 9 × 8 × 7 = 504.

Answer: E

11. E

The question asks for the number of groups of movies a production company can submit for awards consideration. This is a combinations problem, as the order of the movies doesn’t matter. Since there must be at least 3 romantic comedies, the possible groups are 3 romantic comedies and 2 horror movies, 4 romantic comedies and 1 horror movie, or 5 romantic comedies. To find the total number of possible groups, find out how many ways there are to make each type of group and add them up.

If all 5 submitted movies are romantic comedies, then there are ₆C₅ ways to select such a group. It’s possible to use the combinations formula to find this number, but some critical thinking will likely be faster. For each group of five movies, there’s one that’s not picked. There are 6 ways to choose the movie that will be left out, so there are 6 ways to pick a group of 5 movies.

If 4 of the submitted movies are romantic comedies, there are ₆C₄ ways to select these 4:

Each of these 15 groups of 4 could be submitted along with any of the 8 horror movies as the fifth in the set, so there are 8 × 15 = 120 ways to submit 4 romantic comedies and 1 horror movie.

The last case to consider is 3 romantic comedies and 2 horror movies. First, count the romantic comedies:

Now, count the horror movies:

Each of these 28 sets of horror movies can be submitted along with any of the 20 sets of romantic comedies, so there are 20 × 28 = 560 possible sets of 3 romantic comedies and 2 horror movies. To find the total number of possible 5 movie sets, add up the three possibilities: 560 + 120 + 6 = 686. (E) is correct.

Answer: 4

12. 4

Since you need to determine how many machines are needed to roast 84 lb of coffee beans in 2 hours, start by finding out how much an individual machine can roast in 2 hours. If 10 machines can roast 210 lb of coffee beans in 3 hours, they can roast 70 lb in 1 hour. This means that 1 machine can roast 7 lb in 1 hour, or 14 lbs in 2 hours. so the company originally had 6 roasting machines. Be careful, though; the question asks for the number of new machines purchased, not the original number of roasting machines. If they started with 6 and now have 10, they bought 4 machines.

Answer: D

13. D

Picking Numbers is the best strategy here. If p = 2, then 2p = 4 and 4p − 1 = 7. The integers 5 and 6 fall between 4 and 7, so plug p = 2 into the answer choices to see which is equal to 2, the number of integers.

(A)

(B) 2 = 2

(C) 2 + 1 ≠ 2

(D) 2(2) − 2 = 2

(E) 3(2) − 3 ≠ 2

Both (B) and (D) equal 2, so try p = 3. In this case 2p = 6 and 4p − 1 = 11. There are 4 integers in between: 7, 8, 9, and 10. Since p = 3, eliminate (B). Double-check (D): 2(3) − 2 = 6 − 2 = 4; (D) is correct.

Answer: C, D

14. C, D

The question states that a is a multiple of b, but that multiple is given as a range. The equation is also provided, and you’re asked to find what could be. Since x, the multiplier for b, could be any value between (but not including) 1 and 4, there are infinite possible values for . Plug in the limits for x, 1 and 4, to find the range of allowable values for that fraction.

Simplifying a bit makes this task easier. Rewrite as b = 3c so that you can rewrite a = bx as a = 3cx. Divide both sides of this equation by c to get = 3x. If x = 1, then 3x = 3. If x = 4, then 3x = 12. So the allowable range is 3 < < 12. Choices (C) and (D) fall within this range. Choices (B) and (E) do not because the endpoints are not included: 1 < x < 4, not 1 ≤ x ≤ 4.

Answer: 5

15. 5

Since the perimeter of a square is 4 times the length of a side, the length of each side of ABCD is 32 ÷ 4 = 8. The area of a triangle is × base × height. The base of the triangle in the figure is DE, the height is AD, and the area is 12. Thus, 12 = × DE × 8, 12 = 4DE, and DE = 3. Since DE + EC = 8, EC = 8 − DE. Plug in 3 for DE to get EC = 8 − 3 = 5.

Answer: C

16. C

The question provides two quadratic equations for the positive integers x and y and asks for the value of y. Notice that the first equation is the pattern quadratic, (a + b)² = a² + 2ab + b². So, x² + 2xy + y² = (x + y)² = 49. Thus, since x and y are positive, x + y = = 7, but this is not enough information to solve for either x or y. The second equation is another pattern quadratic. Factor x² − y² to (x + y)(x − y) = −7. From the other equation, you know that x + y = 7, so substitute to get 7(x − y) = −7, which means that x − y = −1. Combine the two equations to isolate one of the variables. You can get y to drop out simply by adding them: x + y + x − y = 7 + (−1). Thus, 2x = 6 and x = 3. Substitute 3 for x in the equation x + y = 7 to find that y = 4. Choice (C) is correct.

Some critical thinking could save time on this question. Once you find out that x − y = −1, which means that y is 1 greater than x and that the two must add up to 7, you could easily determine that x and y have to be 3 and 4, respectively.

Answer: B, E

17. B, E

The problem gives ranges for both x and y and asks which of the inequalities in the choices must be true. Therefore, any choice that could be false can be eliminated. For range questions such as this one, examine the extreme values of the variables as limited by the given ranges. For instance, > 3 could be as small as 3.0000001 or even less. (Note that this problem does not specify that x and y must be integers.)

(A) Incorrect. While a value of x close to 7 minus a value of y close to −2 is positive, a value of x close to 3 less a value of y close to 4 is negative. Since the question asks for statements that must be true rather than those that merely could be true, this choice is incorrect.

(B) Correct. You only need to examine the minimum values. Since −2 + 3 > 0, this inequality will be valid for all permitted values of x and y.

(C) Incorrect. Since the maximum value of y is almost 4 and the minimum value of x is just greater than 3, it is possible for y to be greater than x.

(D) Incorrect. Use the lower limit for y and the upper limit for x: 2(−2) − 7 = −11, which is much less than 0.

(E) Correct. Use the lower limit for x and the upper limit for y: 2(3) − 4 = 2, which is greater than 1.

The correct answers are (B) and (E).

Answer: D

18. D

First, determine the year when the combined percent downloads for Latin and Dance was greater than the percent downloads for Pop. In 2012, Pop was 25% and Latin and Dance combined were 35%, which means 2012 is the year in question. The line graph shows that the total number of downloads in 2012 was 28 million. Rounding 28 million up to 30 million and recognizing that 35% is a little more than one-third leads to about 10 million downloads. (D) is the correct choice.

Answer: C

19. C

To find the percent increase in Pop downloads, first find the actual number of Pop downloads for 2008 and for 2012. In 2008, the line graph shows the total number of downloads was 10 million, and the bar graph shows that 40% of those were Pop downloads. That means that the number of Pop downloads in 2008 was 0.40 × 10 million = 4 million. In 2012, the total number of downloads was 28 million, and 25% of those were Pop downloads; so, there were 0.25 × 28 million = 7 million Pop downloads. Applying the percent increase formula to those values results in:

(C) is the correct answer.

Answer: B, D, F

20. B, D, F

Since the bar graph is based on percentages, determine what percent 6 million and 11 million downloads fall between in 2016 and check those against the answer choices. In 2016, there were 40 million total downloads, so the percents that the correct answers need to fall between are 6 million ÷ 40 million = 15% and 11 million ÷ 40 million = 27.5%. Now, go through the choices systematically.

(A): Pop represented 30% of downloads in 2016. That’s outside the range because it is greater than 27.5%.

(B): Country represented 20% of downloads in 2016, which does fall between 15% and 27.5%. (B) is a correct choice.

(C): R&B/Hip-Hop represented 10% of downloads in 2016. That’s less than 15% and is thus outside the range.

(D): Latin represented 15% of downloads in 2016, and since the range is inclusive, (D) is correct.

(E): Dance represented 10% of downloads in 2016. That’s less than 15% and is thus outside the range.

(F): Other represented 15% of downloads in 2016. Like (D), this choice works because the range is inclusive. (F) is correct.

(B), (D), and (F) are the correct choices.

Answer: D

1. D

The clues “as technology grows” and “its constant use” allow for a prediction here: the word in the blank should match the phrase “its constant use,” so a word like “prevalent” or “widespread” would work well. (D) fits that prediction well and is correct. (A) feckless means “useless,” which does not match the example of “a child who can retrieve the answer to any question.” (B) unreliable is wrong for the same reason. (C) irksome means “annoying,” but the sentence does not provide any clues that technology is annoying. Finally, (E) repetitious is incorrect because the sentence does not suggest that technology repeats itself; indeed, the phrase “increasingly sophisticated” indicates change.

Answer: B, D, G

2. B, D, G

Blank (i) offers a strong clue, so it’s a good place to start: languages do something to “new words” while “abandoning old” and “changing others.” Predict “adopting” or “creating.” (B) is a clear match, since embracing means “accepting.” (A) auguring means “predicting.” This is a tempting trap, but it does not match the word “evolve,” which appears earlier in the sentence. Languages would not “change” merely by predicting new words. Lastly, (C) obscuring means “hiding,” but nothing in the sentence suggests that a language would hide new words.

The next easiest blank is likely blank (iii), since the sentence gives examples of modern phrases that came from Shakespeare. Use those examples to predict “credits,” but be flexible with these phrasal answer choices. (G) matches well: the clues in the sentence indicate that these modern English phrases came from Shakespeare. (H) portends several disconcerting means “predicts several disturbing” phrases, but the sentence does not suggest that these phrases are disturbing. The verb in (I), attributes, could work in the context of the sentence, but the other words in the answer choice, few impeccable, make this incorrect, since the sentence does not indicate that Shakespeare made few or “perfect” contributions to modern English.

Finally, predict for blank (ii). The sentence claims that modern English seems to have “little connection” with Shakespeare’s language, and the structural keyword “since” offers the explanation. Speakers of modern English “avoid” or “don’t use” these archaic words. (D) means “shun” and is correct. (E) appropriate means “take for one’s own use,” but that is the opposite of the sentence’s meaning, while (F) mitigate means “reduce” or “alleviate,” but current speakers do not reduce these words.

Answer: A, E, H

3. A, E, H

Begin with blank (i): these animals use jet propulsion to search for prey and avoid or try to get away from predators. (A) works nicely here and is correct. (B) bifurcate means “to divide into two branches,” but that does not describe getting away from predators. (C) dissemble means “to disguise a true feeling,” but cephalopods use jet propulsion to move, not to disguise anything.

The word “although” sets up a contrast between animals, which have used jet propulsion for millennia, and humans. The implication is that humans were not able to use jet propulsion to get around until the internal combustion engine was invented. That can serve as your prediction: “did not ‘use’ jet propulsion.” (E) is a great match for this prediction. (D) fortuitously analyze means “examine by a lucky chance.” There is no suggestion of chance playing a role. Moreover, the sentence indicates that the invention of the internal combustion engine allowed humans to use jet propulsion, not just to examine it. (F) rampantly augment means “add to without restraint.” This is incorrect because the sentence does not imply that the invention happened “without restraint” or that people “added to” jet propulsion.

The final blank follows from the contrast keyword “although,” as well. Animals have used jet propulsion for a long time, and humans were able to use it after the invention of the internal combustion engine. This development of jet propulsion “made a somewhat inefficient method of locomotion ‘workable’ for many modern applications.” (H) matches that prediction. (G) commensurate means “in proportion” and does not match the context of the sentence. (I) sporadic means “scattered,” but the sentence does not imply that the internal combustion engine made jet propulsion “scattered.”

Answer: C, E

4. C, E

“Axiomatic” means “self-evident or beyond question.” The detour road sign “though” sets up a contrast between the apparent truth of the phrase and the debate that it causes. Anticipate the right answer to be a word like “difficult” or “major” debate. (C) means “causing argument” and matches the prediction perfectly. (A) dispassionate means “not influenced by strong feelings,” but a major debate would cause strong feelings. (B) perfunctory means “involving a minimum of effort.” This is incorrect because nothing in the sentence indicates that the debaters are not trying.

Blank (ii) describes the effect that looters who steal artifacts from archaeological sites have on “the country’s claim of ownership.” Since these looters are taking antiquities without regard for the country’s claim, you should predict “ignores” or “undermines.” (E) means “disregards” and describes the actions of the looters well. (D) stabilizes has a positive connotation and does not match the negative implication of the sentence. (F) demotes means “makes something less important.” The looters may view the country’s claim as unimportant, but the act of looting itself (“this” in the original sentence) does not make the country’s claim less important.

Answer: C, E, I

5. C, E, I

The first part of sentence one makes a claim about “avant-garde,” or radical, artists. The straight-ahead road sign “as” shows that the second part of this sentence provides a reason for that claim. Why would radical artists have a hard time gaining acceptance? Because their work confuses and enrages people. Even if the word “avant-garde” is unfamiliar, you can use “produces confusion or even rage” to understand the negative connotation for blank (i). “Controversial” work would have this effect. (C) provocative matches that prediction perfectly and is correct. (A) complacent means “satisfied with things as they are; lacking a desire to change things,” but this is the opposite of “avant-garde.” (B) decorous is wrong for a similar reason: it means “proper,” which is the opposite of the blank’s intended meaning.

For blank (ii), use clues in the previous sentence: “often produces confusion or even rage.” The same works that enraged people might easily have “caused” riots. Process of elimination may help here. (D) suppressed means “restrained,” but these works “often” caused confusion, even rage. (E) engendered means “caused or gave rise to.” This is exactly the effect you’d expect controversial works to have, so (E) is correct. (F) belied means “shown to be false,” but riots cannot be shown to be false. The riot may have been based on something false or otherwise incorrect, but this blank refers to the riot itself.

There are two detour road signs in the second sentence that help with blank (iii). The phrase “even so” indicates that you should expect an outcome that contrasts with the fact that avant-garde artists struggle for acceptance. The word “but” signals a contrast between the immediate result of the works (riots) with a subsequent result (enormous sums when sold). A good prediction for blank (iii) would be “earned.” (I) is correct, since garnered means “acquired.” (G) expended means “used up,” which is the opposite of the intended meaning. (H) underscored means “emphasized,” but the artworks do not merely emphasize the amount of money; they are sold for enormous sums.

Answer: B

6. B

The word “but” creates a contrast between the first and second parts of this sentence. Philosophers have debated about what love really means, but there is one common thread: real love comes from shared understanding and respect. The author entertains the idea that the “diverse uses” of the word “love” have made it harder to achieve a clear definition. Predict “unclear.” (B) works well, since nebulous means “cloudlike, hazy.” (A) benign means “harmless,” but this does not match the sentence’s implication that love is hard to define. (C) pernicious, meaning “destructive,” (D) seditious, or “tending to incite rebellion,” and (E) specious, or “false,” have negative connotations that are too strong for this sentence.

Answer: C, E

7. C, E

The blank is at the end of the sentence, but the main clue comes toward the beginning; “conflicting” indicates a contrast between the results of the studies. The sentence describes “unpleasant results,” so the missing word must describe results that contrast with this. You are looking for a pair of synonyms that have a positive tone and mean something like “pleasant” or “healthy.” (C) salubrious means “healthful,” and (E) beneficent means “advantageous,” so that’s the correct pair. (A) addictive may catch your eye because caffeine can in fact be habit-forming, but the missing word refers to its positive properties. (B) lackadaisical means “without enthusiasm,” which doesn’t fit the context. (D) adventitious may be tempting as it looks similar to “advantageous,” but it actually means “extrinsic” or “not inherent.” Finally, (F) innocuous, or “harmless,” is not strong enough to contrast with “unpleasant;” furthermore, no other word gives the sentence a similar meaning.

Answer: B, E

8. B, E

This sentence features the detour road sign “but.” On the one hand, the critic does not question something about the researcher; on the other hand, the critic argues that her conclusion isn’t supported. The critic finds fault with the researcher’s conclusion, so the missing word will be something with which the critic does not find fault. It may be difficult to formulate a specific prediction, so use process of elimination in the answer choices. Start by eliminating anything with a negative charge: (A) discomfiture (“embarrassment”); (D) mortification (also “embarrassment,” which makes these choices a trap pair of synonyms); and (F) ineptitude (“lack of skill or ability”). (C) egoism (“self-interest”) does not fit the context of the sentence, since the critic does not suggest that the researcher is selfish. The correct answers, then, must be (B) integrity and (E) rectitude, both of which mean “moral correctness” or “honesty.” The idea of honesty fits the context of the sentence: the critic is not suggesting that the researcher lied, just that her evidence was not strong enough to prove her conclusion.

Answer: B, E

9. B, E

The straight-ahead road sign “upon” reveals how the class president reacted to the “incendiary” article. The word “incendiary” literally means “designed to cause fires.” When used metaphorically, however, it means “tending to cause conflict.” After reading the conflict-causing article, the class president “felt compelled” to respond and “voice his objections.” Predict something that follows from the adjective “incendiary”: what would someone write to “voice his objections” in response to such an article? It could be something neutral like “response” or something more charged, like “protest” or “complaint.” There is an additional clue in the word “harangue,” which means “rant,” so “protest” is a good prediction. (B) and (E) match nicely and are correct: they both mean “a verbal attack.”

(A) missive means “letter.” A person could certainly write a letter to an editor, but this has no match among the answer choices, nor is it as charged as the word “harangue” would lead you to expect. (C) tome (“a book, especially a long one”) is not supported by the clues in the sentence. It’s possible the response was long, but the sentence does not indicate that. Additionally, tome has no match among the other choices. A quandary (D) is a “dilemma,” and while a protest or complaint might create a quandary, they are not the same thing. Finally, (F) hypothesis, “an explanation proposed for a given phenomenon,” does not match the context of the sentence, which gives no hint that the class president seeks to explain anything.

Answer: B, F

10. B, F

The subordinate clauses in this sentence may make it difficult to analyze. Break the sentence apart to simplify its meaning. The sentence begins with a contrast word, “though,” which means that the second half of the sentence, “some species display . . .” will discuss some features that not all birds of prey share. The other parts of the sentence that mention “excellent eyesight,” “excellent hunters,” and “high-speed dive” are examples and elaborations that you can ignore unless you need to fine tune your prediction. At this point, however, look for two words that mean “different.” (B) unique and (F) distinctive fit well, since they both draw on the contrast between “all birds of prey” and “some species.” (A) voracious means “wanting a great deal of food.” This may be true of some birds of prey, but it does not follow from the contrast in the sentence. (C) fleeting, “lasting for only a little while,” is incorrect because the sentence does not suggest that the characteristics are only temporary. Given the example of the peregrine falcon, (D) rapid might be tempting. This choice, however, is incorrect because it misses the contrast in the sentence and lacks a match among the other choices. (E) advantageous means “helpful” and is incorrect because it does not create a contrast: all of the characteristics cited in the sentence (“excellent eyesight,” “sharp talons”) could be described as helpful. Moreover, there is no match among the remaining choices.

Answer: C

11. C

This argument begins with a discussion of the “look and say” method for teaching children how to read. Though the author describes one benefit of that method, she ultimately rejects the approach and recommends a phonics-based method. The first highlighted sentence offers a benefit of the whole language method. Eliminate (A), since this sentence does not “summarize” the position. Eliminate (B) and (E) since the first highlighted sentence does not state the author’s main point or conclusion. The second highlighted sentence offers an advantage of the phonics-based approach. From the remaining choices, eliminate (D) because this sentence is not the conclusion of the argument. (The author’s conclusion is that “teachers should use a phonics-based approach.”) (C) is correct.

Answer: D

12. D

The correct answer to this Inference question must be supported by the passage. The passage discusses the correlation between advanced cultures and realistic art. According to the author, realistic art “often” shows an “advanced” civilization. The author does not claim that this is a perfect correlation, but she cites examples of advanced civilizations that produced realistic art (ancient Greeks and Romans). Analyze each answer to find the choice that is supported by the passage, but be careful to avoid anything that is too extreme to be supported or that goes beyond the scope of the paragraph. (A) goes wrong in two ways: “invariably” is too extreme to follow from the author’s tentative claims, and “reject unrealistic art forms” goes beyond the scope of the passage. Perhaps advanced civilizations embrace both realistic and unrealistic art forms. (B) is incorrect because the author does not make a clear causal claim in the passage. Additionally, since the passage makes a qualified assertion (“often”), it’s impossible to extend that claim to other civilizations. (C) compares the likelihood that an advanced culture would produce realistic art instead of “any other type of art.” The paragraph does not include information about the relative frequency of realistic art and “any other type,” so this choice is incorrect. (D) makes a tentative claim, “in some . . . can take . . .,” that is easy to support from the passage. The author claims that Europeans took “nearly a millennium” to develop realistic painting and sculpture after the ancient Romans lost the ability to create them. Tentative or “soft” claims are easier to support than absolute claims. This choice is correct. (E) is incorrect because the author does not discuss modern abstract art.

Answer: A

13. A

According to the passage, Nelson’s tactics were unorthodox, so they could be described as “contrary to conventional military wisdom.” They’re also described as a risk that “paid off,” so the author must think that they contributed, at least in part, to the British victory. (A) is correct. (B) may seem tempting because it lines up with what King George III said in regard to Nelson’s death, but there is no way to know whether the author agrees with it, so it’s incorrect. (C) is incorrect because it’s too extreme; the author thinks that the unconventional tactics contributed to the victory, but again, there is no way to know whether she believes they were essential to the victory.

Answer: E

14. E

This Logic question asks why a particular detail was used. The Santísima Trinidad was mentioned in the middle of the passage as an example to support the point that the British fleet was outgunned and that victory did not seem certain. (E) is a good match for this prediction; the British may not have been confident of victory because of the more powerful enemy fleet. (A) is incorrect; all that was said about Nelson’s battle plan is that it was “unorthodox.” (B) is contradicted by the passage; if this ship was a common design, then it wouldn’t be “the most heavily armed ship in the world.” (C) may seem tempting, since the ship is used in support of the idea that the British weren’t certain that they’d be victorious; however, there’s no discussion of what the Spanish thought about their chances in the battle. (D) is too extreme; the British may not have been entirely confident that they’d win, but that doesn’t mean Nelson thought that they would lose.

Answer: B

15. B

This Logic question requires researching the last paragraph of the passage. The example of Frey differs from that of Seltzer in that he experienced more success before his downfall and was able to write a successful novel later in his career. (B) is the choice that captures the later literary success and is the correct answer. The last sentence says that the media’s view softened later, but that does not mean that their initial reaction was too harsh, which makes (A) incorrect. (C) is incorrect because there is no support in the passage that Frey was an obscure example. The phrase “malicious intent” is too extreme based on the passage and makes (D) incorrect. Frey did not experience permanent damage to his literary career, so (E) is incorrect.

Answer: D

16. D

The main point of the passage is to discuss the experiences of two authors whose memoirs were later shown to be untrue. The choice that most closely matches this understanding is (D). The incorrect answer choices are either too narrow or misrepresent the purpose of the passage with strong negative language. (A) speaks to a direct criticism that does not occur anywhere within the passage. (B) refers to the repercussions, but their effectiveness is never directly addressed in the passage. (C) is incorrect because the author never explicitly takes a side on whether the two authors were treated unfairly. (E) is addressed within the passage, but the debate between the two views is not the main point of the passage.

Answer: A

17. A

The author notes that Seltzer claimed to write the book to give a voice to those ignored by society, but the author goes on to say that this claim was not substantiated by the persona Seltzer adopted when promoting her book. The author implies that Seltzer was looking out for her own interests and states that she did a disservice to the people who actually experienced the events she wrote about. This matches (A) self-serving, which means “to put one’s own welfare and interests before those of others.” (B) unpremeditated and (D) spontaneous both mean “without forethought,” but Seltzer knew that her memoir was a fabrication, so these choices are both incorrect. Seltzer’s book is the opposite of authentic since it never actually happened, so (C) is incorrect. (E) authoritative, or “accurate,” is incorrect for the same reason.

Answer: B

18. B

This Inference question is too broad to make a prediction, so it is best to work through the choices and look for proof in the passage. (A) is not true for either author. Seltzer’s work was a complete fabrication, and Frey’s memoir included many embellishments. (B) has support in the passage because the falsehoods and exaggerations the two authors included in their memoirs were intentional and led to their respective downfalls. (C) is incorrect because it is too sweeping a statement to make, especially considering that Frey wrote another best seller. The passage does not speak on the level of deception in other genres, so (D) is incorrect. (E) is incorrect because the passage never states Frey’s motivations, and while the author implies that Seltzer’s reason for writing was self-serving, there is no explicit mention of a financial motive. The correct answer is (B).

Answer: C

19. C

This is a Detail EXCEPT question, so find the detail that is not mentioned in the passage. Also, keep in mind that Seltzer’s experience is discussed in the second paragraph, so that is where your research should be focused. (A) and (E) are mentioned in the penultimate sentence of the second paragraph as something Seltzer felt she needed to do to lend authenticity to her story, so both choices are incorrect. Seltzer grew up in the suburbs of Los Angeles but changed the setting of her memoir to South Central Los Angeles to lend it credence, so (B) is incorrect. Seltzer’s sister revealed her true identity, so it is reasonable to infer that Seltzer did not elicit her family’s cooperation; thus, (C) is the correct answer. The second sentence in the second paragraph states that Seltzer used the pseudonym Margaret B. Jones so that she could not be readily identified. It can be inferred that this step was taken to add authenticity to a story that could otherwise easily be proved untrue, so (D) is incorrect.

Answer: E

20. E

This Inference question asks for one of the differences in Seltzer’s and Frey’s experiences as described in the passage. A few key differences stand out: Seltzer never had another work published while Frey wrote another best seller, Seltzer’s memoir was wholly untrue while Frey’s was only partly untrue, and Frey experienced more success with A Million Little Pieces than Seltzer did with Love and Consequences. (E) is the best match because Seltzer’s memoir was recalled shortly after it was discovered to have been fabricated, while Frey remained on the best-seller list for fifteen weeks before his fabrications were exposed. (A) is incorrect because the passage never states that Frey’s only motivation was financial gain. Seltzer had her book recalled and never published another, so the negative media attention she received was at least as damaging as that received by Frey, making (B) incorrect. (C) is incorrect because the author never addresses whether the respective consequences to either author were deserved. Frey’s family is never mentioned in the passage, so (D) is incorrect.

Answer: C

1. C

The perimeter of isosceles triangle ABC is 32, the length of one side is 10, and the height is 8. Your job is to compare the longest side of the triangle to 12. There are two ways to create an isosceles triangle with perimeter 32 and one side of length 10. In one scenario, there are two sides, each 10 units long. In this case, the remaining side will be 32 − 10 − 10 = 12 units long, and the triangle will look like this sketch:

In this instance, the height bisects the base of ΔABC to create two right triangles, each with a short leg of 6 and a hypotenuse of 10. So these are 3:4:5 right triangles with sides of 6, 8, and 10. Thus, the height of ΔABC, as stated in the centered information, is 8, and it follows that sides of 10, 10, and 12 are allowable for ΔABC under the constraints provided. The length of the longest side of ΔABC is 12, and the two Quantities are equal.

In the second scenario, the side with length 10 is the side that does not match another side. In this case, the total length of the two equal sides must be 32 − 10 = 22, which means each of the matching sides is half that, 11. So this time, ΔABC would be divided into right triangles with one side equal to 5 and a hypotenuse of 11.

Using the Pythagorean theorem, h² + 5² = 11². So, h² = 121 – 25 = 96. Thus, the height of this triangle is However, the centered information states that the height is 8; therefore, the equal sides can’t be 11. Instead, the equal sides of ΔABC are 10, and the longest side is 12, as shown in the first sketch; (C) is correct.

Answer: A

2. A

The centered information is a function of the variable z. The comparison is between the value of the function when z is and the number 2. Plug in for z and evaluate the function: When dividing by a fraction, invert the fraction and multiply. So, Since this is greater than 2, (A) is correct.

Answer: B

3. B

The centered information provides the distance between two cities and the average speeds between the two cities when traveling by plane and by train. Quantity A is just a way of saying how much longer it takes to travel from A to B by train than by plane. Quantity B is 330 minutes.

Use the basic formula Rate × Time = Distance rearranged to For the plane, that is hours. For the train, the time is hours. The difference is hours. When converted to minutes, that is minutes. (B) is correct.

Alternatively, you could have converted the two speeds to miles per minute by dividing the speeds in miles per hour by 60. The plane’s speed was 300 ÷ 60 = 5 miles per minute, and the train’s speed was 1 mile per minute. Thus, the plane took 400 ÷ 5 = 80 minutes, and the train made the journey in 400 ÷ 1 = 400 minutes. The difference between the two is 320 minutes.

Answer: A

4. A

The centered information describes two raises that Navid received in two separate years. The first raise was $10,000 and the second was $10,800. Quantity A represents the percent increase of the first raise and Quantity B the percent increase of the second. Be careful here. While the second raise may have a greater dollar amount, it may not have been a greater percent increase, since each percent increase is based on a different starting value.

The percent increase formula is

Start by finding the percent increase in 2015:

Now, find the percent increase for 2017:

Thus, despite the fact that the dollar value of the 2017 raise was greater, the 2015 raise was actually a bigger percent increase. Quantity A is greater, so the answer is (A).

Answer: A

5. A

Remember that geometry figures need not be drawn to scale on the GRE, so avoid the temptation to answer the question based on the appearance of the diagram. Since angle ACB makes a straight line along with n and n = 120°, angle ACB must be 60°. Since ℓ₁ and ℓ₂ are parallel, all acute angles formed by a transversal are equal as well as all obtuse angles. Notice that angle ABC makes a straight line along with one of these obtuse angles; this obtuse angle must therefore be equal to m, so it’s also 150°. Thus, angle ABC is 30°. This means that triangle ABC is a 30°-60°-90° triangle, and its side lengths have the ratio x:x:2x, where x is the side opposite the 30° angle. In this triangle, that’s AC. So AC = x and AB = x. Although there’s no way to find out the value of x, AB must be bigger; (A) is correct. It’s also possible to get to this answer without using the 30°-60°-90° side ratio because in a triangle, a side opposite a larger angle is longer than a side opposite a smaller angle.

Answer: A

6. A

The centered information shows line segment RT with a total length of 4 divided into segments y and z where 3y − z = 8. The comparison is between the length of segment RS, which is y, and 2.5. Since the total length of the line segment is 4, you can write the equation y + z = 4. Now, you have two variables and two distinct linear equations. Add the two equations:

Since 3 > 2.5, (A) is correct.

Answer: D

7. D

To make the comparison easier to work with, manipulate the given inequality so that x and z are on the left side and −y is on the right, just as it is in Quantity A on the left and Quantity B on the right. Subtract z and y from both sides of the centered inequality: x + y - z - y < z - z - y simplifies to x - z < - y. If x is negative, then 2x − z is even less than x − z, so Quantity B would be greater. However, if, for instance, x = 2, y = 1, and z = 4, then x − z < −y, so these values are permissible, but 2x - z > - y. So, for those values, Quantity A is greater. (D) is correct.

Answer: C

8. C

The area of a triangle equals × base × height, which for ΔABE is x 2 x 2 = 2. Furthermore, since ΔABE is a right isosceles, the ratio of the sides is 1:1:. Because the equal sides are 2, the hypotenuse, BE, is 2. The area of a rectangle is base × height. In this case, that is BE × DE. Plug in the known values: 2 = 2 × DE. Divide both sides by 2 to get which simplifies to Thus, the ratio of BE to DE is This is equivalent to 4 : 1, so (C) is correct.

Answer: C

9. C

The formula for the circumference of a circle is π × diameter. If the circumference of each circle in the figure is 8π, the diameter of each circle is 8, and the radius is 4. Each side of triangle PQR consists of the full diameter of the circle in the middle plus the radii of the two circles on the ends. For example, side RP consists of the radius of the circle with center R, the diameter of the middle circle above that, and the radius of the circle with center P. Thus, side RP has a length of 4 + 8 + 4 = 16. Since each side of the triangle passes through the same number of radii, each side has the same length. The perimeter of the entire triangle is therefore 16 × 3 = 48. The correct answer is (C).

Answer: D

10. D

Begin by dealing with the negative exponent in the fraction. To handle a negative exponent, take the reciprocal of the base to the positive value of the exponent. In other words, That means The equation then becomes 14 × 6² × 45 = 2x × 3⁴ × 35. At this point, rather than multiplying and dividing with the calculator, break the numbers down into their prime factors. This will keep the numbers small and make it easier to see how the exponents fit in. The result is 2 × 7 × (2 × 3)² × 3 × 3 × 5 = 2x × 3⁴ × 5 × 7. Expand the exponents to get 2 × 7 × 2 × 3 × 2 × 3 × 3 × 3 × 5 = 2x × 3 × 3 × 3 × 3 × 5 × 7. Now divide both sides by all of the common prime factors. Do this simply by crossing off the prime factors that appear on both sides, as follows: . What remains is 2 × 2 × 2 = 2x. Thus x = 3, and (D) is the correct answer.

Answer: C

11. C

The question provides only one equation with two variables, but it asks for the value of the ratio of those two variables rather than the values of the variables themselves. This question could not ask for the value of each variable since it provides only one distinct equation with two variables. It is possible, however, to solve for the ratio of the variables. Start by simplifying the right side: Cross multiply to get rid of the fractions: 5(w – z) = –12w. Distribute: 5w – 5z = –12w. Then, add 12w and 5z to both sides to get 17w = 5z. Finally, divide both sides by z and by 17: (C) is correct.

Answer: 0.4

12. 0.4

The figure can be divided into a right triangle on top of a trapezoid. Use the numbers on the grid to calculate the dimensions of the triangle and the trapezoid. The base of the triangle extends to the left from point B (2.0,−1.2) to the point where a horizontal line would intersect line AB at (1.4,−1.2). The height of the triangle is the distance from this point to point A (1.4,−0.8). So the length of the base is |2.0 − 1.4| = 0.6 and the height is |−0.8 − (−1.2)| = 0.4. Use the equation for the area of a triangle:

The upper parallel side of the trapezoid is the base of the triangle, which is 0.6 long. The lower parallel side is line DC, so the length of that side is |2.2 − 1.4| = 0.8. The height of the trapezoid is |−1.2 − (−1.6)| = 0.4. Use the formula for the area of a trapezoid: So the total area of the figure is 0.12 + 0.28 = 0.4 square units.

Answer: C

13. C

The question asks for the number that is 40% less than 1.25 × 10⁴, which is 12,500. To minimize calculation, find 100% − 40% = 60% of 12,500: 0.60 × 12,500 = 7,500. In scientific notation, this is 7.5 × 10³, which is (C).

Answer: A, D

14. A, D

The right answer(s) for this question must have an odd number of factors in order to be divisible by an odd number of different positive integers. First, eliminate any prime numbers since they are divisible only by themselves and 1. (B) 17 is a prime number. Now check the remaining choices. The factors of 9 are 1, 3, and 9, so (A) is a correct choice. The positive factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 for a total of 8, so eliminate (C). The distinct positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36 for a total of 9, so (D) is a correct choice. Finally, the positive factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Since there are 8 factors, (E) is incorrect. The correct choices are (A) and (D).

Perhaps you noticed that both correct answers are perfect squares. That is because the numbers that are not perfect squares have pairs of factors and thus an even number of factors. However, a perfect square has one single factor that is the square root, thereby creating an odd number of factors. If you make this connection initially, you can quickly identify the correct choices.

Answer: 3

15. 3

Triangle ABC is a right triangle with a short side of 2 cm and a hypotenuse of 4 cm. Because the short side is half the hypotenuse, this is a 30°-60°-90° triangle with the 30° angle at vertex A. The ratio of the sides of this triangle are 1::2, so side AB is x 2 = 2 x 3 = 6.

A perpendicular line from B to line AC creates two more 30°-60°-90° triangles. In the triangle on the left, the perpendicular is the short side and the hypotenuse is 6. The length of the perpendicular is half the length of the hypotenuse, or 3.

Answer: C

16. C

Rearrange the formula to Sum of terms = Average × Number of terms. The sum of all three numbers is 3(5a − 2) = 15a − 6. The average of the other two numbers is 4a + 2b + 1, so their total is twice that, or 8a + 4b + 2. The remaining number must be the difference between these totals: 15a − 6 − (8a + 4b + 2) = 15a − 6 − 8a − 4b − 2 = 7a − 4b − 8. (C) is correct.

Answer: B, D

17. B, D

Test each point. Substitute a value for x and compare the result to the given value for y in the ordered pair.

The correct answers are (B) and (D).

Answer: E

18. E

An efficient way to solve this question is to consider that the number of criminal law attorneys (18%) is three times as large as the number of family law attorneys (6%). Simply multiply the 20,000 family law attorneys by 3 to find that there are 60,000, (E), criminal law attorneys.

Answer: B

19. B

Start by finding the total number of lawyers in 2015. Since there were 28,000 corporate law members representing 14% of all lawyers in 2015, divide 28,000 by 14% to get 200,000 total. Use this to find the number of criminal law attorneys in 2015: 18% of 200,000 is 36,000. Once you know this, you can calculate the number of criminal law attorneys in 2016. First, 4,500 fewer than 36,000 is 31,500. And since criminal law attorneys still make up 18% of all attorneys in 2016, divide 31,500 by 18%. That gives you (B), 175,000.

Answer: E

20. E

The question asks for the percent increase from one value to the next. Use the percent change formula: first find the amount of change between values and then divide that amount by the original value. In 2015, the difference between intellectual property lawyers and personal injury lawyers is 3%. But that’s not the correct answer, because you are looking for the percent increase. The amount of change (3%) divided by the original amount (7%) is roughly 43%, (E).

Perhaps an easier way to think about this would be to pick a real number for total lawyers. Here, because the question deals with percents, a good number to pick would be 100. In that case, out of 100 lawyers in 2015, 7 are intellectual property and 10 are personal injury. For the number of intellectual property lawyers to increase to match the number of personal injury lawyers, there would need to be 3 more intellectual property lawyers. So, the increase from 7 to 10 would be 3, and 3 divided by 7 is roughly 43%.