1. C
The question asks about the primary purpose of the passage. Since this is a general question, it should be answered after the specific questions. The main focus of the passage is Sydney Carton. Lines 9–10 describe him during his school days as the old seesaw Sydney. Up one minute and down the next. Lines 30–31 state that his friend Stryver was always in the front rank, and I [Sydney] was always behind. The passage concludes with a description of Carton’s mood. Look for an answer choice about Carton. Choice (A) describes the purpose of a section of a passage, but it is too specific and does not describe the purpose of the passage as a whole. This is a Right Answer, Wrong Question trap answer; eliminate (A). Similarly, while the speakers briefly discuss the Shrewsbury School, the discussion is not the main point of the passage. Eliminate (B). Because the passage focuses on Carton, it is accurate to say that its purpose is to reveal his character, so keep (C). Because there is no evidence in the passage that Stryver has exploited Carton, eliminate (D). The correct answer is (C).
2. B
The question asks how to best characterize Carton. Notice that this is the first question in a paired set, so it can be done in tandem with Q3. Look at the answer choices for Q3 first. The lines for (3A) say that Carton is up one minute and down the next, now in spirits and now in despondency. Look to see whether these lines support any of the answer choices for Q2. The word mercurial is used to describe someone whose mood changes a lot. Draw a line connecting (3A) and (2B). The lines for (3B) say that Carton did exercises for other boys, and seldom did [his] own. These lines don’t support any of the answer choices in Q2; eliminate (3B). The lines for (3C) mention that Carton and Stryver laughed together, which doesn’t support any of the answer choices in Q2. Eliminate (3C). The lines for (3D) say, It’s a gloomy thing…to talk about one’s own past. This statement doesn’t support any of the answer choices in Q2, so eliminate (3D). Without any support in the answers from Q3, (2A), (2C), and (2D) can be eliminated. The correct answers are (2B) and (3A).
3. A
(See explanation above.)
4. D
The question asks what the word spirits most nearly means in line 11. Go back to the text, find the word spirits, and cross it out. Then read the window carefully, using context clues to determine another word that would fit in the text. Lines 10–11 say that Sydney is up one minute and down the next; now in spirits and now in despondency. Therefore, spirits must mean something like “happiness.” Soul means “the immaterial part of a person;” it doesn’t match “happiness,” so eliminate (A). Liquor refers to alcoholic drinks; it doesn’t mean “happiness,” so eliminate (B). Essence means “the most significant quality of something;” it doesn’t match “happiness,” so eliminate (C). Choices (A), (B), and (C) are Could Be True trap answers based on other meanings of spirits that do not fit the context in the passage. Jubilation matches “happiness,” so keep (D). The correct answer is (D).
5. A
The question asks what can be inferred from Stryver’s statement in lines 17–22. Use the given line reference to find the window. In this paragraph, Stryver tells Carton, “your way is, and always was, a lame way. You summon no energy and purpose,” so it is clear that Stryver dislikes Carton’s behavior. Look for an answer that matches this information. Choice (A) matches the prediction, so keep it. Choice (B) uses the Right Words with the Wrong Meaning; Stryver does not want to literally push Carton into the fireplace. Eliminate (B). Similarly, (C) has the Right Words but the Wrong Meaning; the old Sydney Carton is not used in reference to his literal age but rather is a term of endearment. Eliminate (C). While the passage states that Stryver had a bullying air, there is no evidence that Stryver ever bullied Sydney at school, so eliminate (D). The correct answer is (A).
6. A
The question asks why the author uses italics in line 55. Use the given line reference to find the window. In line 48, Stryver tells Carton, “Pledge me to the pretty witness,” whom he reveals to be Miss Manette. Carton responds with a question: “She pretty?” Therefore, he is in disbelief that Stryver is describing Miss Manette as pretty. Look for something that matches this information. Because incredulity means “disbelief,” (A) is a good description of Carton’s attitude; keep it. Carton is not confused. He knows what he thinks and what Stryver thinks; eliminate (B). There is no indication that Carton is annoyed by Stryver in the lines in question, so eliminate (C). Carton is indicating his belief that Miss Manette is not pretty, not that he feels affection toward her. Eliminate (D). The correct answer is (A).
7. C
The question asks what the passage suggests about Stryver. Notice that this is the first question in a paired set, so it can be done in tandem with Q8. Look at the answer choices for Q8 first. In the lines for (8A), Stryver states, “I had to get into the front rank; I was not born there, was I?”, which suggests he was not born into privilege. Look to see whether these lines support any of the answers for Q7. They do not, so eliminate (8A). The line in (8B) asks simply, “And whose fault was that?”, which doesn’t suggest anything about Stryver, nor correspond to any of the answer choices in Q7. Eliminate (8B). The lines for (8C) say that Miss Manette was the admiration of the whole court. These lines refer only to her looks; they don’t suggest that Stryver is in love with her. These lines don’t support any of the answer choices in Q7, so eliminate (8C). The lines for (8D) say that Stryver thought Carton sympathized with the golden-haired doll, which indicates that Stryver believes Carton was paying attention to her and saw what happened to her at court. This is a response to Carton’s statement, “She pretty?” which was Carton’s way of saying that he did not find Miss Manette attractive. Stryver’s response indicates that he thought Carton was paying attention to Miss Manette because he did think she was pretty, so he does not believe Carton finds Miss Manette unattractive. Draw a line connecting (8D) and (7C). Without any support in the answers from Q8, (7A), (7B), and (7D) can be eliminated. The correct answers are (7C) and (8D).
8. D
(See explanation above.)
9. B
The question asks what the word desert refers to in line 79. Read a window around the line reference. Lines 76–79 say that the air was cold and sad, the dull sky overcast, the river dark and dim, the whole scene like a lifeless desert. The author is describing the setting in the city. Choices (A) and (C) do not describe a setting, so eliminate them. London’s landscape matches the prediction, so keep (B). Choice (D) refers to a feature seen in literal deserts, but the author uses the word figuratively. This is a Right Words, Wrong Meaning answer; eliminate (D). The correct answer is (B).
10. B
The question asks why the “tears” in line 85 are described as wasted. Use the given line reference to find the window. Lines 83–90 say that Carton threw himself down in his clothes on a neglected bed, and its pillow was wet with wasted tears, and that there is no sadder sight than the man of good abilities and good emotions, incapable of their directed exercise, incapable of his own help and his own happiness, sensible of the blight on him, and resigning himself to let it eat him away. Since the passage says that Carton cannot help himself and is resigned, it can be inferred that he will not try to change anything about his circumstances. His tears are wasted because they will not prompt him to make a change for the better. There is no indication of Miss Manette’s feelings, positive or negative, toward Carton, so eliminate (A). Choice (B) matches the prediction, so keep it. The passage mentions only one detail about Carton’s apartment, and the neglected bed is not the focus of Carton’s tears, so eliminate (C). There is no indication that Stryver is exploiting Carton, so eliminate (D). The correct answer is (B).
11. B
The question asks for the best description of the point of view of the passage. Since this is a general question, it should be answered after the specific questions. The author views Estonia’s Singing Revolution in a positive light, and describes Estonia, Latvia, and Lithuania’s right to independence from the Soviet Union. Eliminate (A) because condemnatory is too strong; the passage is focused mostly on Estonia’s Singing Revolution rather than on criticism of the Soviet Union’s actions. Keep (B) because sympathetic matches the positive point of view toward the Baltic states (Estonia, Latvia, and Lithuania). Eliminate (C) and (D) because dismissive and conflicted are negative and do not match the positive point of view. The correct answer is (B).
12. A
The question asks what the author draws a distinction between. Use the given line reference to find the window. Lines 35–38 say that the themes of their music were often grim, but there was always hope in their hearts. Keep (A) because the author makes a distinction between the songs’ tone, which was grim, and the people’s feelings of hope. Eliminate (B) because, although folk songs and anthems are both mentioned, there is no distinction drawn between them. Eliminate (C) because there is no mention of military strength in lines 34–38. The author contrasts the military strength of the two in lines 27–30, making this the Right Answer to the Wrong Question. Eliminate (D) because there is no mention of song festivals in Latvia and Lithuania in these lines, and when the author mentions them (lines 45–46), they are described as similar to Estonia’s. The correct answer is (A).
13. B
The question asks what the phrase “their reluctance to be absorbed” suggests about the Estonians. Since there is no line reference, use chronology and lead words to find the window for the question. Q12 asked about lines 34–38, so the window for Q13 most likely begins after line 38. Scan the passage beginning with line 39, looking for the phrase “their reluctance to be absorbed.” Lines 40–44 state that Estonians established a history of mass song festivals, celebrations that would kindle and fortify the courage to express their love of language and nation, and their reluctance to be absorbed by anyone. Eliminate (A) because there is no mention of speaking Russian. Keep (B) because wanting to have an independent nation matches their love of language and nation and their reluctance to be absorbed by anyone. Eliminate (C) because the paragraph states that there were similar festivals held in Latvia and Lithuania. Eliminate (D) because the passage indicates that the Estonian song festivals started before the Soviets arrived. The correct answer is (B).
14. D
The question asks which choice best supports the claim that the Soviet Union perceived Estonia’s culture as a threat. Notice that the answer choices are lines from the passage. Use the lines given to answer the question. The lines for (A) say that Estonia had always been a nation of singers and discusses the importance of folk songs. However, there is no mention of the Soviet Union in these lines, so eliminate (A). The lines for (B) say Estonians established a history of mass song festivals and discusses those celebrations. Again there is no mention of the Soviet Union, so eliminate (B). The lines for (C) say the festivals were forced to pay tribute to Communist icons and the solidarity of the Soviet peoples, which was not threatening to the Soviet Union, so eliminate (C) . The lines for (D) mention an unofficial national anthem and that it survived the entire Soviet occupation despite a serious attempt by officials to eliminate it; the fact that the Soviet officials tried to eliminate the Estonian anthem indicates that they saw the anthem as a threat, so keep (D) . The correct answer is (D).
15. C
The question asks what the word burden most nearly means in line 66. Go back to the text, find the word burden, and cross it out. Then read the window carefully, using context clues to determine another word that would fit in the text. Lines 62–68 say, A movement of young historians was already defying Soviet authority in speeches and that the burden of protest songs had passed to rock-and-rollers, young men whose energized patriotic tunes blared from every radio. Therefore, burden must mean something like “duty” or “leadership.” Eliminate (A) because weight means “mass” and does not match “duty.” This is a Could Be True trap answer based on another meaning of burden that does not fit the context in the passage. Eliminate (B) because travail means “painful effort” and does not match “duty.” This is another Could Be True trap answer. Keep (C) because responsibility matches “duty” and “leadership.” Eliminate (D) because need does not match “duty.” The correct answer is (C).
16. D
The question asks for the primary rhetorical effect of the last sentence. Read a window around the sentence that is referenced. The last paragraph begins, This was the heart of “The Singing Revolution,” a spontaneous, non-violent, but powerful political movement that united Estonians with poetry and music. The last sentence says Sedition hung in the wind, waiting to be denied. Sedition means “disobeying the government;” this sentence figuratively describes the sense that revolution was about to occur. Eliminate (A) because there is no sense of dread; the words united and powerful indicate a sense of hopefulness about the revolution. Eliminate (B) because there is no discussion of disagreement between violent and non-violent revolutionaries. Eliminate (C) because although it’s true that music and poetry were important in the fight for independence, that is not the focus of the last sentence; this is a Right Answer, Wrong Question trap answer. Keep (D) because communicating the sense of optimistic tension is a rhetorical effect and matches sedition hung in the wind. The correct answer is (D).
17. A
The question asks what the author implies about the Estonian song festivals. Notice that this is the first question in a paired set, so it can be done in tandem with Q18. Look at the answer choices for Q18 first. The lines for (18A) say that the occupied nations had every right to ask for their freedom, and with no need for a legal “divorce.” There is no mention of Estonian song festivals, so these lines do not address Q17; eliminate (18A). The lines for (18B) say, The festivals were a nationwide phenomenon, as were similar festivals held in Latvia and Lithuania. Look to see whether these lines support any of the answers for Q17. Although the lines mention the festivals, they don’t provide specifics to support any of the answers in Q17, so eliminate (18B). The lines for (18C) say, By the late 1980s the nation was simmering. There is no mention of Estonian song festivals, so these lines do not address Q17; eliminate (18C). The lines for (18D) say that This was the heart of “The Singing Revolution,” a spontaneous, non-violent, but powerful political movement that united Estonians with poetry and music. These lines mention the “The Singing Revolution,” which began with the song festivals. Look to see whether these lines support any of the answers for Q17. They support (17A) since the festivals united Estonians and gave them a medium through which national and cultural pride could be expressed. Draw a line connecting (18D) with (17A). Without any support in the answers from Q18, (17B), (17C), and (17D) can be eliminated. The correct answers are (17A) and (18D).
18. D
(See explanation above.)
19. D
The question asks which claim is supported by the diagram. Work through each answer choice using the diagram. Eliminate (A) because the diagram shows both German and Soviet gains in Poland. Eliminate (B) because the Soviet Union did not double in size after the pact; the area of Soviet gains is smaller than the area of the Soviet Union shown in the diagram. Eliminate (C) because contiguous means “having a border in common,” and Estonia and Lithuania do not border each other. Keep (D) because the diagram shows that the Soviet gains did stretch from the Baltic Sea to the Black Sea. The correct answer is (D).
20. A
The question asks which statement in the passage is supported by the diagram. Work through each answer choice using the diagram. Keep (A) because the diagram shows Soviet gains in the Baltic states of Estonia, Latvia, and Lithuania. Eliminate (B) because the diagram shows the results of a 1939 pact and not what happened in 1940. Eliminate (C) because agitations for independence came in the late 1980s, which is much later than the time depicted on the diagram. Eliminate (D) because the firm stand taken in 1940 by the United States is not shown on the diagram. The correct answer is (A).
21. B
The question asks what purpose the diagram serves in relation to the passage. Since this is a general question, it should be answered after the specific questions. Make sure to read the note under the figure. The diagram shows Europe following the Nazi-Soviet Pact of 1939, also known as the Molotov-Ribbentrop Pact. Work through each answer choice using the figure. Although the diagram shows that the Soviet Union made gains in Estonia, the diagram does not give any more information about the relationship beyond what is in the passage; eliminate (A). The diagram does show the results of the Molotov-Ribbentrop Pact, which the passage calls a secret non-aggression treaty (lines 11–14), so keep (B). The diagram does not show anything about the Singing Revolution; eliminate (C). The diagram does show Estonia and the countries surrounding it, but there is no information on the diagram about Estonia’s role in the region; eliminate (D). The correct answer is (B).
22. C
The question asks how to best describe the position that LaFollette takes. Because this is a general question, it should be done after all the specific questions. Lines 21–29 state that LaFollette disagrees with some of his colleagues, arguing against the restriction of citizens’ right to control their own government, so look for an answer that has to do with LaFollette arguing for something with which others disagree. While LaFollette is a lawmaker, no new piece of legislation is being considered in the passage, so (A) is a Mostly Right/Slightly Wrong answer. Eliminate it. Choice (B) is also incorrect: as a senator, LaFollette is not an impartial observer, and he isn’t arbitrating a legal issue in this passage, so eliminate (B). LaFollette can certainly be described as a dissenter arguing for a cause as he is discussing an issue with which some of his colleagues disagree, so keep (C). Nowhere in the text does LaFollette claim to be against war in general, as a pacifist would, so eliminate (D). The correct answer is (C).
23. A
The question asks which distinction LaFollette draws in the passage. Because this is the first question in a paired set, it can be done in tandem with Q24. Consider the answers for Q24 first. The lines for (24A) mention LaFollette being aware of people being unlawfully arrested and otherwise detained even though they committed no crime. Check the answers for Q23 to see if any of the answers are supported by those lines. These lines don’t support any of the answers for Q23, so eliminate (24A). The lines for (24B) introduce LaFollette’s idea that people must surrender some rights for the common good during war, and LaFollette draws a distinction here, noting that the right to control their own Government…is not one of the rights that citizens are called upon to surrender in time of war. This matches with (23A), so draw a line connecting those two answers. The lines for (24C) and (24D) don’t include distinctions, nor do they match any of the answers for Q23, so eliminate those answers. The correct answers are (23A) and (24B).
24. B
(See explanation above.)
25. A
The question asks who is criticized by the press. Since there is no line reference, use chronology and lead words to find the window for the question. This is the first specific question, and Q26 asks about line 22, so the window for Q25 is most likely in the first three paragraphs. Scan the passage beginning with line 1, looking for the lead word press. Lines 1–5 state that the triumphant war press has pursued those Senators and Representatives who voted against war with malicious falsehood and recklessly libelous attacks, going to the extreme limit of charging them with treason against their country. Choice (A) matches this prediction, so keep it. Choice (B) is a Right Words, Wrong Meaning trap answer: the passage states that the press has accused the Senators and Representatives of treason, but it doesn’t say that these people actually committed treason. Eliminate (B). Eliminate (C) because the passage states that the Congress members have spoken out against the war; they have not tried to stifle free speech. Choice (D) is a Right Words, Wrong Meaning trap answer: the passage suggests that the press has committed libel against the Senators and Representatives, not that the Senators and Representatives have committed libel. Eliminate (D). The correct answer is (A).
26. C
The question asks what the word surrender most nearly means in line 22. Go back to the text, find the word surrender, and mark it out. Carefully read the surrounding text to determine another word that would fit in the blank based on the context of the passage. In line 22, LaFollette states that in time of war the citizen must surrender some rights for the common good which he is entitled to enjoy in time of peace, so surrender means something like “give up temporarily.” Declare defeat does not match “give up temporarily.” This is a Could Be True trap answer based on another meaning of surrender that does not fit the context in the passage. Eliminate (A). Throw away doesn’t mean to “give up temporarily,” so eliminate (B). Choice (C), set aside, matches the meaning of “give up temporarily,” so keep it. Submit to doesn’t match “give up temporarily,” so eliminate (D). The correct answer is (C).
27. D
The question asks what is suggested by lines 32–36. Read a window around the line reference. Lines 32–36 state that citizens must beware of those precedents in support of arbitrary action by administrative officials, which excused on the plea of necessity in war time, become the fixed rule when the necessity has passed and normal conditions have been restored. Thus, LaFollette is concerned that officials may restrict free speech during times of war but then fail to remove those restrictions when the war is over. While LaFollette does grant that the citizen must surrender some rights, this is not mentioned in lines 32–36; this is the Right Answer to the Wrong Question, so eliminate (A). While LaFollette does say that some restrictions are arbitrary (meaning not based on reason or necessity), he explicitly denies that all restrictions are arbitrary in lines 21–29, so (B) can be eliminated. Choice (C) is never mentioned in the passage, so eliminate it. Choice (D) matches the prediction: temporary restrictions placed during war time may not be removed when the war is over, becoming permanent, so keep (D). The correct answer is (D).
28. D
The question asks what the word terms most nearly means in line 49. Go back to the text, find the word terms, and mark it out. Carefully read the surrounding text to determine another word that would fit in the blank based on the context of the passage. Lines 43–50 discuss the citizens’ right to discuss every important phase of this war, which include its causes, the way it should be carried out, and the terms upon which peace should be made. Therefore, “terms” must mean something like “requirements.” Periods doesn’t match “requirements.” This is a Could Be True trap answer based on another meaning of terms that does not fit the context in the passage. Eliminate (A). Conversations doesn’t match “requirements,” so eliminate (B). Definitions doesn’t match “requirements;” (C) is another Could Be True trap answer. Eliminate it. Conditions matches “requirements,” so keep (D). The correct answer is (D).
29. B
The question asks what the principal rhetorical effect of the phrase in lines 48–50 is. This is the first question in a paired set, but it is a specific question, so it can be done on its own. Read a window around the line reference. In lines 37–41, the speaker defends the right of free speech. Then, the speaker specifies the citizen’s right to discuss every important phase of this war. Lines 48–50 list the various phases of the war that people should be free to discuss. Eliminate (A) because the speaker is arguing for free speech, not against it, and these lines do not mention difficulties faced by the military and the President. Keep (B) because it matches the prediction. Eliminate (C) because lines 48–50 list topics that citizens should be free to discuss, not reasons members of the press are not able to speak freely. Eliminate (D) because there is no discussion about who understands war best. The correct answer is (B).
30. D
The question is the best evidence question in a paired set. Because Q29 was a specific question, simply look at the lines used to answer the previous question. Lines 37–47 were used to answer the question. Of these lines, only lines 37–41 are given in an answer choice. The correct answer is (D).
31. C
The question asks how the author’s attitude toward “the attempt to stifle” in line 63 can be described. Read a window around the line reference. In lines 63–72, LaFollette ponders the consequences that would occur if the attempt to stifle all discussion of the issues of this war were successful. Throughout the passage, he argues that people should have free speech during war time, and in this paragraph he describes the attempt to stifle free speech as the demand of the war-mad press and war extremists that they monopolize the right of public utterance. Look for an answer that reflects LaFollette’s negative view of the attempt to stifle free speech. He is not sympathetic to efforts to stifle discussion of the war, so eliminate (A). He is not apathetic, or “uncaring,” so eliminate (B). Morose means “gloomy,” which doesn’t describe LaFollette’s attitude in line 63, so eliminate (D). He is actively speaking out about the issue, which indicates that he believes change can be made; therefore, he is upset, but not morose. Keep (C) because frustrated matches the prediction. The correct answer is (C).
32. D
This question asks about the perspective from which the passage is written. Because this is a general question, it should be done after all of the specific questions. Overall, the passage discusses new research findings in biofuel production. Find an answer that matches this prediction. Choice (A) can be eliminated because while the passage concludes that further studies would be needed to determine the environmental impacts of biofuels, there is no request for project funding. Eliminate (B) because the entire passage is about research in biofuel production, not chemistry concepts. Choice (C) can be eliminated because lauding means “praising,” and, while the research discussed in the passage yielded some promising results, according to the last paragraph, further studies would be needed to determine the environmental impacts of biofuel. Therefore, the entire passage is not lauding the successes of an industry. Eliminate (C). An objective observer evaluating new research matches the discussion about biofuel production. The correct answer is (D).
33. C
This question asks about the function of the last sentence of the first paragraph. Use the first paragraph as the window. According to the first paragraph, producing ethanol remains considerably more expensive than gasoline. So researchers are always on the lookout for new ways to trim costs. According to the last sentence of the first paragraph, researchers have a new lead, a microbe that can use abundant nitrogen gas as the fertilizer it needs to produce ethanol from plants. In other words, the microbe may solve the production cost problem. Find an answer that matches this prediction. Choice (A) may seem tempting because the last sentence describes a recent discovery—the microbe. However, the microbe is not a commercial accomplishment. For this reason, eliminate (A). Choice (B) may seem tempting because the paragraph discusses the relative production costs of ethanol and gasoline. However, the last sentence of the first paragraph does not provide a reason as to why one fuel is more expensive than another. Eliminate (B). Choice (C) is consistent with the prediction. The last sentence of the first paragraph proposes that the microbe may be a potential solution for the problem of the high cost of producing ethanol. Eliminate (D) because the final sentence of the paragraph does not restate the results of that year. The correct answer is (C).
34. C
This question asks how nonfood crops produce fewer indirect land use emissions. Because this is this first question in a paired set, this question can be done in tandem with Q35. Look at the answer choices for Q35 first. The lines for (35A) state that nonfood crops such as trees and bamboo need less fertilizer than traditional biofuel crops. This matches (34C). Connect answers (35A) and (34C). The lines in (35B) state that in an ideal world, biofuels would be produced only from plant materials that cannot be eaten. This information does not explain how nonfood crops produce fewer indirect land use emissions. Eliminate (35B). The lines for (35C) state that the enzymes needed to break down plants’ primary structural components…are expensive. It may be tempting to connect this answer with (34B), since (34B) discusses prices. However, this answer does not explain how nonfood crops produce fewer indirect land use emissions. Eliminate (35C). The lines in (35D) explain that an ethanol production plant may be spending more than $1 million on fertilizer a year. It may be tempting to connect this answer with (34B), since (34B) discusses prices. However, this information does not explain how nonfood crops produce fewer indirect land use emissions. Eliminate (35D). The correct answers are (34C) and (35A).
35. A
(See explanation above.)
36. A
The question asks what the phrase ideal world most nearly means in line 37. Go back to the text, find the phrase ideal world, and cross it out. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says that researchers have turned to nonfood crops…for biofuel production because these crops need less fertilizer and they often have a less detrimental impact on the land. The phrase an ideal world is used to introduce the idea that biofuels would be produced only from plant materials that cannot be eaten. In context, the phrase an ideal world means something along the lines of “in the best situation.” Find an answer that matches this prediction. Best-case scenario matches “in the best situation,” so keep (A). Dream sequence may seem tempting, but producing biofuels from only plant materials that cannot be eaten is realistic and not a dream sequence; eliminate (B). Choice (C) may seem tempting, but biofuels are not a model for anything. Choice (D) may also seem tempting, since a utopian society is one that possesses highly desirable or perfect qualities. However, the definition of a utopian society has to do with a society having an ideal social, political, and moral climate, not producing biofuels…only from plant materials that cannot be eaten; eliminate (D). The correct answer is (A).
37. D
This question asks what can be inferred from the results of the Indiana University study involving Zymomonas mobilis. Because this is this first question in a paired set, this question can be done in tandem with Q38. Look at the “best evidence” answer choices for Q38 first. The lines for (38A) state that the research showed that the bacterium produces ethanol more quickly and uses more of the plant material when it uses nitrogen gas than when it is fed nitrogen in fertilizer. If the same holds true in a production plant, this could reduce biofuel production costs. This supports answer (37D). Connect answers (38A) and (37D). The lines for (38B) state that the process is also more environmentally friendly…because there are greenhouse gas emissions associated with producing nitrogen fertilizer. It may be tempting to connect this answer with (37B), since (37B) mentions greenhouse gases. However, (37B) is a reversal. According to the lines in (37B), the amount of greenhouse gases would change. Eliminate both (38B) and (37B). The lines for (38C) state that whereas using Z. mobilis might make it cheaper for producers to use inexpensive, nonfood crops, there could also be added costs and problems. This information does not match any of the possible answers for Q37. Eliminate (38C). The lines for (38D) state that even if nitrogen fertilizers are not used in the fermentation process, they might still be needed to grow the crops. This information matches none of the answers in Q37. Eliminate (38D). The correct answers are (37D) and (38A).
38. A
(See explanation above.)
39. B
This question asks what the word slim most nearly means, as used in line 73. Read the window, cross out the world slim, and replace it with another word or phrase that makes sense based on the context of the passage. Then, eliminate anything that does not match the prediction. The passage states that questions remain about using Z. mobilis, that there could also be added costs and problems, and that overall benefits to the environment may also be slim. In context, the word slim means something along the lines of “small” or “low in number.” Find an answer that matches this prediction. Brittle and useless do not mean “small” or “low in number.” Eliminate (A) and (D). Negligible matches “small,” so keep (B). Choice (C) may seem tempting, but skinny does not match “small” or “low in number.” The correct answer is (B).
40. D
This question asks in what year is the required statutory volume of conventional ethanol closest to that of another fuel type, according to Figure 1. Look at Figure 1. First, locate the statutory volume of conventional ethanol. The statutory renewable fuel volume for conventional ethanol holds steady at approximately 12–15 billion gallons for each of the years shown. Then, look for a year that has another fuel type around 12–15 billion gallons. The only fuel that matches that volume is Cellulosic ethanol in the year 2022. Therefore, the correct answer is (D).
41. B
This question asks which fuel is least likely to meet the volume requirements shown in Figure 1, according to Figure 2. Work through each answer choice by comparing the volume requirements shown in Figure 1 to the volumes in Figure 2. Biomass-based diesel has a consistent requirement of around 1 billion gallons in Figure 1 and is consistently around 1 billion gallons in Figure 2. This would meet the requirements, and the question wants the fuel that is least likely. Eliminate (A). Cellulosic ethanol in Figure 1 goes from approximately zero gallons in 2011 to over 15 billion gallons by 2022 but doesn’t even appear on Figure 2. This discrepancy means that it is unlikely to meet the volume requirements in Figure 1; keep (B). Conventional ethanol in Figure 1 increases to 15 billion gallons by 2015; in Figure 2 it is already close to 14 billion gallons in 2013. It looks as if conventional ethanol will meet the requirements; eliminate (C). Other advanced renewable fuels in Figure 1 start at 0 gallons in 2010 and end at around 5 billion gallons in 2022. In Figure 2, these fuels are slowly increasing, ending at around 2 billion gallons in 2013. This increase means that other advanced renewable fuels are on pace to meet the requirements in Figure 1. Eliminate (D). The correct answer is (B).
42. B
The question asks what the author of Passage 1 most likely believes about the Glen Canyon Dam. Notice that this is the first question in a paired set, so it can be done in tandem with Q43. Look at the answer choices for Q43 first. The lines for (43A) say that At the time Glen Canyon Dam was constructed (1956–63), little consideration was given to how dam operations might affect downstream resources in Grand Canyon National Park. Look to see whether these lines support any of the answers for Q42. They support the statement in (42B) that Glen Canyon Dam was built with a lack of foresight. Draw a line connecting (43A) and (42B). The lines for (43B) say that humpback chub and Colorado pikeminnow were listed as endangered in 1967 and the dam and its operation jeopardized the continued existence of humpback chub. Although these lines may seem to support (42C), this is a Mostly Right/Slightly Wrong trap answer, as the phrase decimated native fish populations is too extreme to describe endangering two species. Eliminate (43B). The lines for (43C) say, Annual spring snowmelt floods were the defining attribute of the pre-dam flow regime. This information is not about the dam itself, so it does not answer Q42; eliminate (43C). The lines for (43D) say that Pre-dam floods disturbed the aquatic ecosystem and native fish species developed strategies to survive those floods. Although it may seem reasonable that if the pre-dam floods disturbed the ecosystem, the dam would calm the ecosystem (42D), this is a Could Be True trap answer since there is not concrete support in the passage that the dam has had a calming effect on the aquatic ecosystem. Eliminate (43D). Without any support in the answers from Q43, (42A), (42C), and (42D) can be eliminated. The correct answers are (42B) and (43A).
43. A
(See explanation above.)
44. A
The question asks why the author of Passage 1 mentions scientists and river recreationists. Since there is no line reference, use chronology and lead words to find the window for the question. Q46 asks about line 25, so the window for Q44 most likely comes from before line 25. Scan the first paragraph, looking for the lead words scientists and river recreationists. Starting at line 10, the passage states National Park Service and U.S. Geological Survey scientists and river recreationists observed the physical transformation of the river in Grand Canyon and then includes details about the physical transformation. Keep (A) because the window gives details on how the area looks drastically different. Eliminate (B) because there is no contrast between scientific observations and casual observations: the scientists and recreationists noticed the same changes. Eliminate (C) because there is no mention of collaboration between the scientists and recreationists. Eliminate (D) because, although the scientists and recreationists did observe harmful changes, the words prove and ruinous are too strong to match the evidence in the passage, and so (D) is a Mostly Right/Slightly Wrong trap answer. The correct answer is (A).
45. C
The question asks what Passage 1 suggests about humpback chub. Since there is no line reference, use chronology and lead words to find the window for the question. Q46 asks about line 25, so the window for Q46 most likely begins before line 25. Scan the first paragraph, looking for the lead words humpback chub. Starting at line 17, the passage states that humpback chub…were listed as endangered in 1967 by the U.S. Fish and Wildlife Service and the dam and its operation jeopardized the continued existence of humpback chub. Lines 30–34 give more information that applies to the humpback chub, saying that native fish species developed strategies to survive periods when the velocity in the main part of the channel was high and large amounts of suspended sediment were being transported. Eliminate (A) because the passage says that the humpback chub were endangered, not extinct. Although the passage does say that several of the native fish species share unusual body shapes, including…small depressed skulls, this is a Could Be True trap answer because the passage doesn’t state that the humpback chub is one of the species that has a small, depressed skull. Eliminate (B). Keep (C) because the humpback chub does survive in changing environments, both changes from the dam and changes due to flooding. Eliminate (D) because thrive is too strong to match what is indicated by the passage; the text says that the fish can survive in high velocity river channels, but not that they thrive there. This is a Mostly Right/Slightly Wrong trap answer. The correct answer is (C).
46. C
The question asks what the word regime most nearly means in line 25. Go back to the text, find the word regime, and cross it out. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says that Annual spring snowmelt floods were the defining attribute of the pre-dam flow regime. Therefore, regime must mean something like “process.” Eliminate (A) because government does not match “process.” This is a Could Be True trap answer based on another meaning of regime that does not fit the context in the passage. Eliminate (B) because tenure means “holding office, land, or a position” and does not match “process.” Keep (C) because system matches “process.” Eliminate (D) because management means “dealing with or controlling people or things” and does not match “process.” The correct answer is (C).
47. B
Go to the second sentence of the second paragraph in Passage 2 and cross out the word suspended. Replace it with your own word using the context of the paragraph. The paragraph mentions that sand is included at high concentration in the flow, so a good replacement would be “combined.” Choice (B) is the best match and therefore the correct answer.
48. C
The question asks what can be concluded about controlled floods. Notice that this is the first question in a paired set, so it can be done in tandem with Q49. Look at the answer choices for Q49 first. The lines for (49A) say that Normal dam operations, therefore, tend to erode, rather than build, sandbars; since there is no mention of controlled floods, these lines do not answer Q48; eliminate (49A). The lines for (49B) say, The suspended sand is transported into eddies where it is then deposited in areas of low stream-flow velocity. This paragraph is about controlled floods, so look to see if these lines support any of the answers to Q48. They do not: although the previous sentence mentions a high concentration of sand and might seem to support (48B), lines 66–68 do not mention the amount of sediment, so eliminate (49B). The lines for (49C) say, Newly deposited sandbars also provide areas for riparian vegetation to grow and are a source of windblown sand. These lines do not support any of answer choices for Q48, so eliminate (49C). The lines for (49D) say, Scientists have also learned that controlled floods may erode sandbars if the concentration of suspended sand during a controlled flood is too low. Eroding sandbars is detrimental, so these lines support (48C). Draw a line connecting (49D) and (48C). Without any support in the answers from Q49, (48A), (48B), and (48D) can be eliminated. The correct answers are (48C) and (49D).
49. D
(See explanation above.)
50. A
The question asks how the author of Passage 1 would most likely respond to the High Flow Experiments described in Passage 2. Because this is a question about both passages, it should be done after all the questions about individual passages. Look for the lead words High Flow Experiments in Passage 2. Lines 86–92 indicate that the High Flow Experiments are the name for the controlled floods at the Glen Canyon Dam. The main focus of Passage 2 is the decline of sandbars after the Glen Canyon Dam was built and how controlled floods can build sandbars (lines 60–63). Look for statements about sandbars and floods in Passage 1. The last two paragraphs discuss pre-dam floods, and lines 40–41 state, Sandbars, riverbanks, and their accompanying aquatic habitats were reshaped during floods. Since the controlled floods can mimic the pre-dam floods and build sandbars, the author of Passage I would view the High Flow Experiments positively. Keep (A) because appreciating is a positive view. Eliminate (B) and (D) because warning and worrying are both negative. Eliminate (C) because questioning is neutral, or somewhat negative. The correct answer is (A).
51. B
The question asks for the statement that best describes the structure of the two passages. Because this is a question about both passages, it should be done after all the questions about individual passages. Consider the relationship between the two passages. Passage 1 discusses the environmental changes due to the installment of the Glen Canyon Dam. Passage 2 focuses on sandbars and how controlled floods can build sandbars. Eliminate (A) because Passage 2 doesn’t address the problem introduced in Passage 1. Passage 1 discusses several problems, including the loss of large beaches, narrowing of rapids, changes in the distribution and composition of riparian vegetation, and endangered species. Passage 2 only focuses on a solution to the problem of declining sandbars. Additionally, Passage 2 discusses a solution that is already part of the current reservoir-release management strategy for Glen Canyon Dam, so it is incorrect to say that it proposes a solution. Keep (B) because Passage 1 includes a historical discussion of the Glen Canyon Dam, and Passage 2 discusses a scientific practice of controlled floods. Eliminate (C) because Passage 1 discusses changes that occurred within a particular ecosystem (the Colorado River Basin) due to the construction of a dam; it does not discuss general principles. Eliminate (D) because Passage 1 does not discuss an experiment, and Passage 2 focuses on strategies that have already been implemented, rather than offering suggestions for the future. The correct answer is (B).
52. D
The question asks for a statement that is true for Passage 1, but not Passage 2. Because this is a question about both passages, it should be done after all the questions about individual passages. Consider the main focus of each passage. Eliminate (A) because Passage 2 does give details of scientific studies of controlled flooding on the river, and because Passage 1 does not explicitly mention studies on the river. Eliminate (B) because both Passage 1 and Passage 2 offer evidence of topographic change. Eliminate (C) because both passages discuss the importance of floods to the river ecosystem. Keep (D) because only Passage 1 mentions specific species, like the humpback chub and Colorado pikeminnow. The correct answer is (D).
1. A
If you can’t cite a reason to use a comma, don’t use one. In this case, commas are not necessary because the fact that she works at the mall is important as a contrast to more serious. Therefore, the answer is (A).
2. C
The idea before the punctuation (She would start applying to law schools soon) is complete. The idea after the comma and conjunction (she wanted to know what the law looked like in action) is also complete. Remember the STOP punctuation rules. Choices (A) and (D) can be eliminated because two complete ideas cannot be joined with just a conjunction or just a comma; both are needed. The comma in (B) is in the wrong place, so the answer is (C).
3. B
Notice the question! It asks which statement is most in keeping with the main idea. The passage centers on the Department of Corrections, and the only choice that introduces this information is (B). The next sentence doesn’t even make sense without the specific information in (B).
4. A
Notice the question! It asks for a statement that reinforces ideas in this sentence as well as the preceding sentence. The ideas in these sentences are about no one paying much attention to the Department of Corrections. Choice (B) contradicts this idea. Choices (C) and (D) contain the wrong focus. Therefore, (A) is the answer.
5. D
The subject of this sentence is meaning, which is singular. Eliminate the choices with plural verbs—(A), (B), and (C)—because they are inconsistent. The correct answer is (D).
6. D
The underlined pronoun refers to Everyone, which is singular. Choice (D) is the only possible answer because it is consistent in number.
7. D
The sentence should come after another question about the treatment of inmates in order to make sense of the phrase by the same token. This question appears in sentence 6, so this sentence should go after sentence 6, as (D) suggests.
8. D
Choices (A), (B), (C), and (D) all say essentially the same thing, but (D) does so in the most concise way possible. Therefore, (D) is correct.
9. B
The subject of this verb is politics and the law, which is plural, thus eliminating (A) and (C). Choice (B) is the correct answer because it is more concise than (D).
10. A
The idea before the conjunction (We may believe that we never come into contact with the law) is complete, and the idea after the conjunction (it is written into everything…ourselves) is also complete. When a conjunctive adverb connects two complete ideas in one sentence, it is preceded by a semicolon and followed by a comma. Therefore, (A) is correct.
11. C
The essay focuses on the transformational experience Amanda had working at the prison, so a single detail about something that happened to her later on is not consistent with the passage. Eliminate (A) and (B). Choice (D) is incorrect because the detail still wouldn’t be consistent if it had included information whether Amanda graduated. The correct answer is (C).
12. B
The correct idiom is disappear from. The sentence as written implies two things have disappeared when it should be just the study of the classics. Eliminate (A). Choices (C) and (D) are not the correct form of the idiom. Choice (B) is the correct answer.
13. A
This sentence is correct as written. Although the phrase for all that might sound foreign, it is being used correctly here. Choice (B) does not make sense. Choices (C) and (D) are basically the same as (A), and remember, if there is no grammatical reason to change the original, don’t. Therefore, (A) is correct.
14. B
The correct idiom uses the words in and right, so (A), (C), and (D) can be eliminated. Choice (B) is correct.
15. B
The correct answer will feature words or phrases that are as precise as possible. The sentence as written does not make clear to whom the pronoun is referring: Alexander or Aristotle. Choice (B) clears up this pronoun ambiguity. Choice (C) can be eliminated because Alexander was born in Pella, and his arrival as a newborn would not have announced an enlightened era, nor is it likely they arrived together. Choice (D) can also be eliminated because it does not clear up the ambiguity problem.
16. D
Notice the question! It asks for a concluding statement that emphasizes the change brought about by Alexander’s rule. Choices (A), (B), and (C) do not address the change from militaristic Philip to enlightened Alexander. Only (D) has the correct emphasis.
17. C
Notice the question! It asks for an introductory phrase that emphasizes continuity from the previous rule. The only choice that refers to the previous rule and explains how the second sentence connects to the first in the paragraph is (C).
18. A
Check the answer choices against the map, and make sure that the information is consistent with the figure. Choices (B) and (D) contain information that cannot be gleaned from the map, while (C) contains information that contradicts the map. Choice (A) is consistent with the map, so it is the correct answer.
19. B
As written, the first part of the sentence creates a comma splice, wherein a comma separates two complete ideas. Choice (A) can be eliminated. Choice (B) is the best of the remaining answer choices because it is the most concise. A conjunction such as although or moreover is not needed due to the however in the preceding sentence. This sentence’s purpose is to explain the preceding sentence.
20. C
All of the information in this part of the sentence is necessary, so there is no reason to use any commas. Eliminate (A), (B), and (D) because they all have unnecessary commas. The correct answer is (C).
21. D
The idea before the period (Alexandria, Egypt, perhaps the most…continues to thrive) is a complete idea. The idea after the period (It is the second…of Egypt) is also a complete idea. Therefore, the two cannot be joined together with only a comma. (Remember your STOP punctuation rules.) Eliminate (B). Of the remaining answer choices, (D) is the most effective way to combine the two sentences because it eliminates the need to repeat the subject, which makes the sentence flow better. Therefore, (D) is correct.
22. A
The sentence as written is consistent in structure with between man and god and the individual and the world, both of which use the conjunction and. As the last item in this list, and should be used between the natural and the unnatural. All other choices are not consistent and change the meaning. Therefore, (A) is the answer.
23. C
The correct answer will contain phrases that are as precise as possible. It is the dime novel that was printed cheaply and for quick consumption, so the words dime novel need to be placed immediately next to the modifier phrase. Choices (A), (B), and (D) all include this misplaced modifier. Only (C) makes the sentence precise.
24. D
Notice the question! It asks for the phrase that gives the most specific information. Choice (D) provides specific names of authors who wrote by way of literary periodicals. Choices (A), (B), and (C) refer to the authors only in vague terms.
25. D
The title of Stowe’s book is necessary information, which means it should not be surrounded by commas, so eliminate (B). Choices (A) and (C) have other unnecessary commas. The correct answer is (D) because it contains no commas at all.
26. A
Choices (B), (C), and (D) all add more information after book, so consider whether that information is necessary to the meaning of the sentence. For (B), the word actual already implies the difference between a book and Stowe’s previous works in a magazine, so the additional words aren’t needed. Eliminate (B). Eliminate (C) because it is already clear that the book would be written by Stowe. Eliminate (D) because it does not need to be stated that the book could be sold to Americans as it is already implied. Choice (A) is concise and clear. The correct answer is (A).
27. C
The average annual income of a man in this period is not in line with the main idea of the paragraph, which discusses the shift from periodicals to novels. To add this statement would be inconsistent with the paragraph’s focus, which is stated in (C).
28. A
Choices (B) and (D) use the wrong verb tense. Choice (C) is not in line with the focus of the paragraph. Additionally, since you do not know if the series is still known this way, (A) is the correct answer.
29. B
Effect is generally a noun, while affect is a verb except in certain unusual circumstances. The underlined portion needs to be a noun, so affects is incorrect. Eliminate (A) and (D). The sentence discusses multiple effects, not something belonging to the effects, so the plural form of the verb is needed, not the possessive form. Eliminate (C). This leaves (B), which is the correct answer.
30. B
The correct answer will feature words or phrases that make the passage as precise as possible. Without the actual names, the phrase William Bonney and James Butler Hickcock became the folk heroes does not make sense. You need the names of transformed folk heroes in order to make sense of the sentence. Eliminate (C) and (D). Choice (A) is incorrect because the rest of sentence does not speak in generalities; it provides two names already. Choice (B) is correct.
31. C
The correct idiom is learned from, not taught from, so eliminate (A). The new media has not brought anything from the dime novel’s popularity because it is something entirely new, so eliminate (D). Learned is more precise than got, so the correct answer is (C).
32. C
As written, the sentence is unclear for whom or what the foundation is being laid, so eliminate (A). The underlined portion needs to follow the word foundation in order to clarify this. The correct answer will make the passage as precise as possible. This is (C).
33. B
The passage is about the dime novel and how it provided a popular mold or form. The answer should mean something like “form.” Integration means mixing together, so eliminate (A). Framework matches with “form,” so keep (B). Plan means preparing for the future, which doesn’t match with “form,” so eliminate (C). Composition means “something made up,” which doesn’t match with “form” or “mold,” so eliminate (D). The correct answer is (B).
34. C
Be sure to compare similar things to maintain consistency and precision. The sentence as written compares methods to humans. Compare methods to methods, or change the construction of the sentence. Eliminate (A) and (D) because both make the same mistake. Choice (B) uses the singular pronoun that to refer to the plural methods, so eliminate it. Choice (C) uses the correct comparison and the plural pronoun, so it is correct.
35. A
All four choices use similar words. Choose the one that expresses the idea most clearly. In this case, the clearest choice is (A). Choice (B) is passive and contains unnecessary commas. Choice (C) contains the awkward phrase main among which is its. Choice (D) uses curious as an adjective instead of a noun, implying that the weaponry is curious about something instead of being a curiosity itself.
36. D
This sentence does not refer to the bats (bats cannot shout). Eliminate (A) and (B). The sentence uses the word you later, so this underlined portion should be consistent with the rest of the sentence. Eliminate (C). Choice (D) correctly replaces they with you.
37. D
All four choices use similar words. Choose the one that expresses the idea most clearly and concisely. In this case, the answer is (D). Instincts does not need to be repeated because the word innate was already used.
38. B
Notice the question! The question asks for a phrase that emphasizes a common misunderstanding about bats’ vision. Choice (A) compares bats’ vision to shrimp, which is not a common misunderstanding. Choices (C) and (D) describe aspects of bats’ hunting but do not emphasize a common misunderstanding. Only (B) discusses the common thought (or cliché) about bats being blind.
39. C
The pronoun its is ambiguous, as it is unclear whether it refers to the tiger moth or the bat. The correct choice features words that are as precise as possible, so eliminate (A). The other choices clear up the ambiguity, but only (C) has the correct possessive singular pronoun needed. Choice (B) uses a plural pronoun, but since only a single system of echolocation is referred to, the singular bat’s is appropriate.
40. B
Use the Vertical Line Test. The first part of the sentence, Most tiger moths can emit clicks that warn bats away from the moths, is a complete idea. The second part of the sentence, suggesting that the moths might be inedible toxic compounds, is an incomplete idea. To connect these ideas, GO or HALF-STOP punctuation is needed. Eliminate (A) and (D) because they are STOP punctuation. Now decide whether a comma is needed. There is a shift in ideas, so a comma is needed. Also, without the comma, it could sound like the moths are suggesting something. Eliminate (C). The correct answer is (B).
41. C
The pronoun refers to the tiger moth, which is the name of a species and therefore a collective noun. Collective nouns are singular, so eliminate (A) because it is inconsistent. When dealing with pronouns, remember that possessives do not use apostrophes, while contractions do use apostrophes. Choice (B) contains a contraction. It would not make sense to say the tiger moth and it is sonar jamming, so eliminate (B). There is no such word as its’, so eliminate (D). The sonar jamming belongs to the tiger moth, so a possessive pronoun is needed, as in (C).
42. A
The commas is correct as written. There should be a comma after each item in a list of three or more items. A comma is needed after counterattack, but not after and or adapt. Choices (B) and (D) contain unnecessary commas, while (C) does not contain any; therefore, (A) is the answer.
43. A
Check the answer choices against the figures. Only (A) can be supported by the diagram. There is no indication of other animals, as in (B); what sounds are or are not heard, as in (D); or bats running into each other, as in (C).
44. D
Paragraph 5 does not fit as a conclusion, so eliminate (A). This paragraph should come after the discussion of the tiger moth and its tactics and before the conclusion of the essay. This indicates the best placement is after the third paragraph, so (D) is the answer.
1. A
The vertex form of a parabola is y = a(x – h)2 + k, where (h, k) denotes the vertex. Plug in the point (3, –3) into the vertex form to get y = a(x – 3)2 – 3. The correct answer is (A).
2. C
You can plug in to make sense of this equation. Say that x = $100. The amount of the keg would then be $107 + $17. The $17 must be the untaxed deposit since it is a flat fee rather than percentage based. Therefore, the tax is $7, which is 7% of the original $100 base price. The answer is (C).
3. D
Whenever there are variables in the question, plug in. Be sure to plug in a number that is divisible by 3. Let d = 300. 
of the original amount of $300 is $100, and that is deducted by the company, leaving Syed with $200. Then, subtract the wire transfer fee to get $200 – $30 = $170, which is the target number. Plug in 300 for d in the answer choices to see which one is equal to the target number of 170. In (A), (300) – 30 = 70. This is not the target number, so eliminate (A). Likewise in (B), (300 – 30) = 90, and in (C), 
(300 – 30) = 180. Neither of these is the target number, so eliminate (B) and (C). In (D), (300) – 30 = 170, which is the target number. The correct answer is (D).
4. C
All of the answers are written in the slope-intercept form y = mx + b, where b is the y-intercept and x and y are points on the line. Eliminate (D) because the y-intercept in that equation is 2. For the remaining answer choices, plug in the x- and y-values to determine which equation works. If x = 1 and y = 6, (A) becomes 
. Solve both sides of the equation to get 
. Eliminate (A). Choice (B) becomes 6 = 1 + 4, so eliminate (B). Choice (C) becomes 6 = 2(1) + 4, or 6 = 6. Therefore, the correct answer is (C).
5. C
Whenever there are variables in the question and the answer choices, think Plugging In. If 2 purchases were made, then p = 2, and the number of bonus points can be calculated as 4(2) + 7 = 8 + 7 = 15. If the number of purchases were then increased by 3, the new p equals 5 and the number of bonus points can be calculated as 4(5) + 7 = 27. The bonus points increased by 27 – 15 = 12. The correct answer is (C).
6. B
This is a good PITA question. Start with (B) and plug in 2 for x and 3 for r in the equation to get V = 24π + 
, which is equal to the target amount of 96π, so (B) is correct.
7. C
Whenever there are variables in the question and in the answers, think Plugging In. Let c = 30. Therefore, b = 2 + (30) = 2 + 10 = 12. Plug 12 in for b in the answers to see which answer equals the target number of 30. Choice (A) becomes 
. Eliminate (A), since it does not equal the target number. Choice (B) becomes 
. Eliminate (B). Choice (C) becomes 3(12 – 2) = 3(10) = 30. Keep (C), but check (D) just in case it also works. Choice (D) becomes 3(12 – 6) = 3(6) = 18. Eliminate (D). The correct answer is (C).
8. D
Treat this question as a translation problem. According to the question, R(h) = four rotations per second less than three times the square of the height of the liquid. The height of the liquid is represented by h. Therefore, three times the square of the height of the liquid = 3h2. Four less than this amount is 3h2 – 4. Since the original speed was 1,000, subtract this value from 1,000 to get the current rate of rotation. The correct answer is (D).
9. B
Start with the easier equation and use Process of Elimination. The easier equation is related to the total number of ounces, c + b, in the tube. According to the question, the tube has 24 ounces, so c + b = 24. Eliminate (A), since it does not include this equation. The other equation in the set is related to the amount of active ingredients. According to the question, c includes 0.25% of sodium fluoride and b contains 0.30% triclosan. 0.25% = 0.0025 and 0.30% = 0.003. Therefore, in the correct equation, c should be associated with 0.0025 and b should be associated with 0.003. Eliminate (C) and (D) because both of these equations get the percentages wrong. The correct answer is (B).
10. C
Whenever the question includes variables and the answer choices are numbers, think PITA. In (A), d = –4, and the equation becomes 
. Solve both sides of the equation to get 
, or 
. Reduce both fractions to get –13 = –5. This is not true, so eliminate (A). In (B), d = 2, and the equation becomes 
. Solve both sides of the equation to get 
, or 
. Reduce both fractions to get 
. Eliminate (B). In (C), d = 4 and the equation becomes 
. Solve both sides of the equation to get 
, or 
. Reduce both fractions to get 
. The correct answer is (C).
11. D
All the answer choices are equal to 4 (which is r2, making r = 2), so you need to focus on where the center of the circle lies. If the circle is tangent to both the x-axis (which is equivalent to the line y = 0) and the line x = 4, then the center must be 2 units from y = 0 and 2 units from x = 4. Choices (A) and (B) both have centers with an x-value of –2 (remember the standard form of the circle equation is (x – h)2 + (y – k)2 = r2, where (h, k) is the center and r is the radius), which is 6 units from x = 4. Eliminate (A) and (B). Choice (C) has a center at (2, –4). The x-value is 2 units from x = 4; however, the y-value is 4 units from y = 0. Eliminate (C) and choose (D).
12. B
According to the question, Reactant A does not react unless B gets to a certain concentration. Therefore, the correct answer will have an initial flat line for A while the line for B is rising. Only graph (B) shows this initial relationship. Therefore, the correct answer is (B).
13. A
All of the answer choices have the same lines graphed, so this question is really about the shading. Plugging In is probably the easiest way to approach this question. Start with (0, 0) because this is an easy value to check. This works in all three equations since 0 ≤ 8, –3 ≤ 0, and 1 ≥ 0. Therefore, this value needs to be shaded as a possible answer. Eliminate (B), (C), and (D) because they do not include this point. The correct answer is (A).
14. B
The question says that tan ∠BCA is 
, so draw segment CA. Since tan = 
, 
. Let AB = 3x and BC = 4x. The question says that the area of the rectangle is 48. The formula for the area of the rectangle is A = lw. Plug in A = 48, l = 3x, and w = 4x into the formula to get 48 = (3x)(4x). Simplify the right side to get 48 = 12x2. Divide both sides by 12 to get 4 = x2. Then take the square root of both sides to get x = 2. Therefore, AB = 3x = 3(2) = 6, and BC = 4x = 4(2) = 8. The question asks for the length of 
, which is the diagonal of the rectangle and equal to diagonal AC. The diagonal of the rectangle is the hypotenuse of a right triangle. Since the two legs are 6 and 8, this is 6-8-10 right triangle, so the hypotenuse is 10. The answer is (B).
15. D
Whenever there are variables in the question and answers, think Plugging In. If m = 2, the expression becomes 
. Plug 2 in for m in the answer choices to see which one equals the target number of –4. Choice (A) becomes 
. This does not match the target number, so eliminate (A). Choice (B) becomes 
. Eliminate (B). Choice (C) becomes 
. Eliminate (C). Choice (D) becomes m – 6 = 2 – 6 = –4. The correct answer is (D).
16. 
or 1.5
Plug the given values into the equation for the volume of a rectangular solid: 18 = (3)(4)(x). Multiply the right side of the equation to find that 18 = 12x. Divide both sides by 12 to find that x = 
. Both 18 and 12 are divisible by 6, so this fraction reduces to 
or 1.5.
17. 53
Jeanne charges 5.50 × 2 = $11 per hour for babysitting. Therefore, her entire earnings for three hours can be calculated as (3 × 11) + 20 = 53. The correct answer is 53.
18. 10
To solve the problem without a graphing calculator, set the two equations equal to each other: –x2 + 5x + 6 = 
x + 12. Multiply the entire equation by 2 to get –2x2 + 10x + 12 = –x + 24. Rewrite the equation to equal 0, so it becomes –2x2 + 11x – 12 = 0. Multiply the entire equation by –1 to get 2x2 – 11x + 12 = 0. Then factor the quadratic to get (2x – 3)(x – 4) = 0. Solve for the two possible values of x: if 2x – 3 = 0, then x = , and if x – 4 = 0, then x = 4. Because the slope of the line is negative, the x-value of the point that is farthest to the right along the x-axis must also be closer to the x-axis. Plug 4 in for x in the second equation to get y = (4) + 12 = – 2 + 12 = 10. The correct answer is 10.
19. 
or 3.66 or 3.67
Whenever there are two equations with the same two variables, the equations can be solved simultaneously by adding or subtracting them. Take the second equation and rewrite it so that the variables are on the left side of the equation: 17r + 22v = 63. Stack the equations and add them together.
13r + 8v = 47
17r + 22v = 63
30r + 30v = 110
Divide the entire equation by 30 to get r + v = 
. This is too big to grid in, so reduce it to 
or 3.66 or 3.67.
20. 2
The area of the current plot is 4 × 6 = 24 square feet, so the new plot will be 24 × 2 = 48 square feet. According to the question, x feet will be added to each side to obtain the new area of 48 feet. Since the length is only 2 feet more than the width, you need two factors of 48 that differ by 2. You may recognize that these factors are 6 and 8. So, the increase was 2 feet in each direction. Alternatively, you can write a quadratic: (4 + x)(6 + x) = 48. Expand the right side of the equation to get x2 + 10x + 24 = 48. Set the equation to 0 by subtracting 48 from both sides to get x2 + 10x – 24 = 0. Factor the equation to get (x + 12)(x – 2) = 0. Therefore, x = –12 or x = 2. Since lengths can never be negative, the only possible value is x = 2. The correct answer is 2.
1. C
Use Process of Elimination. According to the question, P represents the population, so the outcome of the entire equation has something to do with the population. Therefore, eliminate both (A) and (B) because 1.0635 can’t represent the population if P does. In the given equation, the only operations are multiplication and addition, which means that over time the population would increase. Therefore, eliminate (D). The correct answer is (C).
2. B
To solve the quadratic equation, first set the equation equal to 0. The equation becomes x2 + 12x – 64 = 0. Next, factor the equation to get (x + 16)(x – 4) = 0. Therefore, the two possible solutions for the quadratic equation are x + 16 = 0 and x – 4 = 0, so x = –16 or 4. Since the question states that x > 0, x = 4 is the only possible solution. Another way to approach this question is to use PITA. Start with (B), x = 4. Plug 4 into the equation to get 42 + 12(4) = 64. Solve the left side of the equation to get 16 + 48 = 64, or 64 = 64. Since this is a true statement, the correct answer is (B).
3. A
To figure out the total number of shelving units Sai could use, find the total available wall space and divide by the length of the units. The total amount of wall space can be calculated as 119 – 21. Because the length of each unit is 7 feet, the maximum number of units Sai could put up can be calculated as 
. Because this is the maximum number of units Sai could put up, r has to be less than or equal to this number. Therefore, the correct answer is (A).
4. C
Weight is shown on the vertical axis of the graph, given in ounces. Make your own mark indicating 5.75 on this axis; then draw a horizontal line from that mark to the line of best fit. Once you hit it, draw a vertical line straight down to the horizontal axis. It should hit between 75 and 80 days, slightly closer to the mark for 75. This makes (C) the correct answer. Draw your lines carefully, using your answer sheet as a straightedge if necessary.
5. C
Whenever the question includes variables, plug in. If s = 2, the shirts cost 2($24.50) = $49. The tax on the shirts is 0.07($49) = $3.43. So, the shirts with tax and the $6 shipping fee cost $49 + $3.43 + $6 = $58.43. Plug in 2 for s in the answers to see which answer equals the target number of $58.43. In (A), 0.07[24.50(2) + 6] = 3.85. This is not the target number, so eliminate (A). In (B), 1.07(24.50 + 6)(2) = 65.25. Again, this is not the target number, so eliminate (B). In (C), 1.07[24.50(2)] + 6 = 58.43. This is the target number, so keep it, but be sure to check the remaining answer choice. In (D), 1.07(24.50 + 2) + 6 = 34.355, which is not the target number. Therefore, the correct answer is (C).
6. B
The question states that after 6 weeks the plant is 54 centimeters tall. Therefore, when w = 6, h(w) = 54. Plug in 6 for w in the answer choices to see which one equals the target number of 54. In (A), h(w) = 6(6) = 36. Eliminate (A). In (B), h(w) = 9(6) = 54. The correct answer is (B).
7. D
Because the operation between the parentheses is addition, the parentheses can be removed, and the resulting expression becomes 12x2 + 4x + 5y + 3x2 – 2x + 3y. Reorder the terms so that like terms are next to each other: 12x2 + 3x2 + 4x – 2x + 5y + 3y. Combine like terms to get 15x2 + 2x + 8y. The correct answer is (D).
8. D
You do not know how the survey is conducted, nor do you know how many veterinarians were surveyed (it may be the case that only 8 were surveyed). Therefore, you cannot infer that the survey accurately measures all veterinarians’ beliefs about Royal Rat Rations. Choice (A) is not supported. First, you do not know what veterinarians believe in general, and second, veterinarians may be recommending Royal Rat Rations for a reason other than its nutrition. Choice (B) is similarly not supported: besides not knowing veterinarians’ beliefs, this choice assumes that no other rat food is acceptable. Choice (C) is not supported because you do not know the sample size of the survey, nor is there any indication that there is only one veterinarian who does not recommend Royal Rat Rations. Choice (D) is the correct answer: you know the opinions only of the veterinarians surveyed by Royal Rat Rations.
9. D
Use a calculator to translate the fractions into decimals. 
t + 4 = t – 5 becomes 0.5t + 4 = 0.75t – 5. Subtract 0.5t from both sides to get 4 = 0.25t – 5, and then add 5 to both sides. This results in 9 = 0.25t. Use a calculator to divide! t = 36; therefore, the correct answer is (D).
10. C
Taking the two dogs together, Everett has 35 + 55 = 90 pounds of dog. Set up the following proportion to determine the lowest amount of water the dogs need per day: 
. Cross-multiply to get 10x = 765, so x = 76.5. Multiply by 7 days to get the weekly amount of water the dogs need: 76.5 × 7 = 535.5 ounces, or approximately 536 ounces. Only (C) includes 536 as the low-end amount. Therefore, the correct answer is (C).
11. A
In order to answer this question, you need to deal with the ratio as well as the unit conversion. For the large batch of dry rub, Priya’s friend is planning to use 91 ounces of chili powder. Since the paprika and the chili powder must be used in a ratio of 4 to 7, you can set up a proportion to determine how much paprika is needed: 
. Cross-multiply and solve for x to determine that x (i.e., paprika) = 52 ounces. So you have 52 ounces of paprika and 91 ounces of chili powder for a total of 143 ounces. Multiply that by your conversion number, 28.3, to determine that this is equivalent to 4,046.9 grams, which is closest to (A).
12. D
Whenever there are variables in the problem and in the answer choices, plug in. If w = 20, then Luciano’s cup has 20 – 2 = 18 ounces at the end of day 1. At the end of 7 days, Luciano’s cup would have 18 – 8 = 10 ounces. After 11 days, Luciano’s cup would hold 10 – 5 = 5 ounces. Plug in 20 for w in the answer choices to see which answer is equal to the target number of 5. Choice (A) becomes 
. This does not match the target number of 5, so eliminate (A). Choice (B) becomes 
. Eliminate (B). Choice (C) becomes 
(20) – 10 = 10 – 10 = 0. Eliminate (C). Choice (D) becomes 
. This matches the target number; therefore, the correct answer is (D).
13. B
According to the line of best fit, in 1995 there were 20 coyotes in the park. In 2000, there were 140 coyotes in the park. This is an increase of 120 coyotes over a period of 5 years, so 
= an average increase of 24 coyotes per year, which is (B).
14. D
The median number of coyotes in the park in 1995 was 20, and the median number of coyotes in the park in 1996 was 60. (Be careful to RTFQ; the question wants the median, not the line of best fit!) In order to calculate the percent increase, it is necessary to use the percent change formula: 
× 100. The calculation here will be 
× 100 = 
× 100 = 2 × 100 = 200%, which is (D).
15. A
Start with the easier equation and use Process of Elimination. The easier equation is related to the total number of shirts and pants, s + p, sold on a regular day. The question states that on a regular day Bailey’s sells the number of pants and shirts sold during a sale. (60) = 40. Therefore, one of the equations in the correct answer will be s + p = 40. Eliminate (C) and (D) since neither includes this equation. The other equation is related to the money Bailey’s earns on a regular day. According to the question, Bailey’s earns a total of $1,875 on a regular day, so the equation must equal $1,875. Eliminate (B) because the total in the money equation is incorrect. The correct answer is (A).
16. C
There are a few different ways to approach this question. In any approach, the best first step is to figure out how much income Bryan earned during the two-week period without the commission. Since he worked an average of 35 hours per week for two weeks, he worked a total of 70 hours. At a rate of $10.00 per hour base pay, this would add up to $700.00 (70 × 10 = 700). Since Bryan’s earnings were actually $850.00, that means he must have earned $150.00 of commission (850 – 700 = 150). At this point, you can calculate the percent commission algebraically or simply work backward from the answer choices. Algebraically, you know that $150.00 is equal to a certain percent of $5,000.00 in sales, which can be represented as follows: 150 = 
(5,000). Solve for x, and you get 3, which is (C). If instead you wish to work backward from the answer choices, you can take each choice and calculate what 1%, 2%, etc. of $5,000.00 would be, and then add that back to $700.00 to see which choice matches your target of $850.00: (C).
17. C
Cross-multiply to get 3(C + x) = (x – 3)(x + 8). Expand the right side of the equation to get 3(C + x) = x2 + 5x – 24. Distribute the 3 to get 3C + 3x = x2 + 5x – 24. Subtract 3x from both sides of the equation to get 3C = x2 + 2x – 24. Factor the right side of the equation to get 3C = (x + 6)(x – 4). Divide both sides by 3 to get 
. The correct answer is (C). Alternatively, you can plug in for x to get a target value for C, and then use Process of Elimination.
18. A
Start with the easiest piece of information first, and use Process of Elimination. Since h is the number of hours spent hiking and d is the number of hours driving, the total number of hours Lennon spends in the park can be calculated as h + d. The question states that Lennon has up to 6 hours to spend in the park—“up to” means ≤. So, h + d ≤ 6. Eliminate (B), (C), and (D). The correct answer is (A).
19. B
The quality control expert discovered that 13 out of 1,000 randomly selected tennis balls were defective. 
= 0.013, which is equivalent to 1.3%. This means that 100 – 1.3 = 98.7% of tennis balls tested were not defective, and this data most supports (B), which is the correct answer.
20. C
When solving inequalities, the natural impulse is to isolate the variable. In this case, though, look at what the question is asking. The question doesn’t want you to find just the value of z, but rather the value of 9z – 18. To get from the value of – 3z + 6 given in the inequality to this new value, the original inequality must be multiplied by –3. Just multiply the entire inequality by this value, making sure to flip the inequality signs when multiplying by a negative number. The equation becomes –3
> –3(–3z + 6) > –3
or 
> 9z – 18 > 
. The question asks for the greatest possible integer value, so focus on the high end of the given values. The value at that end, , equals 8.57, so the greatest integer less than that is 8. The answer is (C).
21. A
Whenever there are variables in the question and numbers in the answer choices, think PITA. In (A), j = 6, and k = –6. Plug these two values into the first equation to get –24 – 8(6) = 12(–6). Solve for both sides of the equation to get –24 – 48 = –72, or –72 = –72. Therefore, the values work for the first equation. Plug the values into the second equation to get 
. Solve both sides of the equation to get 3 + (–10) = –7, or –7 = –7. Since the values given in (A) work in both equations, the correct answer is (A).
22. C
You know the new proportion must be less than the current 0.34 for biofuels (because the total amount spent on alternative energy is increasing, but the amount spent on biofuels is remaining the same), so you can eliminate (D). Next, determine the amount that will be spent on biofuels in 2017 by multiplying 0.34 by the total of $254 million: 0.34 × 254 = $86.36 million. Because 57 million new dollars will be spent on alternative energy, the new total will be 254 + 57 = $311 million. Divide $86.36 million by $311 million to get the new proportion: 
= 0.28, which is (C).
23. D
In Quadrant II, the x-coordinate is negative, and the y-coordinate is positive. Therefore, eliminate (C). Whenever the question includes variables and the answer choices are numbers, think PITA. Of the remaining choices, (B) is easiest to work with. In (B), the x-value is –4 and the y-value is 2. Plug these values into the second equation to get –4 = –2 + 2. Since this is not a true statement, eliminate (B). Try the values in (A) in the second equation to get 
. This is also not true, so the correct answer is (D).
24. B
Right away, (A) can be eliminated, since point C has a negative y-coordinate. Given any two points, the slope of the line can be determined using the equation 
. Use this formula to find the value of b by setting the slope of 
equal to the slope of 
. Use points (0, 3) and (5b, b) in the left side of the equation and points (5b, b) and (10b, –b) in the right side of the equation to get 
. Simplify both sides of the equation to get 
, or 
. Cross-multiply to get 5(3 – b) = 10b. Divide both sides by 5 to get 3 – b = 2b. Add b to both sides to get 3 = 3b. Divide both sides by 3 to get b = 1. Plug in b =1 for point C to get [10(1), – (1)], or (10, –1). Therefore, the correct answer is (B).
25. A
The formula for compound interest is A = P(1 + r)t, where P is the starting principle, r is the rate expressed as a decimal, and t is the number of times the interest is compounded. Melanie received less than 5% interest, so you can eliminate (B) because 1.05 = 1 + 0.05, which indicates that she was receiving 5% interest. You can also eliminate (C) because over the course of a year, the interest is compounded 4 times, not of a time. Because Melanie invested $1,100 at what she thought was 5% compounded 4 times (12 months in a year ÷ 3 months per period), she expected 1,100(1 + 0.05)4 = $1,337.06 after a year. Instead, she has 1,337.06 – 50 = $1,287.06 after one year. Because t is in years in the answer choices, make t = 1 in (A) and (D) and eliminate any choice that does not equal 1,287.06. Only (A) works.
26. B
You can start by plugging in a value for x; try x = 4. Because angle AOB is 120° and the triangle is isosceles, angles A and B are each 30°. Cut triangle AOB in half to make two 30-60-90 triangles with a hypotenuse of 4 and legs of 2 and 
. The leg with length lies on chord AB. Double it to get the total length: 
or just 
, which is (B) when you put x = 4 into the answer choices.
27. C
Whenever there are variables in the question and in the answer choices, think Plugging In. The question states the value of g, but it is a constant and a weird one at that. Pick numbers for all the variables that will make the math more straightforward. If v = 4 and g = 2, then 
, and 
. Plug these values into the answer choices to see which equation works. Choice (A) becomes 
. Simplify the right side of the equation to get 
or 
. This will not simplify further, so eliminate (A). Choice (B) becomes 
. Simplify the right side of the equation to get 
or 
. Eliminate (B). Choice (C) becomes 
. Distribute the 2 to get 
. Reduce the equation to get 
or 4 = 4. The correct answer is (C).
28. D
ia = 1 when a is a multiple of 4. Use the exponents rule to determine that 413 + x must also be a multiple of 4. Plug in the answers and look for what makes 413 + x a multiple of 4. Only (D) works.
29. C
The zero of g is the value of the variable, in this case x, when the equation is set to 0. This is also called the root or solution of an equation. Set the equation to 0 to get 0 = 2x2 – dx – 6. Plug 6 in for x to get 0 = 2(62) – d(6) – 6. Simplify the equation to get 0 = 72 – 6d – 6, or 0 = 66 – 6d. Solve for d to get –66 = –6d, so 11 = d. Plug 11 in for d and set the quadratic to 0 to get 0 = 2x2 – 11x – 6. Factor the equation to get 0 = (x – 6)(2x + 1). The other zero of the equation is when 2x + 1 – 0. Solve for x to get 2x = –1, or x = 
. The correct answer is (C).
30. D
The flu shot is most effective against Strain C, which is least prevalent in March. To determine the overall efficacy of the flu shot at this time, multiply the prevalence of each strain of flu by the efficacy of the flu shot against that strain, and then add those products to get a weighted average of the efficacy of the shot: (0.23 × 0.35) + (0.25 × 0.13) + (0.13 × 0.76) + (0.39 × 0.68) = 0.477 = 47.7%, which is closest to (D).
31. 3
Solve the equation for v. Take 9 > 3v – 3 and add 3 to both sides to get 12 > 3v. Now divide both sides by 3 to find that 4 > v. Therefore, the largest integer that v could be is 3. Grid in 3.
32. 
or .83
Start by multiplying the second fraction in the denominator of the equation by 
to get 
. Combine the fractions in the denominator to get 
. Reduce the fraction in the denominator to get 
. Dividing by a number is the same as multiplying by its reciprocal, so the equation becomes 
× y = 1. Multiply both sides of the equation by 
to get y = . The correct answer is or .83.
33. 1,279
614 students voting for Candidate A represents 0.48 of the population out of 1. Set up a proportion: 
, where x is the total number of students in the school. Cross-multiply: 0.48x = 614. Divide both sides by 0.48 and you get approximately 1,279.
34. 
or .384 or .385
Draw a right triangle and label a non-right angle θ. SOHCAHTOA tells you that tangent is 
, so the leg opposite θ is 12 and the leg adjacent to θ is 5. Cosine is 
, so you need to find the hypotenuse of the triangle. You can use the Pythagorean Theorem, or you can recognize this as a 5-12-13 Pythagorean triplet. The hypotenuse is therefore 13. The leg adjacent to θ is still 5, so cos θ = 
or .384 or .385.
35. 7,054
First, you need to determine the current exchange rate. The 7% fee is the same (relative to the exchange rate), whether it was applied to the Cedi or USD. Therefore, 7% of 651 Cedi is equal to 32.30 USD. Translate English to math: 0.07(651) = 32.30, or 45.57 Cedi = 32.30 USD. Next, you want the value of an item worth 5,000 USD in Cedi, so set up a proportion: 
. Cross-multiply: (45.57)(5,000) = 32.30x, or 227,850 = 32.30x. Divide both sides by 32.30 and you get x = 7,054.18 USD, which rounds to 7,054.
36. 63.6 or 63.7
First, draw a square inscribed in a circle. Because the diameter of the circle is equal to the diagonal of the square, you can plug in a number like 
for the length of the diameter. Because the diameter forms a 45°-45°-90° triangle, each side of the square has a length of 2. Using the area formula for a square (A = s2), plug in 2 for the s to get A = 22, which simplifies to A = 4. The area of the square is 4. To find the area of the circle, use the formula A = πr2. Because the diameter of the circle is , r = 
. Plug that into the area formula to see that A = π()2, which simplifies to A = 2π. To find the solution, translate the question from English into math. The area of the square is what percent of the area of the circle becomes: 
2π. Solve for x. First, divide each side by 2π, and then multiply each side by 100. The answer is a non-repeating decimal beginning 63.66197…. When entering your answer, simply cut off the decimal so it takes up four spaces. You should enter 63.6 or 63.7.
37. 
– or .7
If the mean of the new set is , then the sum of the diameters of the cylinders divided by the number of cylinders must equal . Set up the equation: = 
, where x is the unknown cylinder. Multiply both sides by 6 to simplify: 
. Combine like terms (use your calculator, but be careful with parentheses!): 
. Subtract 
from both sides and you get 
or .7.
38. 1 ≤ y ≤ 1.25
A set with an even number of elements will have as its median the average of the middle two terms. In the current set, 
and 1 have an average of 
, so the new cylinder must be equal to or greater than 1, so the median will be the average of and 1. The range of the set of five cylinders is the greatest minus the least: 
. Because the new cylinder must be 
inches to greater than , the cylinder must be between 1 and 
inches in diameter. Therefore, in the grid for this question, you can enter 1.1, 1.11, 1.2, 1.21, or any other number between 1 and 1.25.
Please note that the numbers in the table may shift slightly depending on the SAT’s scale from test to test; however, you can still use this table to get an idea of how your performance on the practice tests will translate to the actual SAT.