1. A
Although Jane resists Mr. Rochester, the first sentence of the passage indicates that her conscience and emotions are actually favorably inclined toward Mr. Rochester. Because she has positive feelings toward him, (A) is an accurate description of her attitude. While Mr. Rochester perceives Jane to be uncaring, (B) is incorrect because the narration indicates that she does care but resists her own feelings. Similarly, (C) is incorrect because the first sentence tells us she has positive feelings for Rochester. Because Jane acts calmly, ignoring her emotions, she cannot accurately be described as reckless. Therefore, (D) is also incorrect, so (A) is the correct answer.
2. B
Because Q2 and Q3 are general paired questions, consider Q2 and the textual evidence given in Q3 at the same time. Q2 asks for the reason Jane refused Rochester’s advances. Consider the lines referenced in the answer choices for Q3 and whether they support any of the answers in Q2. Choices (A), (C), and (D) in Q3 do not support any of the answer choices in Q2, so they can be eliminated. However, (3B), I will hold to the principles received by me when I was sane, and not mad—as I am now, provides support for only (2B), so (B) must be the answer to both Q2 and Q3. These answers make sense because they indicate that Jane resists Rochester because she wishes to hold to her principles.
3. B
(See explanation above.)
4. D
There is no evidence that Jane is literally insane. Rather, she is speaking metaphorically about the conflict between her reason and her desires. Therefore, (A) is wrong. Because Jane says the law (not her mental state) has been given by God, (B) is incorrect. Jane says that her insanity tempts her to disregard the worth of her principles, and it is her principles that are preventing her from giving in to Mr. Rochester, so her insanity is tempting her to give in to Rochester. Therefore, (C) is wrong; her insanity does not urge her to reject Rochester, but rather to accept his advances. Choice (D) is correct because her feeling of insanity is directly related to her emotions, as evidenced by the phrase with my veins running fire, and my heart beating faster than I can count its throbs, which Jane provides to explain why she feels insane.
5. C
Because wrought describes Mr. Rochester’s fury, and the passage says that his fury has reached its highest, wrought must mean something like “increased.” Because hammered has nothing to do with increasing fury, (A) is incorrect. Choice (B) also does not have anything to do with “increased,” so eliminate it. Because excited could mean “increased” when applied to someone’s emotions, (C) accurately describes the passage’s use of wrought. Since wrung means squeezed and twisted, (D) does not describe the passage’s use of wrought. The correct answer is (C).
6. A
Choice (A) is correct because Mr. Rochester describes Jane’s soul as strong and her body as weak in paragraph 5. While paragraph 1 states that Rochester loves Jane, and paragraph 4 states that he is angry with her for refusing his advances, Rochester is angry for the entirety of paragraph 5. Therefore, it does not contrast his love with his anger, and (B) is incorrect. Though Rochester speaks of a cage, he never actually mentions a bird; eliminate (C). Similarly, Rochester refers only to Jane’s purity. Because he never calls Jane impure, (D) is not correct.
7. D
Rochester is speaking metaphorically, not about a literal convict, so (A) is incorrect. Because he is talking about Jane, not himself, (B) cannot be correct. When Rochester refers to breaking the prison and Jane’s body, you can tell that the inmate’s prison refers to Jane’s body, not the ideals of the time. Therefore, (C) is incorrect. The inmate refers to Jane’s soul, so (D) accurately describes Rochester’s use of inmate and is the correct answer.
8. C
Think about the evidence in the passage that helped you answer the previous question: Rochester is using the word inmate to refer to Jane’s soul trapped in her body. Because (A) mentions neither soul nor body, (A) is incorrect. Choice (B) refers only to Jane’s body, so it cannot be correct. Choice (C) mentions both Jane’s spirit and body (her brittle frame), providing good support for the answer to the previous question. Choice (D) makes no mention of either soul or body, so it is incorrect. The correct answer is (C).
9. B
Because Jane is having a harder time resisting Rochester now that he is sad, worse means something close to “harder.” Because less desirable, of lower quality, and unskillful all mean things other than “harder,” you can eliminate (A), (C), and (D). Because “harder” matches more difficult, (B) accurately describes the passage’s use of worse and is the correct answer.
10. C
Pathos refers to Jane’s emotions, so the paragraph depicts Jane overcoming her emotions. Therefore, (A) cannot be correct. Jane makes no allusion to social conventions, which makes (B) incorrect. However, because the paragraph depicts Jane overcoming her emotions, (C) is a good description of Jane’s values. Since Jane battles to overcome her feelings, (D) is not an accurate description of her values. Choice (C) is the answer.
11. C
Clinton’s speech speaks out against gender inequality all over the world and advocates in favor of these injustices being amended. Choice (C) best reflects this idea. Although Clinton criticizes how women are treated worldwide, she does not counter any arguments, so eliminate (A). She does not take a scholarly approach to analyze women’s place in society, so eliminate (B). Clinton is not mediating between two parties, so eliminate (D).
12. B
Although women play different roles in society, many of these roles are not appreciated. Choice (B) most accurately reflects this meaning. Choices (A), (C), and (D) have meanings that are related to the word valued but are not used in the context of the word’s use in the passage.
13. D
Clinton discusses the importance of conferences in compelling people to consider important issues. She then mentions the conference in Nairobi as helping to bring to light the crisis of domestic violence. Therefore, (D) is the correct answer. The passage does not claim that the crisis of domestic violence was not solved, so eliminate (A). The passage does not discuss anyone questioning the reason for holding the current conference, so eliminate (B). Although Clinton mentions the fact that the experiences of women tend to go unnoticed, this is not her reason for mentioning the conference in Nairobi. Eliminate (C).
14. B
Think about the evidence in the passage that helped you answer the previous question: It is conferences like this that compel governments and peoples everywhere to listen, look, and face the world’s most pressing problems. She then mentions the conference in Nairobi as helping to bring to light the crisis of domestic violence. Choice (B) provides the most support for why Clinton mentions the conference in Nairobi. The current conference was not held because of the conference in Nairobi, so eliminate (A). Women being the primary caretakers of the world is not the reason for mentioning the conference in Nairobi, so eliminate (C). Women dying from preventable diseases is not the reason for mentioning the conference in Nairobi, so eliminate (D).
15. B
Clinton discusses how some women are able to attend a conference that speaks out against the inequalities against women, while others are not able to do so. Choice (B) most accurately reflects this idea. Clinton does not differentiate between people who work at schools and hospitals, so eliminate (A). Clinton does not mention employed women, unemployed women, or women who can or cannot vote, so eliminate (C) and (D).
16. D
Choices (A), (B), and (C) are each discussed in paragraph 4, so eliminate them. The passage does not discuss women suffering from widespread unemployment, so (D) is the correct answer.
17. C
In paragraph 4, Clinton discusses women who have a voice standing up for women who are unable to stand up for themselves. Choice (C) most accurately reflects this idea. Choices (A), (B), and (D) have meanings that are related to the word speak but are not used in the same context as this word is used in the passage.
18. A
In paragraph 8, Clinton argues that women’s rights are also human rights, which matches (A). Women’s attendance at the conference is not discussed in this paragraph, so eliminate (B). Clinton does not claim that women’s rights have a special nature, just that these rights are the same as human rights, so eliminate (C). Clinton does not suggest that we no longer need to focus on women’s problems; this is the opposite of what is discussed in the passage, so eliminate (D).
19. B
Think about the evidence in the passage that helped you answer the previous question. In paragraph 8, Clinton argues that women’s rights are also human rights. Choice (B) provides the most support for the rhetorical effect of the phrase discussed in the previous question. Although Clinton discusses the respect and protection of women’s rights, this is not the phrase that best supports the rhetorical effect of the discussed phrase, so eliminate (A). Giving examples of the specific rights in question does not provide the best support for the rhetorical effect of the discussed phrase, so eliminate (C). The attendance of women at the conference is not related to the discussed phrase, so eliminate (D).
20. B
In paragraph 2, Clinton discusses the experiences of women throughout the world: Yet much of the work we do is not valued—not by economists, not by historians, not by popular culture, not by government leaders. Choice (B) most accurately reflects this idea. Clinton does not state that these leaders are purposely working against the prosperity of women, so eliminate (A). Choice (C) is contradicted by what the passage states, so eliminate this choice. Although these leaders may not value the work of women, the passage does not state that these leaders have made it unacceptable to discuss women’s rights, so eliminate (D).
21. D
The graphic shows poverty rates in America divided by gender and age. Across all age groups, women experience higher rates of poverty than their male counterparts. This falls in line with the passage’s assertion that women comprise 70 percent of the world’s poor. Therefore, (D) is correct. Choice (A) is incorrect because, while the graphic shows a high gender disparity among those 65 and older, it refers only to American poverty rates. The graphic actually states that 15.4 percent of American women 18 to 65 are impoverished, not that they make up that percentage of the world’s poor. Therefore, (B) is incorrect. And there is no mention of how many children are impoverished worldwide in either the graphic or the passage, so (C) is incorrect.
22. B
The third-to-last sentence of the passage states that Seen throughout the procession is that balance of the monumentally simple and the actual, and goes on to list several more types of balance, that Heraclitus, the philosopher, wrote of in the sixth century B. C. This is support for (B). While the author does discuss the representation of the passage of time in the frieze, this idea is not connected to Heraclitus, so (A) can be eliminated. The mention of Heraclitus also does not support the idea that the frieze is characteristically Greek, so (C) is incorrect. Choice (D) is tempting, if the entirety of the sentence mentioning Heraclitus isn’t included; however, the balance mentioned isn’t between mortals and the goddess Athena.
23. A
In the first paragraph of Passage 1, the author proposes his idea of what the frieze probably represents. In the second paragraph, he describes the frieze. This matches (A). Choice (B) may seem close at first because the author does indicate that the subject of the frieze is still a matter of scholarly dispute. However, he does not question someone else’s interpretation, so (B) is incorrect. Choice (C) falls into the category of “too narrow”: the author does describe the frieze, but only in paragraph 2. Choice (C) doesn’t take paragraph 1 into account. Since no historical overview is given, (D) is also incorrect.
24. D
By using the word unparalleled, the author is saying that it is unusual to see a representation of a festival in classical Greek art that shows deities in attendance. Choices (A), (B), and (C) do not match the meaning of “unusual,” but (D) does. Therefore, (D) is the answer.
25. D
Passage 2 begins with the first paragraph describing ways that the particular piece of art in question is unusual in the world of classical Greek art: it shows deities attending a festival, including Athena, and they are ignoring the peplos. This represents a flagrant breach with tradition that requires explanation. Paragraph 2 continues with an explanation of what it cannot represent. Since the author does not say that the frieze cannot depict the Panathenaic procession, (A) is incorrect. The author also does not discuss the passage of time, so (B) is incorrect. While the author goes on to describe the heroes of Marathon, the question is asking about the purpose of the first two paragraphs, so (C) is a tempting trap answer but must be eliminated. Choice (D) comes the closest to what the author is doing in the first two paragraphs, describing problems in the traditional interpretation of the frieze.
26. A
Paragraph 2 begins by discussing what a classical Athenian, or resident of Athens, would not have thought as he looked at the frieze, that is, that it was a representation of himself. In the second sentence, mortal could be replaced by classical Athenian, because the subject must be something greater than a resident of Athens. Therefore, (B), (C), and (D) do not fit, and (A) is the correct answer.
27. B
Paragraph 2 begins by discussing what a classical Athenian, or resident of Athens, would not have thought as he looked at the frieze: “there I go” or even more vaguely “there we go.” The next sentence mentions that the subject of the frieze must be more than mortal, or more than about the classical Athenian looking at it. Putting these together, you can surmise that when the author says that the classical Athenian wouldn’t say “there I go,” he means that the frieze is not about the classical Athenian. Paragraph 3 confirms this idea by saying we must rule out…that it is a contemporary or generic statement of the Panathenaic procession conducted by the citizens…. Since there was never a discussion of the figures themselves and whether they represented individual citizens, (A) is incorrect. Choice (B) does match pretty closely, so keep it. Choice (C) has more to do with who participated in the procession rather than the subject of the frieze, so eliminate (C). Choice (D) goes too far because the author never says that the subject of the frieze should be obvious to modern viewers. Choice (B) is the correct answer.
28. D
Think about the evidence in the passage that helped you answer the previous question: support for (B) in Q27 comes from paragraphs 2 and 3, so (A) and (B) can be eliminated. While it may be true that the explanation must have been apparent to the classical Athenian who knew this background, this does not support the idea that the frieze cannot represent a human event, so eliminate (C). Choice (D) directly supports (B) in Q27 and is therefore the correct answer.
29. B
The author of Passage 2 proposes that the frieze shows the fighters of Marathon celebrating the prime festival of the goddess Athena…as a thanksgiving for her aid at Marathon and afterwards. This ties into (B), Athenian men who died in battle at Marathon. There is no indication that the author believes the youths were from around the time the Parthenon was built, so eliminate (A). Choice (C) is too broad because it includes all people of Marathon who were worshipped as heroes, whereas the author specifies the fighters of Marathon, so eliminate (C). Choice (D) contradicts the author’s description that the frieze is a representation of the fighters, not purely divine participants, so eliminate it. Choice (B) is the answer.
30. B
Passage 1 does not focus on determining the subject of the frieze—that’s only in the first paragraph. Eliminate (A). Passage 2 considers how Greek citizens might have viewed the frieze, but Passage 1 does not. Eliminate (C). Passage 1 also does not entirely reject the traditional perspective, so eliminate (D). Passage 1 does give a detailed description of the figures in the second paragraph, so (B) is the correct answer.
31. D
Think about the evidence in the passage that helped you answer the previous question: Passage 1 gives a detailed description of the figures in the frieze in the second paragraph. Only (D) references lines that give a detailed description of figures in the frieze, so (D) is the correct answer.
32. C
This question asks about the primary purpose of the passage. Because this is a general question, it should be done after the specific questions. The passage describes the results of a Stanford University study that showed that antibiotic-resistant strains of tuberculosis evolve over the course of treatment and remain virulent. The passage goes on to discuss the concerns raised by the study. The passage concludes by stating that drug-resistant bacteria are here to stay. Find an answer that matches this prediction. Choice (A) can be eliminated because, while the passage does mention classic laboratory experiments, it does not support those findings. Choice (B) can be eliminated because the idea that the findings should cause alarm is the opposite of what the passage says in the last two paragraphs. The passage does review the Stanford University study and discusses the concerns raised by the study. Keep (C). Eliminate (D) because the passage does not criticize the methodology of any study. The correct answer is (C).
33. A
This question asks what the scientists in the Stanford University study discovered about tuberculosis bacteria that “undermined this comforting conventional wisdom.” Notice that this is a paired question with best evidence answers that cover a large part of the text. Therefore, Q33 and Q34 can be done in tandem. Look at the “best evidence” answer choices for Q34 first. The lines for (34A) state that Without RNA, bacteria can’t make the proteins they need to survive. This does not support any of the answers in Q33. Eliminate (34A). The lines in (34B) provide information about when the Stanford group collected tuberculosis bacteria from the sputum of patients. This does not support any of the answers in Q33. Eliminate (34B). The lines in (34C) state that five of the ten resistant strains held their own in these tests, and one actually dominated its antibiotic-susceptible ancestor. This supports the idea in (33A) that bacteria can resist antibiotics without losing strength. Connect (34C) with (33A). The lines for (34D) state that Some changes simply have a low cost to begin with, and, the study also found, the cost depends on the strain in which the mutation occurs. This does not support any of the answers in Q33. Without any support in the answers from Q34, (33B), (33C), and (33D) can be eliminated. The correct answers are (33A) and (34C).
34. C
(See explanation above.)
35. B
This question asks what the word hardy most nearly means, as used in line 26. Read the window, cross out the word hardy, 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. In the passage, the word hardy is used in connection with drug-resistant strains that remain virulent. In other words, these are potent strains that keep their strength. Look for a word that means “strong” or “tough.” Difficult and thick do not match “strong” or “tough.” Eliminate (A) and (D). Strong matches the prediction; keep (B). While (C) may be tempting since a virulent strain would be terrible, no such value judgment about the drug-resistant strains is made in the passage; eliminate (C). The correct answer is (B).
36. B
This question asks what statement about rifampin can be most reasonably inferred from the passage. Use the lead word rifampin and chronology to find the window. The answer to Q35 was in line 26. Therefore, start looking for rifampin after line 26. The first mention of rifampin is in line 30. According to the passage, rifampin…disables the so-called polymerase molecule and prevents the crucial flow of information from DNA to RNA. Without RNA, bacteria can’t make the proteins they need to survive. Find an answer that matches this prediction. Choice (A) may be tempting at first because the passage states that rifampin is one of the preferred first-line treatments for the disease. However, the passage does not say that this drug stopped tuberculosis from being the leading cause of death in the United States. Eliminate (A). Choice (B) is a good paraphrase of the prediction, so keep it. Choice (C) can be eliminated because there is no suggestion in the passage that rifampin makes RNA compatible with DNA. Choice (D) can be eliminated because there is no mention in the passage as to whether rifampin is more effective than other drugs. The correct answer is (B).
37. D
This question asks which type of evidence the Stanford University study relied on. Use the lead word Stanford and chronology to find the window. The answer to Q36 was in line 35, so the answer to this question should come somewhere after line 35. Line 49 contains the word Stanford. According to the passage, the Stanford group collected tuberculosis bacteria from the sputum of patients, first at the beginning of their infections, and a second time after some of those patients developed rifampin-resistant infections. Look for an answer that matches this prediction. Given that the Stanford group did research using human patients, anecdotal opinion, secondhand observations, and animal studies do not match the prediction. Clinical testing matches the prediction. The correct answer is (D).
38. D
This question asks about what scientists believed about antibiotic-resistant strains of tuberculosis prior to the Stanford study. Remember to use answers to questions from earlier in the passage if they are relevant. Q33 asked about conventional wisdom, which thought antibiotic-resistant bacteria were weaker than their non-resistant counterparts. Find an answer that matches this prediction. Choice (A) can be eliminated because prior to the study, the scientists believed the antibiotic-resistant strains had a worse chance of survival. Eliminate (B) because prior to the study, the scientists expected the antibiotic-resistant strains to be less likely to survive. Therefore, it is unlikely that they expected the antibiotic-resistant strains to become the most deadly of diseases. Choice (C) can be eliminated because, while sputum was mentioned earlier in the passage, it was mentioned in relation to how the scientists collected the study samples, not in relation to the scientists’ expectations of the study outcomes. Given that the scientists discovered the resistant bacteria were not weaker than their counterparts and the results of the study were contrary to expectations, it can be concluded that prior to the study, the scientists expected the antibiotic-resistant strains not to survive. The correct answer is (D).
39. C
This question asks what question Sebastien Gagneux plans to answer through further studies. Because this is the first question in a paired set, this question can be done in tandem with Q40. Look at the “best evidence” answer choices for Q40 first. The lines for (40A) state that Gagneux is planning future studies to find these putative compensatory mutations and learn how they restore the performance of strains that acquire antibiotic-resistant mutations. This supports the question in (39C). Connect answers (40A) and (39C). The lines in (40B) quote Levin as saying that the spread of tuberculosis does not depend solely on the efficacy or lack of efficacy of antibiotics. This information is unrelated to Gagneux’s future research plans. Eliminate (40B). The lines for (40C) state that drug-resistant bacteria are here to stay. This information is unrelated to Gagneux’s future research plans and does not support any of the answers for Q39. Eliminate (40C). The lines for (40D) quote Levin as saying that the drug-resistant mutations that aren’t costly are the ones that will take over. It may be tempting to connect (40D) with (39B) since (39B) includes the word cost. However, the information in the lines for (40D) is unrelated to Gagneux’s future research plans. Eliminate (40D). Without any support in the answers from Q40, (39A), (39B), and (39D) can be eliminated. The correct answers are (39C) and (40A).
40. A
(See explanation above.)
41. D
This question asks why the author mentions the alarmist panic in line 76. Use the given line reference to find the window. According to the passage, the authors don’t want their study to fuel an alarmist panic…the data don’t call for it. The passage goes on to quote Levin as saying “the spread of tuberculosis does not depend solely on the efficacy or lack of efficacy of antibiotics.” Therefore, the alarmist panic is related to the public’s reaction to the study results. Find an answer that matches this prediction. Choice (A) can be eliminated because the passage states that the data does not call for an alarmist panic. Therefore, the author is not using the term to bring attention to a threat. Eliminate (B) because there is no mention of 19th century public-health practices in the window. The author is not identifying an inevitable result of antibiotic use, so eliminate (C). Choice (D) matches the prediction. The author is drawing a contrast between the study data (an undesirable reaction) and a reasonable response, which is not alarmist panic, as the data don’t call for it. The correct answer is (D).
42. B
This question asks about the primary function of the final paragraph. Use the final paragraph as the window. The final paragraph broadly summarizes the study findings and makes a general prediction about future bacteria mutations. Find an answer that matches this prediction. Choice (A) can be eliminated because the paragraph does not reevaluate the Stanford University study. Choice (B) is consistent with the prediction, so keep it. Choice (C) can be eliminated because there is no indication that the author believes that the Stanford University study changed society. Eliminate (D) because the last paragraph does not explain the methodology of the Stanford University study. The correct answer is (B).
43. C
Look earlier in the sentence for the phrase the Earth’s surface sank more than 1 mile. Go through the answer choices to find the one that matches this description. Choice (C) is correct because a crater is a “large, bowl-shaped cavity in the earth.” Eliminate (A), (B), and (D), as none of them match this physical description.
44. B
The second paragraph primarily discusses the extensive time range of volcanic eruptions, starting as far back as 400,000 years ago and as recently as 600 years ago. Use POE to find the answer choice that matches this information. There is no evidence of another eruption this century based on the passage, so eliminate (A). Choice (B) works because it shows the large range of time in geologic terms. Choice (C) almost works, but the author is not just trying to be ironic. The information is not relevant to the paragraph, so eliminate (C). Choice (D) is incorrect because a relative term doesn’t fit; recently isn’t being compared to any other variables. Choice (B) is the answer.
45. B
The pronoun that precedes temblor, so it must refer to something earlier in the previous sentence. The first sentence discusses a magnitude 5.4 earthquake struck 6 miles southeast of the caldera, so (B) is correct because the temblor ended two decades of low quake activity.
46. C
The third sentence in paragraph 7 states that the geologists studied trees that were dying on Mammoth Mountain from carbon dioxide, and that this would often precede volcanic eruptions. This information suggests the possibility of a volcanic eruption. Choice (C) is a good match for this information. There is no evidence to support (A) and (B), so eliminate them. There is no mention of geodetic equipment in this paragraph, so eliminate (D) as well. Choice (C) is the answer.
47. D
Think about the evidence in the passage that helped you answer the previous question: the geologists are monitoring the caldera to try to predict a future eruption. Use POE to find the best reference from the passage to the previous question. Eliminate (A) because that sentence refers to eruptions from centuries ago. Choice (B) does not reference geologist activity at all, so get rid of it. Eliminate (C) because it discusses the equipment, not the geologists. Choice (D) works because it details studies from the USGS regarding forms of evidence that often precede volcanic eruptions.
48. A
The final sentence in the last paragraph states that geologists think that the chances of an eruption in the area in any given year are quite small. This contradicts the information in (B) and (C), so eliminate them. Earthquakes are only a small part of the overall passage, so eliminate (D) because it is too limited. Choice (A) is correct.
49. C
Use POE to find the answer choice that is best supported by the passage. Choice (A) is incorrect since it was both the Inyo Craters and Mono Craters that erupted 600 years ago. Choice (B) almost works, but the passage never suggests that Mammoth Mountain is actually active, as opposed to the larger chain—the Long Valley Caldera—it’s part of. Choice (C) is a good fit because the seventh paragraph states that symptoms of volcanic unrest may persist for decades or centuries at large calderas, such as Long Valley Caldera. The information in (D) is mentioned in the first paragraph, but there is no evidence that refers to Mammoth Mountain, so eliminate it. Choice (C) is correct.
50. D
Think about the evidence in the passage that helped you answer the previous question: the seventh paragraph states that symptoms of volcanic unrest may persist for decades or centuries at large calderas, such as Long Valley Caldera. This sentence is referenced by (D), while the other choices do not relate to the correct answer to the previous question. Therefore, (D) is the answer.
51. D
The last few sentences of the seventh paragraph state that symptoms of volcanic unrest may persist for decades or centuries at large calderas, such as Long Valley Caldera. Studies indicate that only about one in six such episodes of unrest at large calderas worldwide actually culminates in an eruption. The swelling of the Long Valley Caldera is part of these symptoms, so this basically says that there is no definitive outcome that results from them. Choice (D) is a good analogy for this information and therefore the correct answer.
52. A
2015 is at the far right end of the graph, at which point the line indicating the number of cumulative earthquakes hits above the 1.2 line. However, each number on the right y-axis needs to be multiplied by one hundred thousand (100,000), so the number of cumulative earthquakes is actually greater than 120,000. Therefore, (A) is the correct answer. Choice (B) is incorrect because earthquakes per week are tracked on the right axis, not the left. Choice (C) is incorrect because 1.2 needs to be multiplied by one hundred thousand (100,000), not one million (1,000,000). Choice (D) is incorrect because cumulative earthquakes for 1988 were at less than 0.2 hundred thousand, or 20,000.
1. B
Use POE to compare the vocabulary options. Gawked means “stared in a confused or negative way,” but the passage mentions natural beauty, so a more positive word is needed. Eliminate (A). Marveled means “looked at with wonder,” which is consistent with the subject of the sentence, so keep (B). Pondered means “thought about,” but “pondered at” isn’t a correct phrasing, so eliminate (C) . Stared is not as precise as marveled because stared simply means “looked at for a period of time” and does not express the wonder at the natural beauty that is implied by the sentence. Eliminate (D) . The correct answer is (B).
2. D
Use POE here, since there doesn’t seem to be a common thread being tested on this question. Eliminate (B) and (C) because pulchritudinous and pretty basically mean the same thing, making these choices interchangeable and impossible to choose between. Go back to the passage and notice that it already uses the phrase marveled at the natural beauty, so using another word to describe its beauty again would be redundant. Therefore, eliminate (A). Choice (D) is the most concise response, and therefore the correct answer.
3. A
Notice the question! You’re asked for a choice that will include detail to clarify day-to-day operations. Look at the next sentence, which describes the activities of the park rangers. It states that they are in charge of the park’s upkeep and maintain the balance between the wildlife and plant species and the human visitors. Both of these correspond with the underlined portion of maintenance and tours. Nothing is stated about the length of the tasks, whether or not they are repetitive, or the political aspects of them, so eliminate (B), (C), and (D). Choice (A) provides the detail the question asks for and is the correct answer.
4. C
The idea before the punctuation, These park rangers are responsible for the upkeep of the parks, is a complete idea, as is the clause, their main responsibility is to maintain the balance between the wildlife and plant species and the human visitors that come to the parks every day, that follows it. Therefore, a comma alone cannot separate two complete ideas, so eliminate (A) and (D). Eliminate (B) as well, because punctuation is needed to separate two complete ideas. Choice (C) is the correct answer because a dash (HALF-STOP punctuation) can be used to separate these complete ideas.
5. B
The paragraph describes the park rangers as scientists, educators, and professionals with backgrounds in law enforcement and firefighting. Look for the answer choice that is consistent with this type of diversity. Eliminate (A) because pollution is not talked about in the paragraph, as well as (C) because the paragraph is not interested in the visitors to the park. Ecology is too limited for (D), so eliminate it. You’re left with (B), which is the correct answer.
6. D
Look to the previous sentence, which describes some of the park rangers, and notice the phrase Some are scientists who revel. Since the next sentence is also describing the park rangers, it needs to be consistent and parallel with the previous sentence, so it should be Some are educators who help. Choice (D) is the correct response.
7. B
Notice that the answer choices are pronouns, so look at the current sentence to determine what the pronoun them refers to; this might be unclear because both posts and municipal services are used in the sentence. Eliminate (A) and (C), which are ambiguous, and (D) because it’s singular and ambiguous. Choice (B) is the clearest, most precise choice and is therefore correct.
8. C
Use POE to find the clearest and most concise response. Choice (A) is awkward because visitors are on the rise doesn’t necessarily refer to their numbers, so eliminate it. Choice (B) is incorrect, as poised on the rise is an idiom error and should be poised to rise. Choice (D) is awkward, unclear, and redundant, as poised on the rise seems to be referring to the numbers, which are also described as growing. (Note that like (B), (D) also contains an idiom error.) Choice (C) is the answer.
9. A
Check the underlined portion of this sentence, which states that the visitation numbers peaked in 1987, and compare it with the chart. This information is true, as is the second phrase, the general trend has been on a steady rise, so keep (A). Eliminate (B) because 1987 isn’t really the mid-1980s and visitation has not tapered off. Choice (C) is simply incorrect, and (D) can be eliminated because the growth has been somewhat erratic and not linear. Choice (A) is correct.
10. B
Punctuation in a list of three things is changing in the answer choices. In a list of three or more things, there must be a comma after every item. Eliminate (A), (C), and (D) because they do not have a comma after the word educational. The correct answer is (B).
11. D
The idea before the punctuation, The park-ranger workforce is so diverse, is a complete idea, as is the clause that follows it, there are actually a few common attributes among park rangers. A comma cannot separate two complete ideas, so eliminate (A). Choice (B), Truly, the park-ranger, simply adds emphasis to the sentence. It does nothing to point out the contrast between the beginning and the end of the sentence. Therefore, (B) is incorrect. Look at (C) and (D), since the transition words because and although are exact opposites, and then refer back to the sentence to see if the two ideas are complimentary or contrasting. The words used in the sentence are diverse and a few common, so pick the transition word that indicates a contrast. Choice (D) is the answer.
12. D
Sentence 2 begins with the phrase This part. Because a pronoun is used, go back and find the noun it refers to. Sentence 4 states that Lincoln granted a special provision for that part of Virginia, so the pronoun this refers to the part of Virginia. Therefore, sentence 2 should go after sentence 4, so (D) is the correct answer.
13. C
The answer choices here suggest that this question is testing pronouns. Go back earlier in the sentence to find what the pronoun refers to. It’s the United States, which is a collective noun and therefore singular. Eliminate (A) and (B). Eliminate (D) as well because a contraction is not necessary here. Choice (C), which is a singular possessive pronoun, is the correct answer.
14. D
This question is testing comma usage, so check to see if the comma is separating two complete ideas or if it’s necessary to break up the incomplete ideas. Neither appears to be the case, and this sentence does not need a break. Remember, if you don’t have a good reason to add a comma, don’t use one. Choice (D) is correct.
15. A
Use POE to determine whether the information in the map is consistent with the answer choices. Choice (A) seems like a good choice because Harpers Ferry is directly at the meeting point of the Shenandoah and Potomac Rivers, so keep it. Eliminate (B) because there is not enough information to support the 20-mile northeast approximation from Bolivar to Harpers Ferry. Choice (C) is also unsupported because Harpers Ferry is across the Shenandoah from Virginia, not Maryland, so eliminate (C). Choice (D) is incorrect because the Adirondack Mountains are not even on the map (they are actually in upstate New York). Choice (A) is correct.
16. C
Use POE for this question, as there doesn’t seem to be a specific rule being tested. Eliminate (A) because it is an ambiguous pronoun that could refer to either the armory or the Civil War. Choice (B) is incorrect because war should not be the subject of this phrase as though it saw Harpers Ferry literally change hands. Same goes for (D), as eight should not be the subject of the phrase. Choice (C) makes it clear that it was Harpers Ferry that changed hands, making it the most precise answer choice and the correct answer.
17. B
If you look at the answer choices, you may notice that there isn’t a huge difference between them; watch out for redundancy and try to be concise. The sentence uses the word crucial already, so eliminate (A), (C), and (D), which add words that mean the same thing as crucial. The answer is (B).
18. A
Notice the question! Use POE to find an answer choice that is consistent with the major importance of Brown’s raid. A national discussion started because of the raid, so keep (A). Choice (B) suggests the raid’s importance, but Herman Melville is not mentioned anywhere else in the passage, so eliminate (B). Eliminate (C) and (D) because neither deals with the impact of the raid after the fact. Choice (A) is the answer.
19. D
The correct answer to this question needs to contrast the positive terms of hero and freedom fighter, so eliminate (B), which is also positive. Eliminate (A) because, taken literally, filthy means “unclean” and doesn’t really contrast hero. Choice (C) is slang, and therefore incorrect. Choice (D) works because vile is consistent with terrorist and contrasts the positive tone of hero.
20. B
Use POE to find the clearest and most concise answer choice. Eliminate (A) and (D) because both use the ambiguous pronoun it. Choice (C) is incorrect because it’s unclear how Brown’s rally was named. This would change the overall meaning of the sentence. Choice (B) is the clearest and most concise, and therefore the correct answer.
21. A
The underlined portion uses a period, so check for complete and incomplete ideas. The period here separates two complete ideas, so the period is STOP punctuation that is being used correctly. Eliminate (B) because it uses GO punctuation, and eliminate (C) because it uses no punctuation at all and therefore creates a run-on sentence. Eliminate (D) because the transition and is used after the semicolon, turning the complete idea into an incomplete one. Choice (A) is correct.
22. D
The underlined portion uses HALF-STOP punctuation (a colon) to separate the two ideas, so the first idea must be complete in order for the colon to work. The first idea is incomplete, so eliminate (A). Also eliminate (B) and (C), as STOP punctuation can be used only between two complete ideas. Choice (D) is the answer because it correctly uses GO punctuation between an incomplete idea and a complete idea.
23. D
Use POE to evaluate the use of punctuation. Since 2014 is not in italics, it must not be part of the name of the film. Thus, it needs to be separated from the name of the film, not directly following it. Eliminate (A) and (B) because 2014 appears right next to The Grand Budapest Hotel without a separation. Choice (C) separates 2014 with a comma, but by putting the name of the movie in parentheses, this choice suggests that the name of the movie is unnecessary. Removing the name of the movie makes the sentence say…Anderson’s recent film, 2014, which is not correct. Eliminate (C) . Choice (D) correctly puts the date in parentheses, which separates it from the name of the film. The correct answer is (D).
24. B
In the following sentence, the author wonders about the sudden interest in Zweig’s work after its obscurity, so an acceptable alternative to the underlined word would be something similar to important. Relevant is the best match, so (B) is the correct answer. Choice (A) is an incorrect spelling, so it is incorrect. Choice (C) is the opposite of what’s needed, and (D) is a misspelling of the opposite of the required term.
25. C
Notice the question! The best way to combine these two sentences would be to turn it into one concise sentence. Choice (A) can be eliminated because the only difference is the semicolon, which basically serves the same purpose as a period. Choice (D) is awkward because eliteness is an improper form of the word elite. Comparing (B) and (C), (C) is more concise. Therefore, (C) is the answer because it’s grammatically correct and concise.
26. A
This question is testing the use of apostrophes, and since the phrase city’s cultural elite indicates possession, check to see whether or not the noun is singular or plural. Since city is singular, then the ’s is correct, so (A) is the correct answer.
27. B
The passage states that Zweig published a near infinitude of works and then goes on to list what the works are. Therefore, the examples of those works are necessary to the sentence. Eliminate (C) and (D) . Also get rid of (A) since the examples are not for other types of work Zweig could get. Choice (B) is the correct answer.
28. A
The paragraph opens by describing Zweig’s relationship with Vienna as tenuous and then goes on to describe him as a committed pacifist. The next sentence states that his pacifism was no longer looked on with such understanding, which means that the conjunction must show a contrast. Eliminate (B) and (C) because they do not indicate a contrast. Eliminate (D) because although should be used to start an incomplete thought (a dependent clause). As used here it creates an incomplete sentence. Choice (A) is correct because however shows a clear shift to a new idea.
29. C
The answer to this question needs to address Zweig’s personal stake in the European conflict, so eliminate (A) and (D), as neither choice addresses Zweig himself. Also eliminate (B) because the emphasis is on his ancestral home, not the Americas. Choice (C) is correct because it states Zweig has such pride in his home country of Vienna.
30. D
Based on the answer choices, this question is testing pronoun uses. Since the pronoun in the sentence refers to the privileged man, eliminate (A); which cannot be used to refer to a person. The correct answer will be an object pronoun, so eliminate (B) because it’s a subject pronoun, and (C) because it’s possessive. Choice (D) is the answer.
31. A
Notice that the question asks for the choice that best supports the idea presented at the beginning of the sentence, which emphasizes more “masculine” figures. Competitive sports might be something that is traditionally considered “masculine.” Therefore, the sentence seems to make sense as is, so (A) is the correct answer. The other choices can be eliminated because none of them refer to masculine behavior or activities.
32. D
Based on the answer choices, this question is testing pronouns. Be careful, however, because the underlined portion is not addressing Zweig, but rather many of us. You can eliminate (A) and (C) because those are singular pronouns and therefore inconsistent. The next phrase states our longing, so the use of our in (D) creates consistency.
33. C
Check out the answer choices, which show that verb tense is the concept being tested here. Look at the earlier part of the sentence that states We know that things cannot be and select the choice that is consistent with the verb know. Choice (C) is consistent and therefore the correct response.
34. A
Based on the answer choices, the question is testing comma usage. In a list of three or more items, a comma must be used after each item in the list and before and, so eliminate (D). Also, (B) and (C) use unnecessary commas after bacon and strips, and there is no reason to slow down the flow of ideas in this sentence. Choice (A) is correct.
35. C
Notice the question and use POE. Although the passage is ultimately concerned with chimpanzees seeking fruit, there is no information that suggests the banana was its traditional diet. Eliminate (A). The chimpanzees waking and sleeping habits are never discussed in the passage, so get rid of (B). Choice (C) works because the following paragraph discusses how the nomadic chimpanzees set up their campsites within striking distance of the ripe fruits. Therefore, keep (C) because it’s consistent with this paragraph. Human evolution isn’t discussed anywhere in the passage, so eliminate (D). The correct answer is (C).
36. B
Notice the question! Look for the choice that serves as a transition and introduction. The previous paragraph ends with for a chimpanzee, every day during a fruit-poor season can be like Black Friday where all the “shoppers” want the same hot item. Use POE to find the choice that correlates with this statement. Eliminate (A) because the value of the deals is irrelevant. Eliminate (C) and (D) because Thanksgiving isn’t necessary for the comparison between how chimpanzees get food and Black Friday. Choice (B) is the answer because it connects the reference to Black Friday in the previous paragraph and at the same time introduces the topic of the current paragraph.
37. A
Look out for the pronoun changes in the answer choices, specifically its and their. The subject of the sentence should be chimpanzees, a plural noun, to match the plural noun in the previous sentence. Therefore, you can eliminate (B) and (C), which have singular nouns. Eliminate (D) because it incorrectly joins a plural noun (chimpanzees) with a singular pronoun (its). Choice (A) correctly uses both a plural noun (chimpanzees) and the plural pronoun (their).
38. C
The definition in the sentence is quick to disappear, so use POE to find the word that most directly matches the meaning. Eliminate (B) and (D) because desiccated means to “dry up,” and eternal would be the opposite of quick to disappear. Eliminate (A) because lively means “energetic” or “animated.” Ephemeral means “brief” or “fleeting,” so it’s a good match, making (C) the correct answer.
39. D
The word than, a comparison word, is used several times in the answer choices. Figure out what is being compared and eliminate answer choices that don’t match. The sentence begins with when the fruits were, so the answer is going to have to compare to a time period. Only (D) does this, so it’s the correct answer.
40. B
Use POE to find a word that is consistent with the paragraph, which is a lack of food. Gobbled, chomped, and ate all refer to the consumption of food, but not necessarily a lack of food, so eliminate (A), (C), and (D). Depleted would fit because it means “used up completely.” Choice (B) is correct.
41. C
The answer choices split between the verbs have and has, so find the subject and pick the verb that is consistent. The subject in this case is findings, which is plural, so eliminate (A) and (D), since has is singular. Eliminate (B) because the verb lead is present tense. With the helping verb have, the past participle is necessary. Choice (C) correctly uses the past participle of the verb lead.
42. A
This question is testing diction, so find the word that is consistent with the context of the sentence. Province, (A), means “type of learning,” which would fit well with the previous sentence, so keep it. Providence means “goodwill from a higher power,” so it doesn’t fit; eliminate (B). Choice (C) can be eliminated because provenance means “origin.” Finally, eliminate (D) since providential means “lucky.” Choice (A) is the answer.
43. B
The answer choices don’t seem to indicate that a clear grammatical rule is being tested here, so use POE. Choice (A) seems to change the intended meaning, since the adverb initially comes after what it’s supposed to be modifying instead of before, which it should; eliminate (A). Choice (D) makes the same mistake, so eliminate it as well. Choice (B) is much clearer and more concise, so hold onto it. Choice (C) uses then, which is the wrong word choice (it indicates time) and should therefore be eliminated. Choice (B) is correct.
44. D
Use the Vertical Line Test, drawing lines around the FANBOYS word and. The first part of the sentence, We learn more and more about what we share with other animals, is a complete idea. The second part of the sentence, with each discovery, we learn a new way to relate to the world around us, is also a complete idea. Because both ideas are complete, STOP or HALF-STOP punctuation is needed. Eliminate (A) and (C) because a FANBOYS word with no comma isn’t STOP punctuation. Choice (B) uses a comma but gets rid of the word and. A comma alone is GO punctuation, so eliminate (B). Choice (D) correctly uses HALF-STOP punctuation to link the two complete ideas. The correct answer is (D).
1. C
Translate the question into an equation. Let x equal the number, and then 2x = x − 4. Solving for x, you find that x = −4. The answer is (C).
2. C
Sonal needs s soil samples. If according to the question, he must have more than 6 samples, then s > 6. Also according to the question, he may have no more than 13 samples, so s ≤ 13. Combining these two expressions, you find that 6 < s ≤ 13. The answer is (C).
3. D
The graph of f(x) has a y-intercept at y = 3. Because of this, you know that when y = 3, x = 0. f(x) must then satisfy the condition that f(0) = 3. This is true only for (A) and (B). Alternatively, by recognizing that each equation is in the slope-intercept form: f(x) = y = mx + b, where b is the y-intercept, you can reach the same conclusion. Next, notice that the slope of the line is positive. That is, as the value of x increases, so too does y. Returning to the slope-intercept form, m gives the slope of the line. Only (D) has a positive coefficient (m). Choice (D), then, is the correct function.
4. A
If x + y = 0, then x = −y. Using this relationship and substituting into the expression x − y, you find that x − y = −y − y = −2y. This is (A).
5. A
This question requires factoring the expression 2x2 − 6x − 8. Begin by factoring 2 from the expression: 2(x2 − 3x − 4). This expression is further factorable, giving 2(x − 4)(x + 1), which is (A).
6. D
The question describes a ramp that forms a triangle, the length of which is the hypotenuse of the triangle. The height of the ramp (3 feet) is the length of the side of the triangle opposite the 35° angle. In general, for some angle θ, 
. In the question, this corresponds to 
. This is (D).
7. D
This question requires evaluating both equations to determine the values of a and b. You can begin by solving either of the two equations for a or b, and then substituting the solution into the other equation. But note that the question asks for the value of a + b, so check to see if there’s a faster way. Can you stack and add (or subtract) the equations? If you stack and add the equations, you get 7a + 7b = 77. Now divide both sides of the equation by 7, resulting in a + b = 11. This is (D).
8. D
When a function f(x) is transformed into a function of the form f(ax), where a is a constant, if a > 0, the function will be compressed horizontally by a factor of a. Here, y = x2 + 4 can be represented as the parent function, and y = 3x2 + 4 as the transformed function compressed horizontally versus the parent function, and thus narrower, by a factor of 3. This is (D). If you’re not sure, try plugging values into each equation to construct a rough graph of each equation and compare them.
9. C
Rearranging and factoring the expression provided in the question, you have t2 − 4t − 90 = 6 ⇒ t2 − 4t − 96 = 0 ⇒ (t − 12)(t + 8) = 0. Therefore, t − 12 = 0 and t + 8 = 0. t must then equal 12 or −8. If t represents the number of tickets Steven buys, then only t = 12 is consistent with the context of the question. If each ticket costs $80, Steven must have spent $80 × 12 = $960. This is (C).
10. C
Find values of c and d by solving the system of equations in order to determine the value of 4c − 4d. There are several ways to go about this. One way is to multiply the terms of the equation 2c + 3d = 17 by −3 to get −6c − 9d = −51. If you stack and add this equation with the second equation, the result is −4d = −12, which solves to d = 3. Plug this value for d into the equation 6c + 5d = 39 to get 6c + 15 = 39, so 6c = 24 and c = 4. Therefore, 4c − 4d = 4(4) − 4(3) = 16 − 12 = 4. This is (C).
11. A
Factoring the left side of the equation x2 + 2xy + y2 = 64 gives (x + y)2 = 64. Taking the square root of both sides of the equation, you find that x + y = 8 or −8. The other equation provides that y − x = 12, so y = x + 12. Substitute this value of y into the first equation: either x + (x + 12) = 8, so 2x + 12 = 8, 2x = −4, and x = −2, or else or x + (x + 12) = −8, so 2x + 12 = −8, so 2x = −20, and x = −10. Therefore, x could be either −2 or −10, and only −10 is an option in the answers, so (A) is correct.
12. D
Translate from English to math using Bite-Sized Pieces. Make the price of a hot yoga lesson h and the price of a zero gravity yoga session z. If she offers 2 hot yoga and 3 zero gravity yoga sessions for $400, then 2h + 3z = 400. Similarly, if 4 hot yoga and 2 zero gravity yoga sessions are $440, then 4h + 2z = 440. Now, be sure to read the final question. You want to know whether Samantha can create a package that’s greater than $800 but has fewer than 13 sessions. If you stack the two equations and then add them together, you get 6h + 5z = 880. In other words, she can offer 6 hot yoga and 5 zero gravity yoga sessions (11 total sessions) for $880. This satisfies her requirements, so you know the answer is “Yes”; eliminate (A) and (B). For (C), because you don’t know the price of each lesson individually, you don’t know yet whether 5 hot yoga and 5 zero gravity yoga sessions will be over $800; leave (C) for now. For (D), if 6 hot yoga and 5 zero gravity yoga sessions were over $800, then adding a zero gravity yoga session will still be over $800. Given what you already know, (D) must be true; choose (D).
13. B
Begin by simplifying the given equation: (3p2 + 14p + 24) − 2(p2 + 7p + 20) = 3p2 + 14p + 24 − 2p2 − 14p − 40 = p2 − 16 = 0. Factoring the left side of the simplified equation, you find that (p − 4)(p + 4) = 16. Solving for p, you find that p = ±4. The value of 3p + 6 must then be either 3(−4) + 6 = −6 or 3(4) + 6 = 18. The latter value is (B).
14. A
Taking note that i = 
, the expression (2 + 8i)(1 − 4i) − (3 − 2i)(6 + 4i) becomes (2 + 8)(1 − 4) − (3 − 2)(6 + 4). Expanding, this becomes 2 − 8 + 8 − 32)2 − (18 + 12 − 12 − 8()2) = 2 − 32()2 − 18 + 8()2 = 8()2 − 32()2 − 16. This further simplifies to −8 + 32 − 16 = 8. This is (A).
15. C
Plug in the answers! The answer choices aren’t in any particular order, and some numbers appear more than once, so you don’t need to start in the middle. Instead, start with 9 because it is in three of the four choices. If x = 9, then 2
= 9 − 3. Since = 3, the left side of the equation is 2 × 3 = 6, and the right side of the equation is 9 − 3 = 6. This works, so 9 is part of the solution set; eliminate (B) because it doesn’t include 9. Next, try x = 1: 2 = − 3, which solves to 2 = −2. This isn’t true, so 1 is not part of the solution set; eliminate (D). Lastly, try x = −1: = −1 −3. You cannot take the square root of a negative number, so this doesn’t work. Eliminate (A) and choose (C).
16. 28
Let s equal the number of staples required by the students and let p be the number of popsicle sticks required. If the number of staples the students will need is three times the number of popsicle sticks they will need, then s = 3p. If the students need 84 staples for this project, then s = 84. Substitute 84 for s to get 84 = 3p. Divide both sides by 3 to get 28 = p. The students will need 28 popsicle sticks.
17. 0
If a parabola intersects the x-axis at the points (5, 0) and (−5, 0), it must be symmetric about the x-axis and centered at x = 0. The x-coordinate of its vertical axis of symmetry must then be 0.
18. 94
The question describes a 100-meter ramp that forms a triangle. The length of this ramp corresponds to the hypotenuse of a triangle. The height of the ramp is the length of the side of the triangle opposite the 20° angle; the horizontal distance from the start of the ramp immediately below the entrance of the mall is the side of the triangle adjacent to the 20° angle. The function that relates adjacent and hypotenuse is cosine: 
. In this problem, cos 20° = 
, where x is the horizontal distance. Solve by multiplying both sides by 100: cos 20° = x. Next, replace cos 20° with 0.939, the value given in the problem: 100(0.939) = x. Multiply 100 by 0.939 to get x = 93.9, which rounds to 94.
19. 7
Let x equal the number. Then, 2x = x − 5 ⇒ x = −5. Three times that number plus seventeen minus that number is 3(−5) + 17 − (−5) = 7.
3x2 + 2x − 8 = (x + 2)(3x − 4) = 0. Solving x + 2 = 0 and 3x − 4 = 0 for x, you find that the two solutions for x are −2 and 
. The question asks you to subtract the value of the smaller solution from the larger solution. This difference is 
.
1. D
The question asks for a graph that represents a specific situation. Translate the question using Bite-Sized Pieces and eliminate after each piece. One piece of information says that the machine is slowly filling a bin with pencils. The graph will show an increase for the first 5 minutes or so. Eliminate (C), as it shows a decrease during this time. Another piece of information says that a jam occurs, preventing pencils from falling into the bin. The graph will show a line with a slope of zero starting at 5 minutes. Eliminate (B), as it shows a vertical line here, which would indicate a number of pencils being dumped into the bin at that instant. Compare the remaining answer choices. The difference between (A) and (D) is whether the number of pencils in the bins decreases to 0 or continues increasing. Since the technician clears the jam and then increases the rate of operation, the number of pencils in the bin will only increase. Eliminate (A). The correct answer is (D).
2. A
The question asks for an equation that models the submarine’s depth below the surface. Translate the information using Bite-Sized Pieces and eliminate after each piece. One piece of information says that the submarine starts at a depth of 100 feet. This has nothing to do with m, the number of minutes after the dive begins, so 100 should not be multiplied by m. Eliminate (D). The depth of the submarine is increased after the dive begins, so something should be added to 100. Eliminate (B) and (C), which subtract from 100, meaning that the submarine is at a smaller depth and closer to the surface and not at increased depths. The correct answer is (A).
3. D
The question asks for a graph that represents a specific situation. Translate the question using Bite-Sized Pieces and eliminate after each piece. One piece of information says that the store charges $1.00 for a single bead. The cost per bead, y, is shown on the vertical axis in cents, so the graph will start at 100 cents. All four graphs in the answer choices do that. From there, the question says that the price per bead goes down. Eliminate (A), as it shows an initial increase, and (C), which shows a flat line initially. Another piece of information says that there is a lowest possible price of 75 cents per bead starting at 5 beads purchased. The graph will show a line with a slope of zero starting at 5 beads on the horizontal axis. Eliminate (B), as it does not level off at some set price but shows a continued price decrease until the price goes down to 0. The correct answer is (D).
4. A
The question asks for the value of g(−4). In function notation, the number inside the parentheses is the x-value that goes into the function, and the value that comes out of the function is the y-value. Plug x = −4 into the function to get 
. The correct answer is (A).
5. A
The question asks for the value of 5d. Use the given equation to solve for d. Subtract 18 from both sides of the equation to get d = −6. Multiply both sides of this equation by 5 to get 5d = −30. The correct answer is (A).
6. C
The question asks for an appropriate sampling method to estimate information about a population. Read each answer carefully and use Process of Elimination. For a study to be reliable, it needs a large sample size that is representative of the population being studied. The question asks for an estimate for the average number of hours of homework assigned to students by the math teachers, so the survey should include a wide variety of participants across different math classes. Choice (A) refers to one math teacher, so it will not provide information about the students who have other math teachers. Eliminate (A). Choice (B) refers to an online poll on the school’s social media, but no information is given about how many math students might see and answer that poll. Keep (B) for now, but check whether there is a better choice. Choice (C) refers to 5 students from each math class, so it will provide a good amount of information about the math classes across the school. This is a better method than an online poll, so keep (C) and eliminate (B). Choice (D) refers to the student with the highest grade in each math class, which may or may not be a representative sample from the entire school. Perhaps those students have higher grades because they spend many more hours studying than their peers. Eliminate (D). The correct answer is (C).
7. B
The question asks for a comparison of Bill and Jeff’s monthly weight loss based on a graph. Number of months is listed along the horizontal axis, and Weight is listed on the vertical axis. For Bill, represented by the solid line, he started at 280 pounds and went down to 140 pounds for a loss of 280 − 140 = 140 pounds. The question asks about pounds…per month, so divide 140 pounds by 7 months to get 20 pounds per month. For Jeff, represented by the dashed line, he started at 230 pounds and went down to 160 pounds for a loss of 230 − 160 = 70 pounds. This was over the same 7 months, so Jeff’s weight loss per month is 10 pounds. The difference is 20 − 10 = 10 pounds. The correct answer is (B).
8. B
The question asks for an equivalent form of an expression. There are variables in the answer choices, so one option is to plug in. Make y = 2. The expression becomes 9(24) + 6(23) + 3 = 9(16) + 6(8) + 3 = 144 + 48 + 3 = 195. This is the target value; circle it. Now plug y = 2 into the answer choices to see which one matches the target value. Choice (A) becomes 3(22)[3(2)2 + 6(2) + 3] = 3(4) [3(4) + 12 + 3] = (12)(12 + 15) = (12)(27) = 324. This does not match the target, so eliminate (A). Choice (B) becomes 3(22)[3(2)2 + 2(2)] + 3 = 3(4)[3(4) + 4] + 3 = (12)(12 + 4) + 3 = (12)(16) + 3 = 192 + 3 = 195. Keep (B), but check the remaining choices just in case. Choice (C) becomes 3(22)[6(2)2 + 3(2) + 1] = 3(4) [6(4) + 6 + 1] = (12)(24 + 7) = (12)(31) = 372. Eliminate (C). Choice (D) becomes 15(27) + 3 = 15(128) + 3 = 1,920 + 3 = 1,923. Eliminate (D). Another option is to use Bite-Sized Pieces and Process of Elimination to tackle this question. The first term in the given expression is 9y4. Choice (D) does not have any term with y4, so eliminate (D). For each remaining answer, multiply the number outside the parentheses by the first term inside the parentheses to see if it results in 9y4. For (A) and (B), this becomes 3y2(3y2) = 9y4. For (C), this becomes 3y2(6y2) = 18y4. Eliminate (C). The next term in the given expression is 6y3, so determine the second term when distributing in (A) and (B). For (A), this becomes 3y2(6y) = 18y3, so eliminate (A). Either way, the correct answer is (B).
9. A
The question asks for an appropriate conclusion regarding the results of a study that was conducted. Read each answer carefully and use Process of Elimination. A margin of error expresses the amount of random sampling error in a survey’s results. The survey provides an estimate of the percentage of birds’ nests that experienced full or partial nest predation. The margin of error is 3%, meaning that results within a range of 3% above and below the estimation are reasonable. The study found that 46% of nests experienced predation, so the reasonable results for this study are between 43% and 49%. Choice (A) says that percentage of North American birds whose nests get raided by predators is likely somewhere between 43% and 49%. This does match the range of reasonable results, so keep (A), but check the remaining answers just in case. Choice (B) says that there is a 3% chance that the study’s finding about nest predation…is incorrect. This is a misunderstanding of margin of error, which is not how likely the study is to be correct but is how far off the results may be. Eliminate (B). Choice (C) refers to the percentage of birds’ nests that will get raided this coming year. This answer may be tempting, but it refers to all birds, not just the North American birds from the study. A correct prediction about all birds cannot be made, so eliminate (C). Choice (D) has the same issue with making a prediction about all birds based on a study of one type of bird, so eliminate (D). The correct answer is (A).
10. B
The question asks for the value of 
. In function notation, the number inside the parentheses is the x-value that goes into the function, and the value that comes out of the function is the y-value. Plug 
into the function to get 
. With a fractional exponent, the numerator is the power and the denominator is the root, so this can be rewritten as 
. Now plug 
into the function to get 
. Finally, add the results to get 4 + 2 = 6. The correct answer is (B).
11. B
The question asks for the price of the clock before tax. Since the question asks for a specific value and the answers contain numbers in increasing order, plug in the answers. Begin by labeling the answers as “clock price” and start with (B), $25.00. The tax is 10% of this price, and ten percent can be written as 
. To take a percent of a number, multiply the percent by the number, so the tax is 
. Add this to the price of the clock to get a total cost of $25.00 + $2.50 = $27.50. This matches the value given in the question, so stop here. The correct answer is (B).
12. C
The question asks for a true statement about two lists of numbers. The answers refer to mean, median, and standard deviation. Of these, the median is the easiest to calculate, so start there. The median of a list of numbers is the middle number when all values are arranged in order. In lists with an even number of items, the median is the average of the middle two numbers. For List X, the middle two numbers are both 13, so there is no need to average to find the median—it is 13. For List Y, the two middle numbers are 11 and 15, so the median is 
. Use this to eliminate answers before calculating anything else. Choices (A) and (D) can be eliminated, as those both say that the medians are different. Compare the remaining choices—both indicate that the standard deviations are the same, so focus on the means of the two lists. For means (averages), use the formula T = AN, in which T is the total, A is the average, and N is the number of things. For List X, the Total is 5 + 8 + 13 + 13 + 15 + 18 = 72. The Number of things is 6, so the formula becomes 72 = (AX)(6). Divide both sides by 6 to get 12 = ΑX. Follow the same steps to calculate the mean of List Y. The Total is 9 + 10 + 11 + 15 + 19 + 20 = 84, the Number of things is 6, and the formula is 84 = (AY)(6). Divide both sides by 6 to get 14 = ΑY. The averages are not the same, so eliminate (B). The correct answer is (C).
13. C
The question asks for the length of one side of the base of a pyramid. Use the geometry basic approach. Start by drawing a figure and labeling it with the given information. The pyramid has a height of 12 and a square base. Label each side of the base as s.
The formula for the volume of a pyramid 
, which becomes 
for a pyramid with a square base. Plug in the given information to get 
, which simplifies to 324 = 4s2. Divide both sides of the equation by 4 to get 81 = s2, then take the square root of both sides to get 9 = s. The correct answer is (C).
14. A
The question asks for which data sets display an increasing trend in test performance on a graph. Check the items in the Roman numerals one at a time and look for a study strategy that shows this trend throughout the experiment. Eliminate after each one. All three Roman numerals appear in at least two answer choices, so start with (I). This is Tutoring, which is represented by the light gray bars. The Weeks are listed along the horizontal axis, and the Test average is listed on the vertical axis. As the weeks increase, the test average for students in the tutoring group increases throughout the entire period. The tutoring group matches the trend, so eliminate (B), as it does not include (I). As the weeks increase, the test average for students in the traditional homework group, represented by the dark gray bars, increases then decreases. The traditional homework group does NOT match the trend, so eliminate (D), as it includes (II). As the weeks increase, the test average for the no homework group, represented by the black bars, increases then decreases. This does NOT match the trend, so eliminate (C), as it includes (III). The correct answer is (A).
15. D
The question asks for the ratio of one group’s test average improvement to that of another group over the same period of time. Read the graph carefully to find the correct numbers to make the ratio. The Traditional Homework group is represented by the dark gray bars. The start of the study is week 0, and this group showed a test average of 70 that week. In week 4, the same group had a test average of 80. The improvement for the group with traditional homework was 80 − 70 = 10 points over this time frame. Repeat the steps for the Tutoring group, represented by the light gray bars. In week 0, the test average was about 73 and in week 4, the test average was 95. This is an improvement of 95 − 73 = 22 points. The ratio of the test average improvement for the traditional homework group to the tutoring group is 10 to 22 or approximately 1 to 2. The correct answer is (D).
16. A
The question asks for the side length of the square base of a pyramid in terms of the pyramid’s volume and height. Although there are variables in the answer choices, plugging in on this question may not be the fastest approach, given that the equation is easy to manipulate. Instead, solve for s. To begin to isolate s, multiply both sides of the equation by 3 to get 3V = hs2. Divide both sides by h to get 
. Take the square root of both sides to get 
. The correct answer is (A).
17. A
The question asks for a probability, which is defined as 
. Read the table carefully to find the numbers to make the probability. The question asks for a student that drinks coffee, of which 26.9% do, so that is the # of outcomes that fit requirements. It doesn’t matter that this is a percent not a number, as all the categories on the chart are percents of the same whole. The chosen coffee drinker is selected from among those who do not drink a cold drink at breakfast. This means that the total # of outcomes is all those who drank hot drinks, or 5.3% + 26.9% = 32.2%. Therefore, the probability is 
. The correct answer is (A).
18. A
The question asks for how much wheat was produced in 2015 based on a percent decrease in wheat production and a percent increase in corn production. Percent change is calculated using the equation 
. Start by plugging the information provided about corn into the percent change equation to calculate the production of corn in 2005, in millions of bushels, which can be called c. The equation for corn becomes 
. Multiply both sides of the equation by c to get 15c = (161 − c) × 100, then distribute on the right side to get 15c = 16,100 − 100c. Add 100c to both sides to get 115c = 16,100, then divide both sides by 115 to get c = 140 million bushels. The question says that the state produced identical amounts of each crop in 2005, so the production of wheat in 2005 was also 140 million bushels. This production decreased by 40% from 2005 to 2015, so the 2015 production of wheat must be less than 140. Eliminate (C) and (D), as these show an increase in production over this time. Since the question asks for a specific value and the answers contain numbers, plug in the remaining answers. Label the answers as “wheat 2015.” Start with (A), 84, since it does not have a decimal. Plug this value into the percent change equation to see if it makes the equation true. The equation for wheat becomes 
. Simplify the numerator on the right to get 
. Multiply both sides by 140 and simplify on the right side to get 5,600 = 5,600. This is true, so stop here. The correct answer is (A).
19. D
The question asks for the amount of a solution to mix with another solution in order to create a certain concentration. Since the question asks for a specific value and the answers contain numbers, plug in the answers. Test each value in the equation from the question and look for a value that makes the equation true. The question states that the trainer will use 10 quarts of the 15% solution, and the a on the right side of the equation is multiplied by 0.15, so a = 10. Begin by labeling the answers as b and start with (B), 90. The equation becomes 0.27(10 + 90) = 0.15(10) + 0.35(90), or 0.27(100) = 1.5 + 31.5. This simplifies to 27 = 33, which is not true, so eliminate (B). A smaller quantity of the higher percent solution is needed to make the equation true, so eliminate (A) and try (C) next. If b = 30, the equation becomes 0.27(10 + 30) = 0.15(10) + 0.35(30), or 0.27(40) = 1.5 + 10.5. This simplifies to 10.8 = 12, which is much closer but is still not true. Eliminate (C). The correct answer is (D).
20. C
The question asks for a true statement about a parabola given the function f(x) = (x − b)2 − 4 with a vertex of (b, 4). There are variables in the answer choices, so one way to approach this would be to plug in for b. Make b = 2, so the function becomes f(x) = (x − 2)2 − 4. Calculator use is allowed, so graph this on a calculator. It will look like this:
The answer choices refer to the y-intercept, which is where the graph crosses the y-axis. At this point, x = 0, so (A) and (D) can be eliminated. Now plug b = 2 into the points in the remaining answer choices to see which matches (0, 0). The point in (B) becomes (0, −2), so eliminate (B). The point in (C) becomes (0, 22 − 4) or (0, 4 − 4), which is (0, 0). Another option is to plug x = 0 into the function. Because all the answer choices refer to the y-intercept, plugging in this value for x will give the y-coordinate of the y-intercept. The function becomes f(0) = (0 − b)2 − 4 = (−b)2 − 4 = b2 − 4. Either way, the correct answer is (C).
21. D
The question asks for the statistical measure that would increase when changes are made to a set of numbers. Only 2 numbers are given in the original set, so plug in a few more to see what would happen. Make the original set {19, 30, 86, and 90}. Once the teacher corrects the mistakes, the set will be {30, 68, 90, and 91}. To compare the lists, start with range, which is easy to calculate. The range of a list of values is the greatest value minus the least value. For the original set, the range is 90 − 19 = 71, and for the new set, it is 91 − 30 = 61. The range did not increase, so eliminate (A). Another easy calculation is the median. The median of a list of numbers is the middle number when all values are arranged in order. In lists with an even number of items, the median is the average of the middle two numbers. For the original set, the median is 
, and for the new set, it is 
. The median did increase, so keep (C) for now. For means (averages), use the formula T = AN, in which T is the total, A is the average, and N is the number of things. For the original set, the Total is 225 and the Number of things is 4, so 225 = A(4). Divide both side by 4 to get 56.25 = A. For the new set, Total is 279, so 279 = A(4) and A = 69.75. The average also increased, so keep (D). Choice (B) refers to the standard deviation of the sets. Standard deviation is a measure of the amount of variation or dispersion of a set of values. There is no way to tell that based on only 2 values from the set, so this cannot be the answer. Eliminate (B). The remaining choices are median and mean. Because the median is the middle number in the list, it may increase or decrease depending on where 19 and 86 appear in the original list. Not enough information is given to determine this. However, there will always be the same number of items in the original list and the new list, so changes in Total will affect the average. When the 19 becomes a 91, the Total increases by 72. When the 86 becomes a 68, the Total decreases by 18. These two changes together cause a new increase in the Total of 72 − 18 = 54, meaning the average must increase. The correct answer is (D).
22. D
The question asks for an equation of the line of best fit on a graph. To find the best equation, compare features of the graph to the answer choices. The graph for this question has a negative slope. The answer choices are in y = mx + b form, in which m is the slope and b is the y-intercept. Eliminate answer choices that do not have a negative value for m. Eliminate (B) and (C), then compare the remaining choices. The difference between (A) and (D) is the slope, so calculate slope using the formula 
. The graph goes through the points (2, 90) and (12, 40), so 
. Eliminate (B). The correct answer is (D).
23. B
The question asks for the best description of the function g. Compare the answer choices. Two choices describe a linear increase or decrease, which is an increase or decrease by the same amount each unit of time, and two choices describe an exponential increase or decrease, which is an increase or decrease by the same percent or fraction each unit of time. Each hour, one half of the remaining players are eliminated, so the number of players is decreasing, not increasing. Eliminate (A) and (C). After one hour, there will be 
players remaining. After another hour, half the remaining players will be eliminated, so there will be 
players remining. The first decrease was 32,500 players, and the second was 16,250 players, so the decrease is not linear. Eliminate (D). The correct answer is (B).
24. C
The question asks for the equation that represents the relationship between two variables. When given a table of values and asked for the correct equation, plug values from the table into the answer choices to see which one works. It won’t matter that the points also have a variable in them, but it will be easiest to use the point with only one variable. According to the table, x = 0 when y = 3b. Plug x = 0 and y = 3b into the answer choice equations to see which is true. Choice (A) becomes 5(0) + 3b = 2b, which simplifies to 0 + 3b = 2b. This is not true, so eliminate (A). Choice (B) becomes 0 − 5(3b) = −3b, which simplifies to 0 − 15b = −3b. Eliminate (B). Choice (C) becomes 5(0) + 3b = 3b, which simplifies to 0 + 3b = 3b. This is true, so keep (C), but check (D) just in case. Choice (D) becomes 0 − 5(3b) = −7b, which simplifies to 0 − 15b = −7b. Eliminate (D). The correct answer is (C).
25. C
The question asks for the value of an expression based on an equation. Although the answers contain numbers, the question asks for the value of an expression instead of a specific value, so plugging in the answers may be tricky. Another way to approach this is by solving the equation for the value of a. To solve for a, distribute on the right side of the equation to get 8a + 20 = 7 + 6a + 15. Simplify the right side to get 8a + 20 = 6a + 22. Subtract 6a from both sides to get 2a + 20 = 22, then subtract 20 from both sides to get 2a = 2. The question asks for the value of 2a + 5, so add 5 to the value of 2a to get 2 + 5 = 7. The correct answer is (C).
26. C
The question asks for the value of the y-coordinate of the solution to a system of equations. The best way to solve the system of y is to find a way to make the x-coordinates disappear when stacking and adding the equations. The larger x coefficient, 6.5, is 5 times the smaller one, 1.3. Multiply the entire the first equation by −5 to get the same coefficient with opposite signs on the x terms. The first equation becomes −5(1.3x − 0.6y) = −5(−0.7) and then −6.5x + 3y = 3.5. Now stack and added the two equations.
Divide both sides of the resulting equation by 1.5 to get y = 2. The correct answer is (C).
27. B
The question asks for the function that represents a specific situation. The number of goosefoot seeds deposited decreased by a certain percent over time, so this question is about exponential decay. Knowing the parts of the growth and decay formula can help with this question. That formula is final amount = (original amount)(1 ± rate)number of changes. In this case, S(c) is the final amount, and the question states that the original amount was 500. All four choices have 500 as the original amount, but (C) and (D) have 500 raised to an exponent instead of a (1 ± rate) in parentheses raised to an exponent. This is not the proper form, so eliminate (C) and (D). The original amount must be multiplied by (1 − rate), because the numbers are decreasing, and the rate here is 7%. This can be expressed as 0.07, so the value in parentheses should be (1 − 0.07) or (0.93). Eliminate (A) because it does not have this rate. The only remaining answer is (B), and it matches the decay formula. Without this formula, it is still possible to answer this question. Plug in a value of c to see how the number of seeds deposited decreased over time. After 1 century, the number of seeds deposited would have decreased by 7% of the initial 500. The number of seeds would then be 500 − (0.07) (500) = 500 − 35 = 465. Plug c = 1 into the answer choices to see which gives a value of 465 for S(c). Only (B) will work. Either way, the correct answer is (B).
28. A
The question asks for the meaning of a number in the context of a model for production cost per item. Start by reading the final question, which asks for the meaning of the number 5.22. Then label the parts of the equation with the information given. The question states that C is the production cost per item and P is the number of products made. The number 5.22 is added to the term with P, so it must be a cost that is unrelated to the number of items produced. Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Choice (A) refers to the initial production cost, which is consistent with the labels. At the start of production, P = 0, and plugging this into the equation results in C = 0.0045(0) + 5.22 = 0 + 5.22. Therefore, when 0 products are made, the cost is still 5.22, so keep (A). Choice (B) refers to the cost increase, in dollars per item, but this is inconsistent with the labels, as 5.22 is not related to P. Eliminate (B). Choices (C) and (D) also refer to cost in dollars per item, so eliminate (C) and (D). The correct answer is (A).
29. C
The question asks for the measurement of an angle on the figure. Use the geometry basic approach. Start by ballparking—the angle is larger than 90°, so eliminate (A). Label the figure with the given information that FG = JK and GH = HJ. If 
, then angle F is also a right angle. Label this as well. No measurements are given, but the relationship between FK and HJ is given. When there is a relationship between numbers, plug in. Make HJ = 2, so GH = 2 and 
. Label these on the figure as well, which should look like this:
Now the figure is starting to look like a rectangle and a triangle. Draw line GJ to better see this. Because FG and JK are parallel and congruent, FGJK is a rectangle. This means that angle GJK is a right angle, and GJ is 
because it is opposite FK. Now focus on finding angle GJH, which is part of the triangle. When there is a 
in a triangle question, the triangle is likely a 45°-45°-90° triangle. In those triangles, the legs are x and the hypotenuse is 
. Triangle GHJ has this relationship of the sides, so angle GJH is a 45° angle. Therefore, angle J is angle GJK + angle GJH or J = 90 + 45 = 135°. The correct answer is (C).
30. A
The question asks for the graph of the given parabola. One option would be to plug in a value for a and graph the parabola on a graphing calculator. If a = −1, the function becomes h(x) = −(x − 2)(x + 4). In function notation, f(x) or h(x) = y, and the graph of y = −(x − 2)(x + 5) will look like this:
None of the graphs match this exactly, but the graphs in (B) and (D) open up and this one opens down. If the value of a is negative, the parabola will open down. Eliminate (B) and (D). The intercepts on this graph are at x = −5 and x = 2. These will be the intercepts no matter what the value of a is, because a determines the direction of the parabola and how narrow or wide it is. The correct answer graph must also have these intercepts, so eliminate (C), which has the wrong signs on the intercepts. Without a graphing calculator, it is still possible to answer this question. The function is given in factored form. If (x − a) is a factor of a polynomial, then a is a solution, and the graph will cross the x-axis at a. The equation has factors of (x − 2) and (x + 5), so the roots must be at 2 and −5. This eliminates (C) and (D), which do not have these roots. To determine if it is (A) or (B), it is necessary to know how the sign of a affects the shape of the parabola. Either way, the correct answer is (A).
31. 1000
The question asks about the value of a in a set of numbers with a mean of 1,650. For means (averages), use the formula T = AN, in which T is the total, A is the average, and N is the number of things. The Total is 650 + a + 1,550 + 1,750 + 2,300 + 2,650 = 8,900 + a, and the Number of things is 6. The formula becomes 8,900 + a = (1,650)(6), which simplifies to 8,900 + a = 9,900. Subtract 8,900 from both sides of the equation to get a = 1,000. The correct answer is 1000.
32. 7
The question asks for the maximum number of burgers John can buy in a specific situation. Translate the English to math using Bite-Sized Pieces to solve. The question states that John buys 6 orders of fries, which cost $3.10 per order. “Per” means to multiply, so the fries cost John 6($3.10) = $18.60. John has $50, so his remaining money is $50 − $18.60 = $31.40. The question states the burgers cost $4.30 each, so divide $31.40 by $4.30 to find that John can buy about 7.3 burgers. The number of burgers must be an integer, so round this down to 7 burgers. The correct answer is 7.
33. 175
The question asks for the value of c + d, which represent two angles on a figure. Use the geometry basic approach. Start by labeling the figure with the given information. Mark a = 118 and b = 67. There are 360° in a quadrilateral, so a + b + c + d = 360. Plug in the values of a and b to get 118 + 67 + c + d = 360, then simplify to get 185 + c + d = 360. Subtract 185 from both sides of the equation to get c + d = 175. The correct answer is 175.
34. 
, 0.66, or 0.67
The question asks for the value of a variable in an equation with infinitely many solutions. When an equation has infinitely many solutions, the two sides of the equation must represent the same expression. Distribute p on the right side of the equation to get −3x + 2 = px − pq. If the two sides are the same expression, then −3x = px. Divide both sides by x to get −3 = p. The equation then becomes −3x + 2 = −3x − (−3)q. Subtract −3x from both sides to get 2 = 3q, then divide both sides by 3 to get 
. The correct answer can be entered as 
, 0.66, or 0.67.
35. 8
The question asks for the value of a constant in the equation of a parabola that intersects the line y = −1 at exactly one point. To intersect at only one point, the line must intersect only the vertex of the parabola. One way to determine the equation of such a parabola is to graph the line y = −1 and the parabola y = x2 − 6x on a graphing calculator. It will look like this:
The vertex of the parabola with no value for c is at (3, −9), so the vertex must move up 8 units to be at (3, −1). To move a function up 8 units, add an 8 to the function, which becomes y = x2 − 6x + 8 in this case. This means that c = 8. Another approach is to solve the equation algebraically. For the parabola to intersect the line exactly once, there must be only one solution to this equation. The factored form must look like (x − a)2. The coefficient on the x term is −6, so the parabola must be (x − 3)2. Using FOIL, multiply this out to get x2 − 3x − 3x + 9, which simplifies to x2 − 6x + 9. To compare this to the original equation, plug in −1 for y to get −1 = x2 − 6x + c. Add 1 to both sides to get 0 = x2 − 6x + c − 1. The x2 and x terms match in both equations, so the remaining constants must also match. Therefore, 9 = c + 1, and c = 8. Either way, the correct answer is 8.
36. 45
The question asks for the value of a function. In function notation, the number inside the parentheses is the x-value that goes into the function, and the value that comes out of the function is the y-value. The question says that the value of the function is 5 when x = b, so f(b) = 5 and f(b) = ab2. This can be written as 5 = ab2. To make this easier to solve, plug in for either of these variables and then solve for the other. To plug in for b, use a value such as 5 to make the math easier. The equation becomes 5 = a(52), which simplifies to 5 = 25a. Divide both sides by 25 to get 
= a. The function can now be defined as 
. The question asks for the value of 3b, which is 3(5) = 15 when b = 5. Plug x = 15 into the f function to get 
, which simplifies to 
. This becomes f(15) = 45. The correct answer is 45.
37. 63
The question asks for the time it will take in seconds for the shuttle to travel 150 kilometers. Begin by reading the question to find information on the shuttle’s speed. The question states that the speed is 8,568 kilometers per hour. To determine the speed in seconds, divide this by the number of seconds in one hour. There are 60 minutes in an hour and 60 seconds in a minute, so there are (60)(60) = 3,600 seconds in an hour. The speed is 
= 2.38 km/s. To find the time it takes to travel 150 kilometers at this speed, use the formula D = RT, in which D is distance, R is rate, and T is time. The formula becomes 150 = 2.387T. Divide both sides by 2.38 to get 63.025 = T. Round this to the nearest second, as indicated by the question, which is 63. The correct answer is 63.
38. 2400
The question asks for a space shuttle’s escape velocity in meters per second based on the escape velocity in kilometers per hour. When dealing with conflicting units, make a proportion, being sure to match up units. To convert hours to seconds, determine the number of seconds in an hour. There are 60 minutes in an hour and 60 seconds in a minute, so there are (60)(60) = 3,600 seconds in an hour. Now convert kilometers to meters using the information in the note. The proportion is 
. Cross-multiply to get x = 8,568,000 meters. The speed in meters per second becomes 
= 2,380 m/s. Round this to the nearest hundred, as indicated by the question, which is 2,400. The correct answer is 2400.
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.
