Chapter 6
Drills: Answers and Explanations
Section 1
1. B The sentence tells you the semester had been challenging and stressful, which would be a negative thing. Since is a change direction trigger, so you know the missing word will have something to do with the students getting a break from the school. Choice (B) makes the most sense.
2. E Start with the second blank. Because Henry got a position as a starter on the varsity team, you know he’s a good athlete. If his teammates are second-string and jealous of his success, we know they aren’t as good as Henry. You can easily eliminate choice (B). Now that you know the teammates are jealous, go back to the first blank. The missing word must have something to do with them being jealous. Envy means a feeling of discontent with another’s advantage, so choice (E) is the best answer.
3. E The sentence tells you that Einstein is one of the most famous scientists in the world, so his winning the Nobel Prize would only increase that fame. The first blank must mean something like increase or earn, so you can eliminate choices (B), (C), and (D). Continuing with those same clues, the second blank must mean something like fame or attention. Between choices (A) and (E), choice (E) is the best answer.
4. C The sentence gives you examples of the black mamba snake’s lethality, so the missing word must mean something about being poisonous. Virulent means venomous hostility, so choice (C) is the best answer.
5. E Because the reviewer denounced the acting, you know the missing word will be negative. The colon is a same direction trigger, so what follows gives you more information about the missing word. The actress’s style is flat and tedious. Since monotonous means lacking in variety or tediously unwavering, choice (E) is definitely the best answer.
6. A The definition of the missing word is included in this sentence: speaking at inordinate length to obstruct a legislative assembly. Choice (A), filibustering, is the word that matches that definition, so it is the correct answer.
7. A Do the first blank first. A wide-reaching enterprise with a monopoly on a market is likely to drive up prices and take advantage of consumers. You can eliminate choices (D) and (E). In order to avoid the monopoly, it’s necessary to have other businesses, or competition, in the market. Therefore, choice (A) is the best answer.
8. C Do the second blank first. Because the first part of the sentence tells you that a vast majority … are advantageous, the blank that refers to the preponderance must also mean advantageous. Choices (B) and (D) can easily be eliminated. Then go back to the first blank. If you are trying to distinguish pathogens from bacteria that are advantageous, the first blank must be a negative word. The pathogens are not helping the host (allies), nor are they indicating the future (portent), so you can also eliminate choices (A) and (E). Choice (C) is the right answer.
9. E Both Locke and Hebb agree that environmental factors are important to human development. However, Locke believes that the environmental factors are the only influence, so you can eliminate choices (B) and (D). Hebb never mentions anything about tabula rasa, so you can eliminate choice (A). Neither mentions government regulations at all, so that one can also be eliminate, leaving you with choice (E), the right answer.
10. D Hebb uses the analogy to explain how the two ideas are so tightly knitted, it’s impossible to say which determines an individual’s characteristics. Be careful about choice (C). It looks good at first, but the question is asking about nature specifically, not the general meaning of the analogy. Choice (D) is the right answer.
11. C Locke felt that experience was the only way humans learn and develop. He said that we are born blank slates and that our experiences must “write” who we are on our minds. There are no innate characteristics. Choice (C) is the best answer.
12. C Passage 1 is a theory from a seventeenth-century philosopher and Passage 2 is the viewpoint of a twentieth-century psychologist. Eliminate choice (B), because the Passage 1 is not the modern assumption. Choice (D) is also wrong, because only one perspective is presented in Passage 1. There is no problem/solution, so also eliminate choice (E). Choice (C) is the right answer.
13. A Although the first few paragraphs detail Toomer’s importance during the Harlem Renaissance, the end of the passage states that Toomer’s early literary output can be more thoroughly understood than his later personal life. Choices (B) and (C) are disproven in the first paragraph, and choice (E) is disproven in the fourth paragraph. Choice (D) is also slightly off: it cannot be said that Toomer’s essays were inconsistent, only that there were so few of them.
14. C Because these two paragraphs are particularly about Jean Toomer, choices (A) and (E) can be eliminated. Both paragraphs are concerned with how other artists and thinkers thought of Toomer, however, so the best answer must be (C).
15. E Because Braithwaite’s review of Cane is so glowing, his praise can be described as total or complete, as in choice (E). All other choices provide alternate meanings of the word “unreserved,” but they do not work in this context.
16. E The first paragraph states, Toomer gained huge accolades from the white literary world as well, and well-known authors such as Sherwood Anderson and Waldo Frank considered him one of their own. In this context, Sherwood Anderson and Waldo Frank are used as representatives of the white literary world, lending support to choice (E). Choice (A) cannot work because there is no indication that Toomer was courting this white readership, particularly not with any urgency.
17. D The sentence in question is the topic sentence of the second paragraph. It introduces the ideas that are to come. The paragraph goes on to say that Toomer could incorporate influences from white as well as black artists, and he melded them into a new, innovative style that mixed poetry, prose, jazz, folklore, and spiritualism. As in choice (D), these are aspects of Toomer’s art that showed black and white artists alike a new artistic freedom.
18. A The sentence that directly precedes “These scraps” is as follows: Toomer himself may not have thought of these marriages as interracial: particularly by the 1940s, Toomer insisted that his race was “American” and by the end of his life, he may have even identified as a white man. The repetition of the word may shows the author’s uncertainty as to Toomer’s exact attitudes. “These scraps” must then refer to the scant biographical evidence that literary historians have in piecing together Toomer’s later life, as suggested by choice (A).
19. A The fourth paragraph discusses the increase in race activism, though it says of Toomer, By then, and until his death in 1967, Toomer was much more taken with local issues, and his main concern was with his church, the Friend’s Society of Quakers, and the high school students whom he taught there. In other words, Toomer was not as interested in race activism as were many of his African American contemporaries. In this sense, his views were atypical, as suggested by choice (A). Choice (E) offers a similar answer, but it is too extreme and is disproven by the quotation in the following paragraph. It was not that he had no interest in contemporary race relations but more that his interest was different.
20. C Pay careful attention to the sentence that contains the word in question: By then, and until his death in 1967, Toomer was much more taken with local issues, and his main concern was with his church, the Friend’s Society of Quakers, and the high school students whom he taught there. “Taken with” in this context means “occupied with” or “interested in,” and as the sentence then states, Toomer was much more interested in smaller, local problems than in national race problems.
21. B The topic sentence of this paragraph reads as follows: If Toomer’s early literary output can be more thoroughly understood than his later personal life, or his later racial identification, it can only be because Toomer himself wanted it to be so. This sentence suggests that the paragraph itself will discuss Toomer’s own attitudes, eliminating choices (A) and (D). We learn in earlier paragraphs that Toomer did not have a typical “commitment to racial equality,” eliminating choice (E), and he did not contradict himself in public and private, eliminating choice (C). Only choice (B) reflects the actual content of the paragraph.
22. E As the quotation from Toomer demonstrates, he saw race as a more complex thing than mere black and white. We can deduce, then, that he would’ve found the contemporary debates far too simple, as choice (E) suggests. His own views were “racially complex,” but “black and white” refers to the contemporary debates in which Toomer was not a participant, eliminating choice (C). We may consider his views “socially progressive,” but the passage does not state that they are, so choice (B) must also be eliminated.
23. B The sentence before the one cited in the question reads as follows: Because Toomer was such a truly great artist, literary historians will always long for more information about his life. In other words, literary historians would like more information about his life. Among the answer choices, choice (B) would best supply this information.
24. E The full sentence in question reads as follows: We should be wary of the rigid categories that Toomer fought against all his life, and if anything, perhaps Toomer’s refusal to fit into these categories can help us to modify our own. This sentence is a reference to our own contemporary views on race, which, the sentence suggests, Toomer might be able to help us modify, as paraphrased in choice (E). Although we may consider his views more advanced, the passage does not refer to them in this way, eliminating choice (D).
Section 3
25. B The sentence tells you that the holiday travelers are arguing impatiently. You have the change direction trigger of unlike, so you know the missing word must mean the opposite of that. Additionally, you know that Francisco was quietly waiting. Tranquil means peaceful, calm, or quiet, so choice (B) is the best answer.
26. C Do the first blank first. If there are unique markings in a coded message, a cryptologist would be able to solve or decode the message. Eliminate choices (B) and (E). The but is a change direction trigger, so if the cryptologist is able to decode the message, then the missing word would mean not able to decode. Eliminate choices (A) and (D), leaving choice (C) as the best answer.
27. C The health department is unleashing massive efforts to annihilate, which would make it seem like the department is stopping the pandemic. However, the in spite of trigger lets you know the word will actually be the opposite of that, so choice (C) is the best answer.
28. E Do the first blank first. The diverse Scottish clans are represented by a vast number of tartan cloths, so the missing word must mean large number. Eliminate choices (B) and (C). The second blank refers to the connection between the tartans and the clans themselves. It wouldn’t make sense that the official tartans would represent a clan transmission, so eliminate choice (A). Textile looks like a good option since a tartan is a cloth, but the tartan is the cloth, not a representation of the cloth, so you can also eliminate choice (D). Choice (E) is the best answer.
29. C If the foods are instantly nauseating, they will be disgusting or revolting. Choice (C) is the best answer.
30. B Although there is an analogy in the passage connecting the immune system with the structure of law enforcement, that analogy is used to explain the parts of the immune system. The primary purpose of the passage is to describe that system. Choice (A) can be eliminated because the passage isn’t discussing good health—it’s simply discussing the parts of the immune system. For that same reason, choice (C) can also be eliminated. Choice (D) is irrelevant, loosely tied to the law enforcement analogy, but just barely. Choice (E) connects back to the analogy, but it’s not the primary purpose of the passage. Choice (B) is the best answer.
31. D The passage compares the immune system to a law enforcement structure, and then continues to make similar connections on a more granular level. This is an extended analogy, making choice (D) the best answer.
32. A The description of the style begins with always be honest and then continues with even if statements. This lets you know that the most important thing is the honesty. Although profits, assessments, and promises are all mentioned in the passage, it’s the honesty that is the most important quality. Choice (A) is the best answer.
33. C At the end of the passage, Kerrigan says you will lose them when they find you haven’t been honest. The honesty may or may not result in large payoffs, validated work, or word-of-mouth business, but the passage clearly makes the connection between honesty and solid client relationships. Choice (C) is the best answer.
34. D Antoine of Passage 1 does not approve of the new announcer, so his comparison of the announcer’s voice to a hockey puck is unfavorable, eliminating choice (B). He is commenting on one specific announcer, which eliminates choice (C). Only choice (D) effectively captures Antoine’s disapproving attitude.
35. D The line in Passage 1 offers Antoine’s critique of the new announcer. Antoine’s preferred announcer, Pierre, is even-toned, almost dull. The author of Passage 2 likes similar announcers, those whose announcing can be characterized by dispassionate action. Therefore, the author of Passage 2 would likely find Antoine’s critique “agreeable,” as suggested by choice (D). Choices (A), (B), and (E) should be eliminated because they take the simile from Passage 1 too literally.
36. A The author of Passage 1 describes two different announcers, Pierre and Jack/Jimmy. Pierre is the type of announcer described in the quoted lines from Passage 2. Jack/Jimmy, however, is not characterized by this kind of even-tempered commentary. Instead, the timbre of his voice flew around as erratically as the puck itself, and Jack/Jimmy’s voice is described as too-perfect. Although there is some indication in Passage 1 that new announcers tend to be more animated, there is no such indication in Passage 2, which eliminates choice (C). Furthermore, although Antoine does not like the new hockey announcer, his general attitude cannot be described as “unnecessarily pessimistic,” because it is not general enough to be so, which eliminates choice (E).
37. A Passage 2 draws an analogy between good hockey announcers and good parents and teachers. He stresses their ability to educate in the face of anything or anyone, whether punishingly dull or wildly exciting. He goes on to say, All of them let you know that, rain or shine, at least someone is keeping it together. The last sentence, particularly, indicates someone who is firm and not overtaken by emotional overstatements, as suggested in choice (A). Although part of choice (E), “educating,” could work, there is no indication that all “dispassionate action” is dull, only that it can be when necessary.
38. B Antoine’s preferred announcer, Pierre, is even-toned, almost dull. The author of Passage 2 likes similar announcers, those whose announcing can be characterized by dispassionate action. Therefore, Pierre could be a “good representative” of a certain type of hockey announcer, as suggested by choice (B). Although Pierre has been replaced, there is no indication, particularly not in Passage 2, that such a type of announcer would be “unaware” of the new type of announcer, which eliminates choice (E).
39. C The author of Passage 2 has a positive attitude toward Dan Schantz, so choices (A), (D), and (E) can be eliminated. Choice (B), however, is too extreme an expression of a positive attitude. Choice (C) is milder and more in keeping with the tone of the essay, so it is the best choice.
40. D The phrase to spin yarns appears in the first sentence, and it is reiterated in the later sentences in the paragraph, which refer to some kind of narrative and our minds wanting stories. While choices (A), (B), and (E) offer alternate meanings of the word yarns, only choice (D) works in this context.
41. E The metaphor of connecting dots appears in this context: We want any nearby dots to be connected. Effect with no cause, correlation with no causation: we can’t assimilate these ideas because they don’t have that narrative structure. In other words, even if these dots aren’t connected, our minds want them to be and thus connect them, as choice (E) suggests. Although the connections may not exist in the real world, the passage does not imply that the details themselves do not exist, thus eliminating choice (C).
42. D The full sentence reads as follows: Our minds want stories, even if those stories need to be twisted and mangled into existence. In other words, we can have a difficult time creating stories, but we have the need nonetheless, as choice (D) suggests. The author does not reflect on whether this is a good or bad trait, thus eliminating choices (A) and (E). The discussion of history does not come until later in the passage, thus eliminating choice (B).
43. C The phrase appears in this context: Historians and onlookers alike have spent over a century debating the causes, the effects, and the place of this event in the ongoing plot of American history. Neuroscientists have referred to a “need for narrative.” The passage as a whole is about narrative, and the word plot relates to narratives, suggesting that the history of the American Civil War is another one of these narratives, full of related events, as choice (C) indicates. Choice (B) cannot work because the plot referred to here is not that of a mystery, nor are any historical mysteries discussed. The author does not refer to this need for narrative as a special talent, thus eliminating choice (D).
44. D The first two paragraphs discuss the need for narrative in a general way, even citing the findings of neuroscientists and the work of historians. The third and fourth paragraphs focus more specifically on personality, which can be explained with a specific application of the general theory of the need for narrative. Choice (D) best captures this transition. The latter half does discuss literary texts, but not exclusively, and the first half is focused on much more than historical events, so choice (A) can be eliminated. Choice (C) cannot work because the “need for narrative” is ultimately a psychological concept that is discussed throughout the passage, and it is not critiqued.
45. C The early twentieth century is discussed in these lines: In the early twentieth century, the very notion of “consistent” stories broke down, and characters became less rigidly defined as a result. Suddenly, amid a cultural shift away from religious certainty, one’s environment, one’s historical era, one’s family history could all come to bear on the maze of human personality. In other words, this era was characterized by complexity rather than simplicity, so any discussion of personality must be more complex than the titles in choices (A), (B), and (E). Choice (D) is off-topic. Only choice (C) adequately captures the complexity described in the passage.
46. E This shift away from religious certainty is discussed in these lines: In the early twentieth century, the very notion of “consistent” stories broke down, and characters became less rigidly defined as a result. Suddenly, amid a cultural shift away from religious certainty, one’s environment, one’s historical era, one’s family history could all come to bear on the maze of human personality. In other words, personality had become a newly complex object with many things influencing it, as choice (E) suggests. Choice (A) cannot work because understandings of personality have not been consistent throughout history. Choice (D) does not work because there is no evidence in the passage that non-psychologists critique the theories of psychologists.
47. B The word contain appears in this sentence: Psychologists began to spend entire careers studying human personalities, but for all these changes, the goal was still the same: contain the human experience, find the story that can encapsulate all of human complexity. Use the second part of the sentence as a clue. The word contain must mean something like find the story that can encapsulate, and the closest approximation from this list of answer choices is choice (B). The other choices offer synonyms for the word contain, but they do not work in this particular context.
48. E The last sentence of a passage will typically offer some kind of summary of a passage, and this sentence does just that. The passage as a whole discusses the need for narrative in many aspects of life, including how we understand ourselves. The last sentence asks, rhetorically, Because after all that has come before us, and all that will come later, if we’re not part of the big story, what are we? Choice (E) captures this basic idea well in suggesting that without the big story, our lives would be different. Although the last sentence does look to the future a bit, it does not make any claims about the stories that people in the future will tell themselves, thus eliminating choice (C). Also, while there are some implied comparisons between the “narrative” of history and that of fiction, these comparisons are not addressed in this final sentence, eliminating choice (D).
Section 2
1. C When asked for the value of a variable, Plug In the Answers (PITA). Starting with the least value, see if each answer is divisible by 2, 4, and 5. 8 is divisible by 2 and 4 but not by 5, so (A) can be eliminated. 10 is divisible by 2 and 5 but not by 4, so (B) can be eliminated. 20 is divisible by 2, 4 and 5, and it is the least number left on the list. Although 40 is also divisible by 2, 4, and 5, it is greater than 20, so (D) can be eliminated. Choice (C) is the credited response.
2. A The angle in the upper right of the triangle is opposite the 45° angle, so it is also 45°. A triangle has 180°, so 85 + 45 + z = 180. Therefore, 130 + z = 180, so z = 50. Choice (A) is the credited response.
3. B There are 45 books on the shelf, of which 
are biographies. (45) = 9 biographies. 3 are not about women, and 9 – 3 = 6, so 6 are about women. Choice (B) is the credited response.
4. E If t2 = 16, take the square root of both sides to get t = 4. The value of t could also be –4, but the question states that t is positive. Now, plug t = 4 into the equation (t – 1)2, which is (4 – 1)2 = (3)2 = 9. Choice (E) is the credited response.
5. C Translate the English into math. If a + 3a < 5b + (–b), then 4a < 4b. Divide both sides by 4, so a < b, and (C) is the credited response. Plugging in numbers for a and b would also work, as long as the sum of a and 3a is less than the sum of 5b and –b. Try a = 2 and b = 3. a + 3a = 2 + 6 = 8. 5b + (–b) = 15 + (–3) = 12. 8 < 12, which fits the requirement in the question. Therefore, (A), (B), (D), and (E) can be eliminated.
6. A For average problems, draw an average pie. Set A has 3 numbers and an average of 4. Put those numbers in the lower left and lower right spots, respectively, as shown below. To get the total, multiply 3 by 4, which is 12.
Therefore, 1 + t + 7 = 12, t + 8 = 12, and t = 4. Now, plug t = 4 into set B. The total of set B is 2 + 4 + 6 = 12. Draw another average pie, filling in the total and the number of things.
Total ÷ number of things = average, so 12 ¸ 3 = 4. Therefore, choice (A) is the credited response.
7. B When the question asks for a specific value, use PITA. For choice (C), p = 6. 
= 
= 
= 9.54. This value is more than the 9 in the equation, so (C) can be eliminated. Choices (D) and (E) are even larger than 6 and will yield answers larger than 9.54, so (D) and (E) can be eliminated as well. For choice (B), p = 5. 
= 
= 
= 8.94. This is very close to 9, so (B) is the credited response.
8. C For coordinate geometry questions, start with a sketch of the given information. Now, sketch in the location of point H. It will be above point G, with a negative x-coordinate and a positive y-coordinate, as shown below.
Based on the sketch, (A), (B), and (E) can be eliminated, as those are not in the correct quadrant. Point F is 3 units below the x-axis, so point H will be 3 units above the x-axis. Therefore, (C) is the credited response.
9. D The chart contains a lot of numbers with weird fractions, so start by ballparking. If the women’s ring diameter is 16
, it is larger than 16
, so (A) and (B) can be eliminated. Now, rather than try to find a common denominator for all these fractions, convert each remaining number into decimals. The given value of 16 equals 16.75. Size 6 in (C) goes from 16, which equals 16.5, to 16
, which equals 16.67. The given 16.75 is outside this range, so (C) can be eliminated. Size 6 in (D) goes from 16.67 to 16
, which equals 16.83. The given 16.75 is in this range, so (D) is the credited response.
10. D With variables in the question, the best approach is to Plug In. PITA would mean a lot of algebraic manipulation to solve the equation for x. To answer this question, it is easier to plug in integer values of x. If x = 1, y = 
= 0. This is not one of the fractions in the answer choices, so try the next integer value for x. If x = 2, y = 
. This is also not one of the fractions in the answer choices, so keep going until one works. If x = 3, y = 
= . If x = 4, y = 
= . If x = 4, y = 
= 
. This is the value in (D), making (D) the credited response.
11. A When given ranges for variables but not actual values, plug in some numbers. If p = 5 and q = 11, p + q = 5 + 11 = 16, which is less than 18. Since case I is true for these numbers, it cannot be eliminated at this point. q – p = 11 – 5 = 6, which is not less than 6. Therefore, case II is false, and (B) and (D) can be eliminated. 2p = 2(5) = 10, which is not equal to 11. Therefore, case III is false, and (C) and (E) can be eliminated. Choice (A) is the credited response.
12. D If line a is parallel to line b, then the big angle created by the intersection of lines b and d will be equal to r°, which equals 140°. There are 180° in a line, so the big angle and the small angle formed by this intersection must add up to 180°. Thus, the angle in the lower left of the triangle equals 40°, since 180 – 140 = 40. There are 180° in a triangle, so 40 + 90 + s = 180. Therefore, s equals 50°, and (D) is the credited response.
13. E This question seems like a good candidate for PITA, since it is asking for a specific value. However, the total is based on three different kinds of blocks, the numbers for which are based on other quantities. Therefore, start plugging in different values for the number of red blocks. If there is only 1 red block, there will be 4 yellow blocks, as the number of yellow is 3 more than the number of red. There are 2 times as many blue as yellow blocks, so there will be 8 blue blocks. The total number of blocks equals 1 + 4 + 8 = 13. This is the smallest possible total, so (A) and (B) can be eliminated, since they are less than 13. If there are 2 red blocks, there will be 5 yellow blocks and 10 blue blocks. The total number of blocks equals 2 + 5 + 10 = 17, so (E) is the credited response.
14. E For multiple functions, plug the x-value given into the correct function. For this problem, that means k(4) = (j(4))3. Now, bring in the other function, plugging in the same x-value, to get k(4) = (j(4))3 = (
+ 1)3. This equals (2 + 1)3 = 33, so k(4) = 27 and (E) is the credited response.
15. A The chart indicates that 20 percent of the businesses in town are clothing stores, and the question states that there are 100 clothing stores. Use this information to calculate the total number of businesses in town. 100 = 
× Total. Solve this equation for the total by multiplying both sides by 
, yielding a total of 500 businesses. Now use this total to calculate the number of bookstores and jewelry stores. For bookstores, the number equals 
× 500 = 35. For jewelry stores, the number equals 
× 500 = 25. The difference between the two numbers is 10, so (A) is the credited response.
16. D With variables in the answer choices, Plug In. If m = 3 and n = 5, point A is at (3, 10) and point B is at (6, 20). The slope can be found with any two points, and the slope formula is 
. The slope of this line is 
or 
. Plug m and n into the given in the answer choices to see which one has a slope equal to. Choice (A) is y = 
x, which has the wrong slope, so it can be eliminated. Choice (B) is y = 
x, so it can be eliminated. Choice (C) is y = x + 3 and can be eliminated. Choice (D) is y = 
x and (E) is y = x + 5. A quick sketch of the two points and the line containing them will show that it goes through the origin. Therefore, there should be no y-intercept and the credited response is (D). Another option would be to plug one of the points, such as (3, 10), into the two remaining equations. Choice (D) becomes 10 = (3), which is true and the credited response. Choice (E) becomes 10 = (3) + 5, which is false, so (E) can be eliminated.
17. C This is a logic question, so check each statement to determine if it is necessarily true about the shoes. Case I states that if a shoe is not black, then it is not a boot. The question only stated that boots were all black, but there could be other black shoes, such as sandals or sneakers. Therefore, I is not necessarily true, so (A) and (D) can be eliminated. Case II has the same problem – other types of shoes could also be black. Therefore, (B) and (E) can be eliminated. Only case III is true, so (C) is the credited response.
18. C The volume of a cylinder is the product of the area of the circular bottom, A = πr2, and the height, h, so V = πr2h. Given the variable d for the diameter of one ball, plug in a number for d, such as d = 4. Therefore, the radius of the cylinder is 2. The height is made up of three balls, or 3d, so the height is 12. Plug these values into the formula for volume, which yields π(22)(12) = 48π, the target number. Now plug d = 4 into the answer choices to see which is equal to the target number. Choice (A) is 16π, which is not equal to 48π, so (A) can be eliminated. Choice (B) is 2π(16) or 32π and can also be eliminated. Choice (C) is π(64) or 48π, which is the target answer. Check out (D) and (E) to make sure they can be eliminated. Choice (D) is 64π and (E) is 3π(64) or 192π. Both of these can be eliminated, so (C) is the credited response.
19. B The best way to tackle this problem is to just start listing out numbers that fit the requirements, since the greatest possible number of choices from the answers is 24. It is important to be systematic, though, so no numbers that work are left off the list. For the hundreds place, the number must be a 7, and the tens place must be a 1. The last digit must be a prime number, so it could be 2, 3, 5, or 7. There must be at least one 2 in the number, so start by assuming that the last digit is 2.
20. E Given a geometry problem with no figure, draw one. The question states that side 
is shorter than the other two sides. So draw an isosceles triangle with a base slightly shorter than the two equal legs, as shown below.
Section 4
21. A In the first equation, subtract 3 from both sides to find that p = 9. Plug in 9 for p in the second equation: 9 – q = 5. Subtract 9 from both sides of the equation, then divide by –1 to find that q = 4. The credited response is (A).
22. E First, list out the numbers in each set. For sets A and B, only list up to the highest answer choice, in this case 18. Set A = {2, 4, 6, 8, 10, 12, 14, 16, 18, …}. Set B = {9, 18, …}. Set C = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}. Now check the answers to see which number is a member of both sets A and B, but not of set C. 6 is in all three sets, so eliminate (A). 9 is only in set B, so eliminate (B). 12 is in sets A and C, but not in set B, so eliminate (C). 15 is only in set C, so eliminate (D). 18 is in both sets A and B but not in set C, so the credited response is (E).
23. C Make sure to read the labels on the axis of the chart. Draw a vertical line at the 25 minute mark, then draw a horizontal line at the 400 calories mark. Count the number of dots that are above and to the right of where those two lines meet. There are four dots. The credited response is (C).
24. E Start by drawing the point (3, 8). Then draw line p perpendicular to line m through point (3, 8). Use your eye to determine where the lines intersect. All the points on line m have a y value of 5 and all the points on line p have an x value of 3. The lines will cross at point (3, 5). The credited response is (E).
25. E Geometry basics: Draw, Label, Formulas. The figure is drawn already. The triangle is equilateral so all of the sides are the same. Since the perimeter is 54, divide that by three to find the sides of the triangle are 18. Label the sides in the figure. To find circumference of the circle, write the circumference formula: C = πd. Notice that the side of the triangle is the diameter of the circle, so the diameter of the circle is also 18. Put that into the formula: C = 18π. The credited response is (E).
26. B “What is the value” with numbers in the answers … PITA! Normally you should start with choice (C) because it’s in the middle, but it’s an ugly number. It will be easier to start with (B) because it’s a whole number. The question asks for x so start with choice (B) and plug in –1 for x. If x = –1 then each tick mark is 
, which makes y = and z = 
. Plug y and z into the equation to check. + = 
= 2, which matches the question. The credited response is (B).
27. A Variables in the question and the answer choices: Plug In! Remember that t is in years and that the number of hit records doubles every 6 months. Let’s plug in 3 for t, which means that the number of hit records will double 6 times. Starting with 1 hit record, it doubles to 2 (6 months), then doubles to 4 (one year), then doubles to 8 (1 year 6 months), then doubles to 16 (2 years), then doubles to 32 (2 years 6 months), then doubles to 64 (3 years). So when t = 3, the target is 64. Plug 3 into each of the answer choices. Choice (A) is 22×3 = 26 = 64, which matches the target. Remember to check all of the answers to be safe. The credited response is (A).
28. D Since the parabola is symmetrical across the line x = −1, the x-intercepts are equidistant from the point (−1, 0). First find the distance from (−1, 0) to (–5, 0) by subtracting the x-coordinates: −1 − (−5) = 
+ 
= 
. The other x-coordinate is the same distance from (−1, 0), so add to find the other x-coordinate: + (−1) = − = 
= 2. The other x-intercept is (2, 0), so m = 2. The credited response is (D).
29. 4 Since each term is three times the previous term, y × 3 = 36 and, thus, y = 12. Then, x × 3 = 12, and, thus, x = 4.
30. 40 It’s safest to use the calculator on this question. Make sure to either do it in small steps and correct order of operations (PEMDAS) or be careful when typing the parentheses. To solve, plug in 15 for m in the equation: P(m) = 125,000
= 125,000
= 125,000
= 40.
31. 105 All the angles in a square are 90°. Since the small angle at point C is 15°, the large angle above it must be 90 – 15 = 75. All straight lines have 180°, so 75 + y = 180. Subtract 75 from both sides of the equation to find that y = 105.
32. 15 Recognize that the problem gives a relationship and a total value. Set up the ratio box. The actual total number of marbles is 40, so write that in the bottom right box. Probability is a “part to whole” relationship; on the Ratio row, write 5 for red and 8 for total.
The Ratio row adds across, so write 3 for blue. Find that the multiplier from 8 to 40 is 5, which is the same multiplier for everything. Multiply to find that there are 25 red marbles and 15 blue marbles. The question asked for blue, so the answer is 15.
33. 20 Geometry basics: Draw, Label, Formulas. There’s no figure, so draw the two triangles. Then write the area formula: A = bh. The problem provides the area but neither the base nor height, so Plug In! For triangle A write 120 = bh, so bh = 240. Plug in numbers that work, such as b = 12 and h = 20. Since the base of triangle A is three times that of triangle B, divide the base of triangle A by 3 to get 
= 4. Since the height of triangle A is two times that of triangle B, divide the height of triangle A by 2 to get 
= 10. Now use the area formula again with the numbers of triangle B to find A = bh = (4)(10) = 20.
34. 13 Translate the English to Math. First translate “Sue and David together own 57 hamsters” to “s + d = 57”. “David owns” translates to “d =”, “5 more than” translates to “5 +”, and “3 times the number of hamsters that Sue owns” translates to “3 × s”. Put it together to get d = 5 + 3s. Now substitute 5 + 3s for d in the first equation to get s + (5 + 3s) = 57. Simplify and solve: 4s + 5 = 57, then 4s = 52, then s = 13. Sue owns 13 hamsters.
35. 
Definition: “bisects” means “cuts in half.” Since there are no numbers given, Plug In! Starting with the first given angle, plug in 40 for ∠COG. Since 
bisects ∠COG, both ∠COE and ∠EOG are 20. If 
bisects ∠AOE then ∠AOC and ∠COE are equal, so they are both 20. If 
bisects ∠AOC then ∠AOB and ∠BOC are equal, so they both equal 10. If 
bisects ∠EOG then ∠EOF and ∠FOG are equal, so they both equal 10. Add the angles to find that ∠COG = 40 and ∠AOF = 50. Therefore 
.
36. 0 < n < 1
37. 187 This is a pattern question. Doing the quick calculation will likely lead to a trap answer. Be careful and list out the pattern. There are five pages in each section, so list 1, 2, 3, 4, 5. Then list the page numbers of each section. To save a little time, recognize the pattern. The last page of each section is 5 more than the last page of the previous section, so continue to add 5 until section 7. The last page is 187.
38. 
or 0.185
Section 5
1. C The phrase An opener for 1999’s “Geniuses, Savants, and Prodigies” conference is a modifying phrase, so whatever comes immediately after the comma must be the person or thing described in the phrase. Since the piano did not serve as an opener, the original sentence contains a misplaced modifier. David Helfgott was the person who was an opener, so his name should appear immediately after the comma. Eliminate both choices (A) and (B). Choices (D) and (E) both place David Helfgott immediately after the comma, but because they use the word who, they both create incomplete sentences. Only choice (C) correctly fixes the misplaced modifier and does not introduce any new errors.
2. E If you trim the fat and eliminate the descriptive phrase a flightless dodo bird once native to the island of Mauritius, you’re left with The dodo bird … that was being discovered in 1958. The original sentence is incomplete, since the phrase that was being discovered in 1958 serves as a descriptive phrase and does not contain a main verb. Choices (A), (B), (C), and (D) all repeat the original error since none of them turn the sentence into a complete thought. Only choice (E) fixes the error in the original sentence.
3. B The second half of the sentence needs to modify the first half. As it’s currently written, the second half of the sentence does not clearly state what did the initiating, and therefore does not modify the first half of the sentence. Eliminate choice (A). Choice (B) correctly modifies the first half of the sentence, and it contains no additional errors. Choices (C) and (E) both turn the second half of the sentence into complete thoughts. Since the first half of the sentence is also a complete thought, both choices (C) and (E) create comma splices, so eliminate them. Choice (D) is wordy and does not fix the error in the original sentence. The correct answer is (B).
4. B The phrase Determined to finish the game despite the rain is a modifying phrase that must describe whatever appears immediately after the comma. Since the football team, and not the football team’s fight, was determined, this sentence contains a misplaced modifier. Choices (A) and (E) repeat this error. Choices (C) and (D) also contain misplaced modifiers, since these choices make it seem as though the trophy, not the football team, was determined. Choice (B) fixes the error and does not introduce any new errors, so it is the correct answer.
5. D The original sentence uses the word being. Whenever possible, avoid choosing answers that use being, so eliminate choices (A) and (C). Choice (B) creates a fragment and unnecessarily uses the word they. Choice (D) does not use the word being and does not introduce any new errors, so choice (D) is the correct answer. Choice (E) removes the verb are and replaces it with as. Without the main verb, the sentence is incomplete, so choice (E) is not the correct answer.
6. B As the sentence is currently written, the phrase an awe-inspiring and enormous painting that covers nearly 650 square feet modifies Jacques-Luis David. However, since The Coronation of Napoleon, not David, is a painting, the sentence contains a misplaced modifier. Choice (E) repeats this error, so you can eliminate choices (A) and (E). Choice (B) fixes the error by adding the verb is, so that the second half of the sentence is no longer a modifying phrase. The verb is refers back to The Coronation of Napoleon, so the intended meaning of the sentence is now clear. This choice does not introduce any new errors, so choice (B) is the correct answer.
7. E As the sentence is currently written, the new phone is the subject of the verb deducting. However, since the phone is not the person or thing doing the deducting, the sentence is incorrect as written, and you can eliminate choice (A). Choice (C) changes the meaning of the sentence by implying that the cost was somehow a fraction of the deduction, and is therefore incorrect. Choices (B) and (D) both use –ing verbs, whereas choice (E) does not. If possible, you generally want to eliminate –ing verbs, so choice (E) is the best choice.
8. C The pronoun them does not clearly refer to any other noun in the sentence. Therefore, this sentence contains a pronoun ambiguity error. Choices (A), (B), and (E) repeat the original error, and are therefore incorrect. Choice (C) is much more concise than choice (D), and is therefore the correct answer.
9. B This sentence incorrectly uses was needing rather than needed. Additionally, this sentence contains two complete thoughts joined by a comma, and is therefore a comma splice. Eliminate choice (A). Choice (E) repeats the comma splice error and is also incorrect. Choice (C) uses the modifying phrase Having gone to the car dealership. This phrase should modify whatever appears immediately after the comma. However, the word buying appears immediately after the comma in this case. Since the word buying cannot go anywhere, this choice contains a misplaced modifier. Choice (D) is passive, and incorrectly places the modifying phrase where she needed to buy a new car immediately after Lindsay, rather than after car dealership. Choice (B) fixes both of the errors in the original sentence and does not introduce any new errors, so choice (B) is the correct answer.
10. E The pronoun they is unnecessary and turns the first half of the sentence into a fragment. Therefore, choice (A) is incorrect. Choice (B) changes the intended meaning of the sentence by making it appear as though the detectives were determined to catch the criminal simply because they wanted to identify the criminal. Choice (D) similarly changes the meaning. In choice (C) the clause The detectives identified the criminal is a complete thought, and the clause they were determined to catch the man who stole the jewelry is also a complete thought. Since this choice joins two complete thoughts with a comma, thus creating a comma splice, this choice is incorrect. Choice (E) fixes the error in the original sentence and does not introduce any new errors, so choice (E) is the correct answer.
11. E The original sentence lists two things that employees want: more responsibility and to increase their monthly earnings. Since responsibility is a noun, and increase is a verb, and these two words are in a list, the list is not parallel. Therefore, choice (A) is incorrect. Choice (B) is passive, since the compound subject of the sentence is more responsibility and an increase, the verb is are wanted, and the employees, who are the people doing the action, are not the subject of the sentence. Choice (C) changes the meaning of the sentence by suggesting that the reason that many employees volunteer to work overtime is that they want more responsibility. Choice (C) is therefore incorrect. Choice (D) begins the sentence with while. However, this sentence does not contain two contrasting thoughts, and thus should not begin with while. Choice (E) fixes the error in the original sentence and does not introduce any new errors, so it is the correct answer.
12. C The subject of the sentence is works, which is plural, and the verb is ranges, which is singular. Therefore, this choice has a subject-verb agreement error. Eliminate choice (A). Choices (B) and (E) change the verb to an –ing form and turn the sentence into a fragment. Choice (D) adds the word that, which would indicate that an additional thought should come after the phrase that range from Russian ballets to neoclassical compositions and chamber works. Choice (D) makes the sentence incomplete, and is therefore incorrect. Choice (C) fixes the subject-verb agreement error by making the verb plural, so choice (C) is the correct answer.
13. A Choice (B) is disjointed and contains the word being. Whenever possible, avoid choosing answers that include the word being. Eliminate choice (B). Choice (D) also uses being and is incorrect. Choice (C) uses an unnecessary and, and is therefore a run-on. Choice (E) lists two facts about the authors’ works: they are difficult to comprehend and symbolizing obscures … the author’s main point. Since these two items are not in parallel form, this choice contains a parallelism error. Choice (A) correctly joins two complete thoughts with a semicolon and does not contain any additional errors. Choice (A) is the correct answer.
14. D In the original sentence, being banned is an incorrect form of the verb. Remember to avoid the word being whenever possible. Eliminate choice (A). Do not use helping verbs such as should or have with verbs such as urge that communicate a wish or a command. Choices (B) and (C) both break this rule, and are therefore incorrect. Choice (E) changes the meaning by using the phrase for initiating, thus suggesting that the league suggested the ban for the purpose of initiating the movement. Choice (D) correctly uses the subjunctive voice, stating that the Anti-Saloon League urged that the sale … be banned. Choice (D) is the correct answer.
15. D The clause Charlemagne was crowned in 768 A.D. as King of the Franks is a complete thought. The clause he was the oldest son of Pepin the Short and Bertrada of Laon is also a complete thought. Since this sentence links two complete ideas with a comma, this sentence contains a comma splice error. Eliminate choice (A). Choice (E) repeats this type of error by setting the complete thought in 768 A.D. he was crowned King of the Franks off by commas. Choice (B) uses the pronoun they, which does not clearly refer to any group of people mentioned in the sentence, and is therefore incorrect (C) uses a comma followed by the word and, and should therefore link two complete thoughts. However, since the first half of the sentence is a fragment, choice (C) is incorrect. Choice (D) fixes the original error in the sentence and does not introduce any new errors, so choice (D) is the correct answer.
16. B The singular pronoun it refers to the plural noun bulbs, so the original sentence has a pronoun agreement error. Choices (A) and (E) repeat the original error and thus are incorrect. Choice (C) turns the sentence into an incomplete thought and is therefore incorrect. Choice (D) uses the plural pronoun their to refer to the singular noun bulb, so choice (D) has a pronoun agreement error. Choice (B) fixes the error, and does not introduce any new errors, so choice (B) is the correct answer.
17. D This sentence uses the word consider twice, and therefore has a redundancy error. Choices (A) and (C) repeat this error, and are therefore incorrect. Choice (B) redundantly uses the word it, and is therefore incorrect Since consider … as to be is the wrong idiom, choice (E) is incorrect. Choice (D) fixes the original error in the sentence, and does not introduce any new errors, so choice (D) is the correct answer.
18. D The original sentence uses the conjunction and, therefore making the sentence incomplete. Eliminate choice (A). Choices (B) and (C) inappropriately change the verb to would create. They both also compare Hemingway’s writing style to any other American writer. Since writing styles should be compared to other writing styles, rather that writing styles to writers, both of these choices also contain comparison errors. Choice (E) changes was different to was differing, and therefore uses the wrong form. Choice (D) corrects the error in the original sentence and does not introduce any new errors, so choice (D) is the correct answer.
19. C According to the sentence, crusaders did two things: they succeeded not in gaining access … but to leave. Since gaining and to leave are not in the same verb form, this sentence contains a parallelism error. Choices (A), (B), (D), and (E) all contain similar parallelism errors, and are therefore incorrect. Only choice (C) fixes the original error and does not introduce any new errors.
20. D In the original sentence, the subject is reputations, which is plural, but the verb is appears, which is singular. Therefore, this sentence contains a subject-verb agreement issue. Eliminate choice (A). Choice (B) changes the subject of the sentence to either, which is singular, but it later replaces either with the pronoun their, which is plural, so choice (B) is incorrect. Choice (C) uses the singular subject either, but changes the verb to appear, which is plural, so choice (C) is not the credited answer. Choice (E) does fix the original error but is written in passive voice. Choice (D) is the correct answer.
21. C Choice (C) contains two errors. First, this sentence uses between … or. The correct idiom is between … and. Therefore, this sentence contains an idiom error. Second, this sentence contains a parallelism error. There are two things Abigail must choose between: the upscale bistro and eating at the diner. In a correct version, Abigail can either choose between eating at the upscale bistro and eating at the diner, or she can choose between the upscale bistro and the diner, but she cannot choose between a bistro (a thing) and eating (an action).
22. D The subject of the sentence is each, which is singular. However, this sentence uses the pronoun they, which is plural, to replace the singular subject each. Thus, this sentence contains a pronoun agreement error. Additionally, since the pronoun should be the singular he or she, the verb find, which is plural, should be finds, which is singular. Choice (D) therefore contains two errors and is the correct answer.
23. C If you use the phrase not only, you must include the words but also later in the sentence. However, this sentence instead uses and also, and therefore contains an idiom error. Thus, choice (C) is the correct answer.
24. B In this sentence, the adjective reputed modifies the adjective safe. However, an adverb, not another adjective, should modify an adjective, so the sentence should say that the outlaws committed crimes in a reputedly safe part of the country. Choice (B) therefore contains an error and is the correct answer.
25. A Choice (A) contains an idiom error, since the verb asserted should not be paired with the preposition on. Correctly written, the sentence should say that Descartes confidently asserted his ability.
26. B The pronoun they is plural, but refers to the noun chef, which is singular, so choice (B) contains a pronoun agreement error. The correct answer is choice (B).
27. C The verb is is singular, but the subject of the verb is the plural noun tenants. Therefore choice (C) contains a subject-verb agreement error, which makes it the correct answer.
28. E The verb argued in choice (A) is in past tense and agrees with the subject, so there is no error in choice (A). In choice (B), many of them correctly refers back to those those convicted, so you can eliminate choice (B). Choice (C) uses the correct preposition and is therefore not the correct answer. Choice (D) properly pairs either with the conjunction or, so choice (D) does not contain an error. There are no errors in this sentence, so the correct answer is (E).
29. B This sentence begins by using the pronoun you, but later incorrectly replaces that pronoun with one, rather than you. Thus, choice (B) is the correct answer.
30. B Choice (B) uses the present perfect verb have attempted. The present perfect tense indicates that an action began in the past, and is still continuing today. However, the sentence indicates that the action occurred in 1990. Since the action occurred at one definite point in the past, the verb have attempted is in the wrong tense and should be in the simple past tense. Thus, choice (B) contains an error and is the correct answer.
31. E Choice (A) correctly begins a modifier which describes cave paintings. Because paintings is plural, many of which agrees in number with paintings. The plural verb are in choice (B) agrees with the plural noun paintings, so choice (B) can be eliminated. Choice (C) correctly uses a plural noun, remnants, to refer back to the paintings, so you can eliminate choice (C). Choice (D) has no errors in verb tense. Because the sentence is correct as written, choice (E) is the correct answer.
32. A In a sentence which uses the pairing neither … nor, the verb must agree with the last element in the list. In this case, the last element in the list is team, which is singular. However, the verb were is plural, so choice (A) contains a subject-verb agreement error.
33. C Choice (C) uses the plural pronoun them to refer to the singular noun cloud. Therefore, choice (C) contains a grammatical error and is the correct answer.
34. D This sentence compares two things: the game of Go and chess pieces. However, in order for the comparison to be parallel, the sentence must either compare the game of Go and the game of chess, or it must compare Go pieces and chess pieces. Therefore choice (D) contains a comparison error and is the correct answer.
35. B This sentence uses the verb is compelling, which is in a tense that indicates continuous action. However, since this sentence discusses an action that should happen only once, rather than on a continuous basis, this sentence contains a verb tense error. Eliminate choice (A). Choice (C) changes the intended meaning of the sentence by suggesting that some form of tragedy must befall the people discussed in the sentence, so choice (C) is incorrect. Choice (D) incorrectly uses the pronoun you to refer to the people mentioned in the previous sentence, and thus contains a pronoun agreement error. Choice (E) uses the singular noun person to refer to the noun people, which is plural, so choice (E) contains a noun agreement error. Choice (B) fixes the error in the original sentence and does not introduce any new errors, so choice (B) is the correct answer.
36. B Choice (A) combines the two sentences, but the conjunction and does not correctly connect the two thoughts since they are not directly related. Choice (B) is more concise than choice (A), and correctly joins the two sentences without introducing any new errors. Choice (C) connects the two thoughts using a semicolon. However, a semicolon should connect two complete thoughts. In this case, the first part of the sentence, which reads, The story of the poor London boy Tom Canty, which demonstrates the lesson is not a complete thought. Therefore, Choice (C) contains an error and is not the correct answer. Choice (D) changes the intended meaning of the sentence by placing the phrase a poor boy from London immediately after Mark Twain, thus suggesting that Mark Twain, not Tom Canty, was the poor boy from London. Additionally, this sentence contains two complete thoughts joined by a comma, and thus contains a comma splice error. Choice (E) places the modifying phrase demonstrating the lesson through the story of poor London boy Tom Canty at the end of the sentence. This sentence changes the meaning so that it is unclear exactly what is demonstrating the lesson, and therefore contains a misplaced modifier error. Choice (B) is the only answer remaining and is therefore correct.
37. A The end of the second paragraph discusses the fact that Tom learns to appreciate the things that he does have, rather than envying what others have. However, the paragraph does not really explain how Tom learns this lesson, merely stating that life in the prince’s court was more complicated than he had anticipated. Therefore, the author could strengthen his or her point by including more details about what caused Tom to miss and gain such appreciation for his home in London. Choice (A) correctly identifies the pieces of information missing from the second paragraph, and is the correct answer. While adding information about the ways in which the customs in Prince Edward’s court were intricate might be helpful, the ways in which those customs relate to the customs in other courts is irrelevant to the topic. Therefore, choice (B) is not the correct answer. The paragraph and the essay as a whole do not relate to the reasons that Tom’s family became poverty-stricken, but instead relate to how Tom learned to appreciate his life despite that poverty. Thus, choice (C) is not the correct answer. The second paragraph does relate to how Tom gained an appreciation for his home in London, but it does not relate to the literary devices that Mark Twain used to convey that lesson. Eliminate choice (D). Finally, the second paragraph focuses on Tom, rather than Mark Twain, so a discussion of Twain’s life would be out of place at this point in the essay. Therefore choice (E) is incorrect.
38. E Choice (A) uses the singular pronoun one to replace the plural pronoun they, and therefore contains a pronoun agreement error. Both choices (B) and (C) inappropriately change the pronoun in the sentence to you, rather than they. Since the pronoun refers to many people, the pronoun you is incorrect, so you can eliminate choices (B) and (C). Choice (D) changes the present tense verb fail to the past perfect verb have failed. Since the rest of the verbs in the sentence are in the present tense, and the sentence does not call for a tense change, this choice contains a verb tense error. Choice (E) correctly joins the two sentences and does not introduce any new errors, so choice (E) is the correct answer.
39. E Sentence 3 provides a transition from the main topic of the essay to the example of The Prince and the Pauper and is therefore an important part of the first paragraph. Without sentence 4, readers would not know which book the author is discussing, so sentence 4 is also a critical part of the first paragraph. Sentence 8 demonstrates how the example of The Prince and the Pauper relates to the main topic of the essay, and is therefore necessary to the essay. Sentence 9 relates the example of the book back to the essay’s thesis by showing how the example relates to people in general. Therefore, sentence 9 should remain in the essay. Sentence 10 links the idea in sentence 9 to the idea in sentence 12, and is therefore a valuable part of the essay. However, sentence 11 introduces irrelevant information. The previous sentence discusses the idea that it is possible to appreciate those who love us before we lose them, and the sentence that follows discusses the idea that few people actually learn this lesson before it is too late. Thus, sentences 10 and 12 discuss related ideas, but sentence 11, which points out that many believe that Tom is a more engaging character than Prince Edward, provides unnecessary information. The correct answer is choice (E).
