PSAT/NMSQT Prep with Practice Tests - Princeton Review 2021
Practice Test 1: Answers and explanations
Practice Test 1
PRACTICE TEST 1 ANSWER KEY
PRACTICE TEST 1 EXPLANATIONS
Section 1—Reading
1.A
The question asks about the main purpose of the passage. Because this is a general question, it should be done after all of the specific questions. The beginning of the passage describes the death of a wealthy financier and the impact of his death, stating that he died without making one loyal friend to mourn him, but that it seemed to those living in the great vortices of business as if the earth too shuddered under a blow. The following paragraphs discuss Manderson’s life and his rise to power in the financial world. Choice (A) matches this structure, so keep it. The passage mentions a change in Manderson’s life, but it also says that how the change came about none could with authority say, so eliminate (B). The passage does mention that Manderson died without making any loyal friends, but the focus of the passage as a whole is not why he failed to make friends, so (C) can also be eliminated. While the passage does explain that Manderson was more successful after he changed from a gambler of genius to one who worked with steady labour, the passage focuses on Manderson specifically, not on the advantages of hard work over risky speculations in general. Eliminate (D). The correct answer is (A).
2.D
This question asks what Manderson was chiefly known for. Notice that it’s the first question in a paired set, so it can be done in tandem with Q3. Start with the answers to Q3. The lines for (3A) state that Manderson imposed [himself] upon the mind of the trading world in a way that hadn’t been done before. While these lines do describe Manderson, they don’t support any of the specific answers in Q2. Eliminate (3A). The lines for (3B) say that Manderson was the unquestioned guardian of stability, the stamper-out of manipulated crises, the foe of the raiding chieftains that infest the borders of Wall Street. These lines support choice (2D) (power and determination to protect), so connect those two choices. The lines for (3C) refer to the origin of Manderson’s family money, which doesn’t support any of the answers for Q2. Eliminate (3C). Choice (3D) talks about his early career, which is not how Manderson was chiefly known, nor does it support any of the choices in Q2. Eliminate (3D). Without any support from Q3, choices (2A), (2B), and (2C) can be eliminated. The correct answers are (2D) and (3B).
3.B
(See explanation above.)
4.C
This question asks what the passage suggests about Manderson’s death. Notice that it’s the first question in a paired set, so it can be done in tandem with Q5. Look at the answers for Q5 first. The lines for (5A) say that when Manderson was killed, the world lost nothing worth a single tear. These lines don’t support any of the answers for Q4, so eliminate (5A). The lines in (5B) say that his death was a harsh reminder of the vanity of such wealth and that even though he didn’t have one loyal friend to mourn him, the news of his death caused those living in the great vortices of business to feel as if the earth…shuddered under a blow. These lines support (4C), so draw a line to connect those two answer choices. The lines in (5C) don’t reference Manderson’s death at all, and therefore do not support any of the answers for Q4. Eliminate (5C). The lines in (5D) discuss Manderson’s change after his father’s death, which doesn’t support any of the answers for Q4. Without support from Q5, (4A), (4B), and (4D) can be eliminated. The correct answers are (4C) and (5B).
5.B
(See explanation above.)
6.C
The question asks what the word quiet most nearly means in line 39. Go back to the text, find the word quiet, and highlight it. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says that they had rooted in him an instinct for quiet magnificence, the larger costliness which does not shriek of itself with a thousand tongues. The word quiet is contrasted with the phrase shriek of itself with a thousand tongues. Therefore, quiet must mean something like “subtle” or “reserved.” Silent, still, and secluded are all possible definitions of the word quiet, but none of them is consistent with the prediction. Eliminate (A), (B), and (D). Understated is consistent with “subtle” and “reserved.” The correct answer is (C).
7.A
The question asks what the reference to St. Helena serves to do in the passage. Find the line reference and carefully read the window to figure out what the reference to St. Helena does within the context of the passage. Lines 46—49 state that at St. Helena it was laid down that war is a beautiful occupation and so the young Manderson had found the…dogfight of the Stock Exchange. The reference to St. Helena introduces a comparison between war and work at the Stock Exchange, so eliminate any answer choices that are not consistent with this prediction. Choice (A) matches the prediction, so keep it. There is no dilemma nor mention of coworkers, so eliminate (B). The sentence does not refer to an event in the history of the Stock Exchange, so (C) can be eliminated. The lines about St. Helena do not suggest that Manderson rejected war as a career path, so eliminate (D). The correct answer is (A).
8.D
The question asks what best describes Manderson’s change in line 52. Carefully read the window to find evidence about the change. The passage states that after his father’s death, Manderson turned to steady labour in his father’s banking business, closing his ears to the sound of the battles of the Street. The correct answer should have something to do with Manderson becoming a serious banker after his earlier days at the Stock Exchange. He did not become a rival taking over a business, so eliminate (A). Although the window mentions battles, he was never a soldier, so eliminate (B). He becomes a powerful businessman, not a trusted clerk, so eliminate (C). Choice (D) is consistent with the prediction. The correct answer is (D).
9.B
The question asks what the word elastic most nearly means in line 55. Go back to the text, find the word elastic, and highlight it. Carefully read the window and use context clues to determine another word that would fit in the text. The sentence as a whole discusses the fact that Manderson changed from a gambler of genius to one who worked with steady labour. Therefore, the missing word must mean something like “adaptable.” Rubbery, expandable, and looped are all possible definitions of the word elastic, but none of them is consistent with the prediction. Eliminate (A), (C), and (D). Flexible is consistent with “adaptable.” The correct answer is (B).
10.D
The question asks what the word dominant most nearly means in line 2. Go back to the text, find the word dominant, and highlight it. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says, With governments fretting over how to feed more than nine billion people by 2050, a dominant narrative calls for increasing global food production by 70 to 100 percent. Therefore, the word dominant could be replaced with something like “major.” Neither aggressive, forceful, nor outstanding matches “major.” These are all Could Be True trap answers based on other meanings of “dominant” that are not supported by the text. Eliminate (A), (B), and (C). Choice (D), prominent, matches “major,” so keep (D). The correct answer is (D).
11.C
The question asks what has increased as a result of agriculture. This is the first question in a paired set, but it is easy to find, so it can be done on its own. Use lead words and the order of the questions to find the window. Q10 asks about line 2, so the window for Q11 most likely begins after that line. Look for the lead word agriculture. Lines 4—9 state that agriculture already represents one of the greatest threats to planetary health. It is responsible for 70 percent of the planet’s freshwater withdrawals, 80 percent of the world’s tropical and subtropical deforestation, and 30 to 35 percent of human-caused greenhouse gas emissions. Therefore, agriculture has led to an increase in environmental problems. Eliminate the answers that don’t match this prediction. Choice (A) is a Right Answer, Wrong Question trap answer: the passage does mention the flow of a European river, but it is not mentioned as something that increased due to agriculture, so eliminate (A). The passage doesn’t discuss the cost of goods, so eliminate (B). Keep (C) because it matches the prediction. Choice (D) is a Right Answer, Wrong Question trap answer: the passage mentions the number of people who suffer from hunger, but it does not say the number increased as a result of agriculture; eliminate (D). The correct answer is (C).
12.A
The question is the best evidence question in a paired set. Since Q11 was easy to find, simply look at the lines used to answer Q11. The prediction for Q11 came from lines 4—9. Part of this window is included in (A). The correct answer is (A).
13.B
The question asks what the author indicates about the amount of food wasted annually across the globe. Notice that this is the first question in a paired set, so it can be done in tandem with Q14. Look at the answers for Q14 first. The lines for (14A) say that nearly 800 million people worldwide suffer from hunger. These lines don’t discuss the amount of food wasted, so eliminate (14A). The lines for (14B) state that we squander enough food—globally, 2.9 trillion pounds a year—to feed every one of [the people suffering from hunger] more than twice over. Check the answers for Q13 to see if this information supports any of the answers; it supports (13B), so draw a line connecting (13B) with (14B). The lines for (14C) say, By the end of 2015 the UN and the U.S. had pledged to halve food waste by 2030. This information doesn’t support any of the answers to Q13, so eliminate (14C). The lines for (14D) say that countries and companies are devising and adopting standardized metrics to quantify waste. These lines don’t support any of the answers for Q13, so eliminate (14D). Without any support in the answers from Q14, (13A), (13C), and (13D) can be eliminated. The correct answers are (13B) and (14B).
14.B
(See explanation above.)
15.D
The question asks for the purpose of the phrase whether sausages or snickerdoodles. Use the given line reference to find the window. Lines 24—28 state, Wasting food takes an environmental toll as well. Producing food that no one eats—whether sausages or snickerdoodles—also squanders the water, fertilizer, pesticides, seeds, fuel, and land needed to grow it. The quantities aren’t trivial. The main point of this paragraph is that the environmental harm caused by food waste is significant, and the phrase whether sausages or snickerdoodles helps the author illustrate this point. Eliminate answers that don’t match this prediction. Eliminate (A) because the author does not compare values of different food groups. Eliminate (B) because the author does not state that environmentalists object to the waste of these two foods most strongly. Eliminate (C) because sausages and snickerdoodles are not given as examples of particularly wasteful foods, nor does the author try to caution her readers against consuming any type of food. Keep (D) because it matches the prediction. The correct answer is (D).
16.D
The question asks what the word obscene most nearly means in line 38. Go back to the text, find the word obscene, and highlight it. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says that if food waste were a country, it would be the third largest producer of greenhouse gases in the world and that on a planet of finite resources, with the expectation of at least two billion more residents by 2050, this waste is obscene. Therefore, the word obscene could be replaced by something like “appalling.” Censored means “suppressed;” it does not match “appalling,” so eliminate (A). Improper means “inappropriate” and does not match “appalling,” so eliminate (B). Vulgar means “lacking good taste” and does not match “appalling,” so eliminate (C). Outrageous matches “appalling,” so keep (D). Note that (A), (B), and (C) are Could Be True trap answers based on alternate meanings of obscene that are not supported by the text. The correct answer is (D).
17.A
The question asks which idea is supported by both the passage and the information in Figure 1. First, work through each answer using the figure. Choice (A) is supported by Figure 1: in developed nations, food discarded by retail markets and consumers accounts for 14.7% of dairy waste, while in developing nations, waste by retail markets and consumers accounts for only 8.5% of waste. Keep (A). Choice (B) is not supported by Figure 1, because the figure does not include information about a lack of adequate food storage. Eliminate (B). Choice (C) is not supported by the figure. Figure 1 only shows what percent of the food within each region is wasted; it doesn’t give a basis for comparing the actual amounts of food wasted in developing versus developed nations. Eliminate (C). Choice (D) is not supported by the figure. Figure 1 shows that 16.4% of food is lost during production and processing in developing nations, while only 5.2% of food is lost during production and processing in developed nations. Eliminate (D). Check to see whether (A) is supported by the passage. Lines 17—23 indicate that in comparison with developing nations, developed nations waste more food farther down the supply chain, when retailers order, serve, or display too much and when consumers ignore leftovers in the back of the fridge or toss perishables before they’ve expired. This information supports (A). The correct answer is (A).
18.C
The question asks which statement from the passage is most directly supported by Figure 2. Work through each answer choice using the figure. The lines for (A) state, With governments fretting over how to feed more than nine billion people by 2050, a dominant narrative calls for increasing global food production by 70 to 100 percent. Figure 2 does not include information about increasing global food production. Eliminate (A). The lines for (B) state, developed nations waste more food farther down the supply chain due to the actions of retailers and consumers. Figure 2 doesn’t include information about the ways developed nations in particular waste food, so eliminate (B). The lines for (C) state, Along the supply chain fruits and vegetables are lost or wasted at higher rates than other foods. Easily bruised and vulnerable to temperature swings en route from farm to table, they’re also usually the first to get tossed at home. Figure 2 supports this statement, since it shows a higher percentage of waste for fruits and vegetables than for the other types of food in the graph. Keep (C). The lines for (D) state, Countless businesses, such as grocery stores, restaurants, and cafeterias, have stepped forward to combat waste by quantifying how much edible food isn’t consumed, optimizing their purchasing, shrinking portion sizes, and beefing up efforts to move excess to charities. Figure 2 doesn’t include information about measures businesses are taking to combat food waste, so eliminate (D). The correct answer is (C).
19.C
The question asks about the overall structure of the passage. Since this is a general question, it should be answered after the specific questions. The passage begins by summarizing and describing the results of two experiments that address higher-order visual perception in mice. The following paragraphs describe those experiments in more detail. Eliminate answers that don’t match this prediction. Though the first paragraph does contain an overview of the experiments and their results, the rest of the text does not discuss two hypotheses. Eliminate (A). Choice (B) uses ideas from the passage but answers the wrong question: the last sentence of the first paragraph presents a perceived scientific truth (that mice were thought to be non-visual) and then an alternative conclusion based on the experiments described. However, this only describes the structure of the end of the first paragraph, not that of the whole passage. Eliminate (B). Keep (C) because it matches the prediction. Eliminate (D), which is a Mostly Right, Slightly Wrong trap answer: the beginning of the passage does describe the outcome of a study, but this is not followed by an extension of the outcome to another field. The correct answer is (C).
20.A
The question asks what the word solution most nearly means in line 12. Go back to the text, find the word solution, and cross it out. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says that mice were injected with saline solution. Therefore, solution must refer to a liquid that contains saline and other components, so it must mean something like “composite liquid.” Mixture matches “composite liquid,” so keep (A). Answer does not match “composite liquid,” so eliminate (B). Resolution means “solution to a problem,” which does not match “composite liquid,” so eliminate (C). Key does not match “composite liquid,” so eliminate (D). Note that (B), (C), and (D) are Could Be True trap answers based on other meanings of solution that are not supported by the text. The correct answer is (A).
21.A
The question asks for an underlying assumption that Professor Watanabe makes regarding “staying time.” This is the first question in a paired set, but it is easy to find, so it can be done on its own. Since there is no line reference, use lead words and the order of the questions to find the window for the question. Q20 asks about line 12, so the window for Q21 most likely begins after line 12. Scan the second paragraph, looking for the lead words staying time. The paragraph says that staying time is a measure of how long the mice stayed in the compartments with their respective paintings. The last sentence of the paragraph says, As mice know that morphine causes pleasure, they should stay longer near the painting associated with the morphine injection if able to discriminate between paintings. Therefore, Professor Watanabe assumes that the mice are able to associate paintings with pleasure, or reward, and that this results in them staying longer near a particular painting. Eliminate answers that don’t match this prediction. Keep (A) because it matches the prediction. Eliminate (B), because it is a Right Words, Wrong Meaning trap answer: the passage does not suggest that giving the mice rewards will give them better vision. Eliminate (C) for the same reason: the passage does not suggest that mice spend more time viewing the paintings they saw when receiving a reward because they are experiencing the same pleasure derived from the reward. There is no measure of whether the mice are experiencing pleasure again or to what degree they might. Eliminate (D) because the passage does not compare the staying time of mice with those of pigeons and Java Sparrows. The correct answer is (A).
22.D
The question is the best evidence question in a paired set. Because Q21 was a specific question, simply look at the lines used to answer the previous question. Two different lines were used in the prediction: Sensors recorded the staying time of mice in the compartments with their respective paintings and As mice know that morphine causes pleasure, they should stay longer near the painting associated with the morphine injection if able to discriminate between paintings. Of these two lines, only the second one is an answer choice. The correct answer is (D).
23.B
The question asks what the word discrimination most nearly means in line 46. Go back to the text, find the word discrimination, and cross it out. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says, If mice are capable of discrimination, they should touch the painting associated with the milk reward. In other words, a mouse capable of discrimination would be able to recognize and choose the painting associated with the milk. Therefore, discrimination must mean something like “noticing the difference between things.” Prejudice means “preconceived judgement;” it does not match “noticing the difference between things,” so eliminate (A). Differentiation means “noticing the difference between things,” which matches the prediction, so keep (B). Bias means “favoring something without considering other options,” which does not match “noticing the difference between things,” so eliminate (C). Insight does not match “noticing the difference between things,” so eliminate (D). Note that (A), (C), and (D) are Could Be True trap answers based on other meanings of discrimination that are not supported by the text. The correct answer is (B).
24.D
The question asks for an inference that explains why Professor Watanabe showed the paintings to the mice prior to the conditioning experiments. Since there is no line reference, use lead words and the order of the questions to find the window for the question. Q23 asks about line 46, so the window for Q24 most likely begins after that line. Scan the fourth paragraph, looking for the lead word conditioning. The paragraph says that the conditioning in Experiment 1 was the injection of morphine into the mice when they viewed certain paintings, encouraging them to associate pleasure with a specific painting. Prior to this, the paragraph discusses the first experiment without morphine, in which mice that were shown paintings from multiple artists did not show a preference for a particular painting or artist. Therefore, mice were shown paintings without any pleasure reward first to make sure they did not have a preference for a particular painting or artist before beginning the experiment with the morphine. Eliminate answers that don’t match this prediction. Eliminate (A) because it is a Right Words, Wrong Meaning trap answer: Professor Watanabe did not show paintings to the mice first in order to prove that the staying times increased by 80%. Eliminate (B) because the passage does not say that the mice were shown paintings first to familiarize them with the artists. Eliminate (C) because the passage does not discuss the mice’s sense of anticipation for rewards. Keep (D) because it matches the prediction. The correct answer is (D).
25.D
The question asks for evidence that supports the claim that mice are more visually adept than they were conventionally believed to be. Use the line references given in the answer choices to find a statement that supports this claim. Choices (A) and (B) discuss a lack of preference for Picasso or Renoir and the mice’s inability to discriminate between the two artists, but neither discusses a conventional belief. Eliminate (A) and (B). Choice (C) discusses a conventional understanding about mice (it has been thought that they are non-visual animals), but it does not mention anything about them being more visually adept than this belief suggests. Eliminate (C). Choice (D) says that the experiment demonstrates that mice have much better visual perception abilities than previously thought, which supports the idea that mice are more visually adept than they were conventionally believed to be. The correct answer is (D).
26.C
The question asks for the primary purpose of the final paragraph. Read the final paragraph, which says, This experiment demonstrates that mice have much better visual perception abilities than previously thought. It then broadens the significance of this idea, saying that the perception of complex visual stimuli like paintings extends to non-human animals. Eliminate answers that don’t match this prediction. Eliminate (A) because the final paragraph does not describe an error; it describes a change in understanding. Eliminate (B) because the last paragraph does not justify the methods described earlier in the passage. Keep (C) because it matches the prediction. Eliminate (D) because, though the paragraph mentions the broad significance of the findings, it does not suggest a topic for future research. The correct answer is (C).
27.B
The question asks for the purpose that the figure serves in relation to the passage as a whole. The passage describes a recent study and discusses the significance of that study’s findings. The figure shows data from the “staying time” experiment, which was Experiment 1. Eliminate answers that are inconsistent with either the passage or the figure. Eliminate (A) because the passage does not indicate that the two experiments had conflicting conclusions. Keep (B) because it is consistent with both the purpose of the figure and information from the passage. Eliminate (C) because the figure does not introduce a possible source of error or cast doubt on Professor Watanabe’s conclusions. Eliminate (D) because the figure agrees with the results in the passage; it does not suggest a different interpretation than that presented in the passage. The correct answer is (B).
28.C
The question asks for a conclusion about mice, in general, based on information in the passage and in the figure. Since this is a general question, it should be answered after the specific questions. The figure shows data from Experiment 1, and the passage says that Experiment 1 showed that mice stayed longer at paintings that they associated with pleasure from a morphine injection. Eliminate answers that are inconsistent with either the passage or the figure. Choice (A) is a Right Answer, Wrong Question trap answer: it uses words from the description of Experiment 2, but the figure only relates to Experiment 1. Eliminate (A). Eliminate (B) because the figure and the passage both support the idea that the mice did not have a greater appreciation for either Picasso or Renoir before conditioning, which contradicts (B). Keep (C) because the figure and the passage both show that the mice had increased staying times following conditioning with morphine. Eliminate (D) because it is a Right Words, Wrong Meaning trap answer: the passage does not compare the degrees to which milk and morphine influenced the mice’s actions. The correct answer is (C).
29.B
The question asks about the position that Jay (the author) takes in the essay. Since this is a general question, it should be answered after the specific questions. Over the course of the passage, Jay, a Founding Father, argues that the United States should not be split into smaller, separate nations. Eliminate answers that don’t match this prediction. Choice (A) can be eliminated because Jay is definitely not an impartial onlooker pointing out both sides of an issue. Choice (B) matches the prediction, so keep it. Choice (C) can be eliminated because, for Jay, this is not a historical decision but rather a current event. Choice (D) can also be eliminated because Jay argues for a particular side in his essay. He is not looking for a compromise. The correct answer is (B).
30.C
The question asks what the word vest most nearly means in line 12. Go back to the text, find the word vest, and highlight it. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says that nothing is more certain than the indispensable necessity of government, and…the people must cede to it some of their natural rights in order to vest it with requisite powers. In other words, the people must give over to the government some of their natural rights in order to “provide” or “give” the government its necessary power. Therefore, vest must mean something like “provide” or “give.” Choice (A) might initially look attractive because a vest is also an article of clothing, but that does not match the prediction. Choice (A) is a Could Be True trap answer that is based on another meaning of vest that is not supported by the passage. Eliminate (A). Choice (B), abandon, doesn’t match “provide” or “give,” so eliminate (B). Choice (C), endow, means “to give,” which is consistent with the prediction. Choice (D), belong, does not match the prediction. The correct answer is (C).
31.B
The question asks which of the following questions about the American political system arose shortly before the passage was written. Notice that this is the first question in a paired set, so it can be done in tandem with Q32. Look at the answers for Q32 first. The lines for (32A) say that nothing is more certain than the indispensable power of government, and that the people must cede to it some of their natural rights in order to provide it with necessary powers. These lines do not address Q31, so eliminate (32A). The lines for (32B) say that politicians now appear who insist that a previously stated opinion is erroneous, and that instead we ought to seek [safety and happiness] in a division of the States into distinct parts. The previously stated opinion (lines 20—24) was that the prosperity of the people of America depended on their continuing firmly unified, and the author states that this opinion was uncontradicted until recently. In other words, the debate mentioned in the lines for (32B) arose shortly before the passage was written. Therefore, check the answers for Q31 to see whether any of the answers are supported by these lines. This information matches (31B), whether America should be governed as one nation or as independent states. Draw a line connecting (31B) and (32B). The lines for (32C) say that America has been blessed…with a variety of soils and productions…for the delight and accommodation of its inhabitants. These lines do not address Q31, so eliminate (32C). The lines for (32D) say that America is one connected country with one united people, claiming that its people are bound by common language, religion, principles, and customs as well as the history of a long and bloody war. This information does not address a political question or debate that would have occurred before the passage was written. Eliminate (32D). Without support from Q32, (31A), (31C), and (31D) can be eliminated. The correct answers are (31B) and (32B).
32.B
(See explanation above.)
33.C
The question asks what Jay indicates about those who support dividing the country into separate confederacies. Notice that this is the first question in a paired set, so it can be done in tandem with Q34. Look at the answers for Q34 first. The lines for (34A) say that the prosperity of the people of America depended on their continuing firmly united. While this answer might initially seem to connect with (33A), there is no evidence in the text that he believes those who support dividing the country are encouraging political turmoil. Eliminate (34A). The lines for (34B) simply say that division has its advocates, but there is no mention of Jay’s belief about those advocates. Eliminate (34B). The lines for (34C) warn that it would not be wise to advocate for division without being fully convinced that [separating the country is] founded in truth and sound policy. These lines support (33C). Connect those two answers. Choice (32D) describes how independent America was not composed of detached and distant territories, but…connected, fertile, wide-spreading country. There is nothing about those who advocate for dividing the county, so these lines don’t support any of the answers for Q33. Eliminate (34D). Without support from Q34, (33A), (33B), and (33D) can be eliminated. The correct answers are (33C) and (34C).
34.C
(See explanation above.)
35.B
The question asks about a distinction Jay makes in the passage. Use the given line reference to find the window. The text states that it gives [Jay] pleasure to observe that independent America was not composed of detached and distant territories, but that one connected, fertile, wide-spreading country was the portion of our western sons of liberty. The correct answer should be consistent with the distinction between detached territories and one connected country. Choice (A) is not consistent with this prediction, so it can be eliminated. Choice (B) is a solid paraphrase of the prediction, so keep it. There is nothing in the text about deserted marketplaces, so eliminate (C). Choice (D) can also be eliminated because Jay’s distinction here is about detached and connected physical space, not the ideas of division and independence. The correct answer is (B).
36.D
The question asks about the purpose of Jay’s reference to innumerable streams…navigable waters…and noble rivers. Use the given line reference to find the window. Jay first describes the benefits of the streams (for the delight and accommodation of its inhabitants), the waters (a kind of chain round its borders, as if to bind it together), and the rivers (highways for the easy communication of friendly aids). For Jay, these waters are beneficial. He continues by saying that [w]ith equal pleasure I have as often taken notice that Providence has been pleased to give this one connected country to one united people. He then goes on to describe how the people are also connected. Therefore, the correct answer must have something to do with Jay using the examples to represent the connectedness of the people of the country. Choice (A) can be eliminated because Jay isn’t arguing to protect natural resources. Choice (B) can be eliminated because there is no evidence that the references to water are meant to get people out exploring. Choice (C) can be eliminated because the references to water aren’t summarizing anything; they are representing something. Choice (D) is consistent with the prediction, as Jay uses the description of the waters as a comparison that supports his argument about the connectedness of the people. The correct answer is (D).
37.A
The question asks what Jay means when he says with equal pleasure. Use the given line reference to find the window. Notice that this line reference is from the same window as the previous question. The text states that Jay likes both the connectedness of the land and the connectedness of the people of the United States. Eliminate any answer choices that aren’t consistent with this prediction. Choice (A) is a paraphrase of the prediction, so keep it. Choice (B) can be eliminated because Jay does not feel equally happy about unification and division. Although (C) might seem logical, there is no evidence for it in the text, and it can be eliminated. Choice (D) might also make sense, but again, there is no direct evidence for it in the text, so it can be eliminated. The correct answer is (A).
38.C
The question asks for the purpose of the list in lines 55—59. Use the given line reference to find the window. In lines 53—55, Jay states that Providence has been pleased to give this one connected country to one united people. He then goes on to list the ways in which the people are united: Jay states that the people of the United States are a people descended from the same ancestors, speaking the same language, professing the same religion, attached to the same principles of government, very similar in their manners and customs. In other words, the list supports Jay’s argument that the people of the United States are a unified people. Choice (A) mentions a method, but there is no discussion about a method in the window, so eliminate (A). Choice (B) says that the list is summarizing points that Jay has dismissed, but this list is related to a claim that Jay supports, so (B) can be eliminated. Choice (C) is consistent with the text, so keep it. Choice (D) mentions issues that Jay’s audience must settle, but the list is a set of examples that support a claim, not a list of undecided issues. Eliminate (D). The correct answer is (C).
39.B
The question asks for evidence from Passage 1 that supports the claim that space is an “inhospitable environment for life.” Use the line references given in the answer choices to find a statement that supports this claim. The lines for (A) say that the tardigrades were exposed to the vacuum of space. These lines do not describe the space environment, so eliminate (A). The lines for (B) say that the tardigrades had no air and were subjected to extreme dehydration, freezing temperatures, weightlessness and lashings of both cosmic and solar radiation. These lines support the claim that space is an inhospitable environment, so keep (B). The lines for (C) say that the tardigrades survived the raw vacuum of space, but they do not describe the space environment, so eliminate (C). The lines for (D) state that the tardigrades spent time in low Earth orbit, but they don’t describe the space environment, so eliminate (D). The correct answer is (B).
40.C
The question asks what the word tolerate most nearly means in line 15. Go back to the text, find the word tolerate, and highlight it. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says that tardigrades can tolerate extreme environments that would kill almost any other animal. Therefore, tolerate must mean something like “survive.” Permit does not match “survive,” so eliminate (A). Indulge does not match “survive,” so eliminate (B). Endure matches “survive,” so keep (C). Ignore does not match “survive,” so eliminate (D). Note that (A), (B), and (D) are Could Be True trap answers based on other meanings of tolerate that are not supported by the text. The correct answer is (C).
41.D
The question asks which unique trait allows tardigrades to survive in hostile environments. Notice that this is the first question in a paired set, so it can be done in tandem with Q42. Look at the answer choices for Q42 first. The lines for (42A) say that a team of scientists launched a squad of tiny animals into space aboard a Russian satellite. These lines do not address Q41, so eliminate (42A). The lines for (42B) state that tardigrades are aquatic invertebrates and that they are nigh-invincible. Although the lines mention the tardigrades’ shuffling walk, they do not say that the shuffling walk helps tardigrades survive in hostile environments. Eliminate (43B). The lines for (42C) say that tardigrades survive by replacing almost all of the water in their bodies with a sugar called trehalose. This information matches (41D). Draw a line connecting (42C) and (41D). The lines in (42D) state that tardigrades can be revived by a drop of water. Check the answers for Q41 to see whether any of the answers are supported by these lines. None of the answers in Q41 match the information in (42D), so eliminate (42D). Without any support in the answers from Q42, (41A), (41B), and (41C) can be eliminated. The correct answers are (41D) and (42C).
42.C
(See explanation above.)
43.B
The question asks what the word robust most nearly means in line 45. Go back to the text, find the word robust, and highlight it. Then read the window carefully, using context clues to determine another word that would fit in the text. The text says that the world’s most robust animals may very well survive until the sun stops shining and that tardigrades are famed for their resiliency. Therefore, robust must mean something like “resilient.” Round does not match “resilient,” so eliminate (A). Tough matches “resilient,” so keep (B). Flavorful does not match “resilient,” so eliminate (C). Healthy does not match “resilient,” so eliminate (D). Note that (C) and (D) are Could Be True trap answers based on other meanings of robust that are not supported by the text. The correct answer is (B).
44.C
The question asks whether the author of Passage 2 would agree with a student’s claim that tardigrades would likely face extinction before humans. Since there is no line reference, use lead words to find the window. Look for the lead words extinction, humans, and tardigrades. The second paragraph mentions humans and extinction. The paragraph states, Astrophysical events such as asteroid strikes have been fingered as the causes of past mass extinctions on Earth. Such violent cataclysms could easily wipe out humans. The third paragraph states that an asteroid collision with earth would be catastrophic for many life-forms on the surface, but tardigrades would have a refuge. The next paragraph adds, “Tardigrades can live around volcanic vents at the bottom of the ocean, which means they have a huge shield against the kind of events that would be catastrophic for humans.” Therefore, the author would probably not agree that tardigrades are likely to face extinction before humans. Eliminate answers that don’t match this prediction. Eliminate (A) and (B). Keep (C) because it matches the prediction. Eliminate (D) because the passage indicates that tardigrades are not vulnerable to asteroid strikes. The correct answer is (C).
45.C
The question asks for the main purpose of both Passage 1 and 2. Consider one passage at a time. Passage 1 discusses a study that found that tardigrades can survive in space. Eliminate answers that don’t match this prediction. Eliminate (B) because Passage 1 focuses on only one invertebrate, and tardigrades are more able to withstand extreme environments than other species. Eliminate (D) because Passage 1 does not discuss catastrophic scenarios, and it only discusses one invertebrate, the tardigrade. Passage 2 discusses what phenomena could lead to the extinction of the tardigrade. No method of testing is discussed in Passage 2, so eliminate (A). Keep (C) because it matches the predictions for both passages. The correct answer is (C).
46.D
The question asks what is true of “water bears” (line 13) based on information in Passage 2. Use the given line reference to find the window in Passage 1. The lines say, Tardigrades are small aquatic invertebrates that are also known as “water bears.” Since water bears is another name for tardigrades, the answer should include a statement that is true of tardigrades. Use lead words from the answers to find the relevant information, and eliminate answers that are not supported. Eliminate (A) because both passages state that tardigrades are invertebrates, not vertebrates. Choice (A) is a Mostly Right, Slightly Wrong trap answer. Eliminate (B) because tuns is mentioned only in Passage 1 and describes the dormant state of tardigrades; the passage does not state that tardigrades are related to tuns. Choice (B) is a Right Words, Wrong Meaning trap answer. Eliminate (C) because trehalose is only mentioned in Passage 1, and the text indicates that tardigrades can replace almost all of the water in their bodies with…trehalose; it doesn’t say that tardigrades are made of trehalose. Keep (D) because line 48 describes tardigrades as eight-legged. The correct answer is (D).
47.D
The question asks which environment could be the natural habitat of the “water-dwelling creatures” mentioned in line 47, based on Passages 1 and 2. Use the given line reference to find the window in Passage 2. Lines 46—47 state, Tardigrades are tiny water-dwelling creatures famed for their resiliency. Therefore, the water-dwelling creatures are tardigrades, so the correct answer should give a possible natural habitat of tardigrades, based on the passages. Use lead words from the answers to find the relevant information, and eliminate answers that aren’t supported. Lines 77—80 suggest that some species of tardigrades live around volcanic vents in the ocean; however, the passage doesn’t say that they live in volcanic lava domes, so (A) is a Right Words, Wrong Meaning trap answer. Eliminate (A). Lines 1—3 say that scientists launched the tardigrades into space, so space is not their natural habitat. Eliminate (B). Water pipes are not mentioned in either passage, so eliminate (C). Lines 39—40 mention the tardigrades’ precarious environment, which are damp pools or patches of water on moss or lichen, which support (D). The correct answer is (D).
Section 2—Writing and Language
1.B
The vocabulary is changing in the answer choices, so the question is testing word choice. Look for a word whose definition is consistent with the other ideas in the sentence. The sentence discusses what aren’t on the list, and the next sentence uses the phrase As one would expect. Therefore, the definition should mean “something unexpected.” Exceptions means “exclusion or objections,” so eliminate (A). Surprises means “unexpected,” so keep (B). Outliers means “those outside of the norm,” so eliminate (C). Abominations means “greatly disliked,” so eliminate (D). The correct answer is (B).
2.D
The number of words is changing in the answer choices, so the question is testing concision. First, determine whether the extra words are necessary. In this case, all the answers mean the same thing, so the shortest answer is probably going to be the best. To confirm, the choice should be consistent with the rest of the sentence. The sentence lists two things. The second should be consistent with the first, so Americans and Europeans would be consistent. The correct answer is (D).
3.C
Pronouns are changing in the answer choices, so the question is testing consistency of pronouns. A pronoun must be consistent with the noun it is replacing. The pronoun refers to the noun winner, which is singular. To be consistent, the pronoun in the answer choice must also be singular. Their and they’re are plural, so eliminate (A) and (D). While one’s is singular, it is only consistent with the word “one,” which does not appear in the sentence, so eliminate (B). His or her is singular and is consistent with winner. The correct answer is (C).
4.B
Note the question! The question asks for the main topic of the paragraph, so it’s testing consistency of ideas. Determine the topic discussed in the paragraph and select the choice that is consistent with that idea. The paragraph discusses how winners in most categories come from the elite research institutions, yet winners of the Nobel Prize in Literature…have not attended the same schools. The correct answer will be consistent with the topic of winners from different institutions or schools. Stating that the winners in all categories tend to be affiliated with the same universities is the opposite, so eliminate (A). One surprise…with the educational backgrounds of some winners is consistent, so keep (B). The best research is done by college students and their professors is not consistent, so eliminate (C). Stating that the winners are highly intelligent is not consistent, so eliminate (D). The correct answer is (B).
5.A
The punctuation is changing in the answer choices, so the question is testing STOP and GO punctuation. Use the Vertical Line Test and identify the ideas as complete or incomplete. Draw the vertical line between the words categories and though. The phrase These winners share an average age (64) and geographical diversity with those in other categories is a complete idea. The phrase though they have not attended the same schools is an incomplete idea. To connect a complete idea to an incomplete idea, GO or HALF-STOP punctuation is needed. The semicolon and the period are STOP punctuation, so eliminate (B) and (D). The words though and however are changing in (A) and (C). Both words indicate a separate idea that contrasts with the previous idea. The word however makes the second part of the sentence complete, which does not work with GO punctuation. Eliminate (C). The correct answer is (A).
6.D
The entire phrases are changing in the answer choices, so the question is testing concision and precision. Also, the commas are changing in the answer choices, so the question is testing the four ways to use a comma. In this sentence, the commas are used to separate out unnecessary info. Both (A) and (B) use the name Toni Morrison as both the object of the prize (it went to her) and the subject of the verb earned. The name cannot do both jobs, so eliminate (A) and (B). Both (C) and (D) correctly separate out Toni Morrison as she is already identified as the winner or the recipient. Since (C) and (D) are both grammatically correct, choose the more concise answer. The phrase whose name was is not needed, so eliminate (C). The correct answer is (D).
7.C
Both the pronouns and the verbs are changing in the answer choices, so the question is testing consistency. A pronoun must be consistent in number with the noun it is replacing. The pronoun refers to the noun committee, which is singular. To be consistent, the pronoun in the answer choice must also be singular. The pronouns they and we are plural, so eliminate (A), (B), and (D). The pronoun it is singular. The correct answer is (C).
8.A
Verbs are changing in the answer choices, so the question is testing consistency of verbs. A verb must be consistent with its subject and with the other verbs in the sentence. The subject of the verb is Work, which is singular. To be consistent, the verb in the answer choices must also be singular. Eliminate (B) and (C) because they are plural. Requires is in the present tense and has required is in the present perfect. Since there are no other verbs in the sentence, select the choice that is consistent with the verb in the following sentence. The following sentence uses the verb provide, which is present tense. Eliminate (D). The correct answer is (A).
9.D
One thing that is changing in the answer choices is the number of words, so the question is testing concision. Both findings and discoveries mean the same thing, so it is redundant to list both. Eliminate (A), (B), and (C). The correct answer is (D).
10.C
Note the question! The question asks where sentence 6 should be placed, so it’s testing consistency. Determine the subject matter of the sentence, and find the other sentence that also discusses that information. Sentence 6 mentions literature needs no such place, and uses the word however. For consistency, sentence 6 should be placed after a discussion of place and before a discussion of literature. Sentences 2 and 3 discuss an atmosphere for economics, medicine, and the sciences and sentence 4 discusses literature. Therefore, sentence 6 should be placed between sentences 3 and 4. The correct answer is (C).
11.B
Note the question! The question asks for the choice that would most effectively support the assertion made in this sentence and paragraph, so it’s testing consistency of ideas. The main idea of the paragraph is that great thinkers and scholars do not live only at the big research universities, so the correct answer will be consistent with this idea. The claim that you’d find the most open minds at the best schools is not consistent, so eliminate (A). Discussing different educational sources such as a high-end graduate program, a community college, or the workforce is consistent, so keep (B). Claiming that Literature laureates are an exception is not consistent, so eliminate (C). Discussing an author of fiction is not consistent, so eliminate (D). The correct answer is (B).
12.C
Commas are changing in the answer choices, so the question is testing the four ways to use a comma. The sentence contains a list of four things: 1) dog, 2) cat, 3) fish, and 4) horse. There should be a comma after each item in the list before the word and or or. Therefore, there must be a comma after fish. Eliminate (A) and (D). There is no need for a comma after or, so eliminate (B). The correct answer is (C).
13.A
The vocabulary is changing in the answer choices, so the question is testing word choice. Ose fewer when comparing concrete, countable items. Use less when comparing uncountable nouns. The sentence is comparing the number of graduates, which is countable, so use fewer. Eliminate (B) and (D). Next, than indicates a comparison while then indicates time. The sentence is comparing the graduates each year, so eliminate (C). The correct answer is (A).
14.D
Note the question! The question asks for the statement that best supports the statement made earlier in this sentence, so it’s testing consistency of ideas. The beginning of the sentence states that it may be time to bring the dream back. The dream is the dream of being veterinarians from the first sentence. Thus, the underlined portion must be consistent with the idea of fulfilling the dream of becoming a vet. The U.S. economy is not consistent, so eliminate (A). The number of children born is not consistent, so eliminate (B). That some veterinarians will retire does not necessarily mean there will be an increase in the number of jobs typically available, so eliminate (C). Stating that the veterinary profession will grow is consistent, so keep (D). The correct answer is (D).
15.B
Note the question! The question asks for the choice that has accurate data based on the graph, so it’s testing consistency. First, understand the labels and the data from the graph. The graph shows the percent change in employment, projected 2010—20 and lists three groups of jobs. Next, read each choice and determine whether it’s consistent with the data in the graph. Other professions will grow even more quickly is not consistent because the veterinary technicians have the highest percent change; eliminate (A). Veterinary technicians will grow at over three times the rate of all occupations in the United States is consistent with the data because 52% is greater than 3 × 14% = 42%; keep (B). A health technician has equally positive job prospects is not consistent because the bar for veterinary technicians is at 52% and the bar for health technicians is at 26%; eliminate (C). Those who have not gone to veterinary school are not mentioned on the graph, so eliminate (D). The correct answer is (B).
16.B
The punctuation is changing in the answer choices, so the question is testing STOP and GO punctuation. Use the Vertical Line Test and identify the ideas as complete or incomplete. Draw the vertical line between the words pets and from. The first phrase is a complete idea, and the second phrase is an incomplete idea. Therefore, either GO or HALF-STOP punctuation is needed. The period and the semicolon are STOP punctuation, so eliminate (A) and (C). The dash is a HALF-STOP, so keep (B). The comma in (D) has been moved between the words from and basic, which separates the meaning of the ideas incorrectly; eliminate (D). The correct answer is (B).
17.C
The pronouns and nouns are changing in the answer choices, so the question is testing precision. Determine the subject of the pronoun, and choose an answer that makes the meaning consistent and precise. The subject of are required to perform more and more procedures should be the veterinarians, but that isn’t clearly implied by a pronoun such as they or them. Since the veterinarians are not mentioned in the sentence, the noun veterinarians must be used to precisely state the correct subject. The correct answer is (C).
18.C
Note the question! The question asks for the choice that emphasizes that many pet owners consider their pets to be more human than animal, so it’s testing consistency of ideas. Showing that pets are shared between friends is not consistent with more human than animal, so eliminate (A). Getting a puppy for Christmas is not consistent, so eliminate (B). Owners who self identify as pet “parents” is consistent, so keep (C). Pets are a great way to teach children about death is not consistent, so eliminate (D). The correct answer is (C).
19.B
Note the question! The question asks where sentence 5 should be placed, so it’s testing consistency. Determine the subject matter of the sentence, and find the other sentence that also discusses that information. Sentence 5 discusses pet owners believing their pets are more “human” than ever before. Sentence 2 discusses the owners. Since it starts with the phrase In fact, it indicates a continuation of the idea. Therefore, sentence 5 should be placed before sentence 2. The correct answer is (B).
20.A
Commas are changing in the answer choices, so the question is testing the four ways to use a comma. The sentence does not contain a list, so look for unnecessary information. The phrase for instance is unnecessary information, so it should be surrounded by commas. The correct answer is (A).
21.D
The number of words is changing in the answer choices, so the question is testing concision. The sentence must be about pets’ minds or the way they think, but it does not need to reference both. Eliminate (A) because it contains a repetition of the ideas of minds and the way they think. Eliminate (C) because it changes the meaning and therefore is not precise. Between (B) and (D), (B) is wordier and therefore not as concise; eliminate (B). The correct answer is (D).
22.D
The pronoun and nouns are changing in the answer choices, so this question is testing precision. Look for a word that provides the most precise definition. Eliminate (A), (B), and (C) because they are vague. The stability is the most precise. The correct answer is (D).
23.C
The transition is changing in the answer choices, so the question is testing consistency of ideas. Determine how the ideas in the sentence relate to each other and select the transition that properly links them. The first part of the sentence states that it may seem commonplace today, and the second part states that this is a relatively recent development. These are opposite ideas, so a transition that indicates a shift in ideas is needed. A lack of a transition, the word because, or the word really all indicate a similar idea, so eliminate (A), (B), and (D). While indicates a shift in ideas. The correct answer is (C).
24.A
Note the question! The question asks for information most consistent with the rest of the sentence, so it’s testing consistency of ideas. Since the sentence starts with More than twenty years earlier and the previous sentence gives the year as 1944, the information in (B) and (C) is redundant, so eliminate (B) and (C). The rest of the sentence discusses the veterans of the bloodiest war on record, so the correct answer will be consistent with this idea. The conclusion of World War I is consistent, so keep (A). The G.I. Bill is not consistent, so eliminate (D). The correct answer is (A).
25.D
Pronouns are changing in the answer choices, so the question is testing precision and consistency of pronouns. They’re means “they are,” which does not work in the sentence; eliminate (A). It is not a precise pronoun, and there is not a noun that it would clearly represent; eliminate (B). Their indicates possession, but the following word was cannot be possessed; eliminate (C). The correct answer is (D).
26.C
The phrases are changing in the answer choices, so the question is testing precision and consistency. First, the placement of 1932 is changing, which changes the meaning. To be precise, the sentence should state that the march happened in 1932. Eliminate (A), which states that the veterans were from 1932. Eliminate (D), which states that the bonuses were in 1932. To be consistent with the meaning of the paragraph, the veterans went to Washington to demand their bonuses. Eliminate (B), which states that Washington invited the veterans. The correct answer is (C).
27.B
Commas are changing in the answer choices, so the question is testing the four ways to use a comma. The sentence does not contain a list, so look for unnecessary information. All of the phrases are necessary, so there is no need for any commas. The correct answer is (B).
28.A
Note the question! The question asks for the choice that agrees with the ideas discussed in this paragraph, so it’s testing consistency of ideas. The first sentence states that the government sought to avoid another such standoff, so the answer will be consistent with this idea. The end of the second sentence mentions economic collapse. Hoping to avoid…these catastrophes is consistent, so keep (A). Stating the date 1944 is not consistent, so eliminate (B). Pearl Harbor is not consistent, so eliminate (C). Historians don’t understand is not consistent, so eliminate (D). The correct answer is (A).
29.D
Note the question! The question asks for the best placement of the underlined portion, so it’s testing precision. Place the underlined portion in the correct position to keep the precise meaning of the sentence. The phrase in university education must follow the phrase that it’s modifying. It is the revolution that is in university education. The correct answer is (D).
30.A
Verbs are changing in the answer choices, so the question is testing consistency of verbs. A verb must be consistent with its subject, the other verbs in the sentence, and the time indicators. The time indicator is by the early 1960s, so the verb must be in the past tense. Eliminate (B) and (C). The verb in the previous sentence is had used, so had changed is consistent. The correct answer is (A).
31.A
Note the question! The question asks for the choice that best supports the idea presented in the previous sentence, so it’s testing consistency of ideas. The previous sentence states that college was not limited to the very wealthy, so the answer will be consistent with this idea. Eliminate (B) and (D) because they state the opposite idea. The criteria for selection is not consistent, so eliminate (C). A springboard for the upwardly mobile is consistent because it suggests that people who came from less wealthy backgrounds could attend college and move up in society. The correct answer is (A).
32.B
Note the question! The question asks for the best introduction for the topic of this paragraph, so it’s testing consistency of ideas. The previous paragraph left off in the 1960s. This paragraph introduces 2008 and discusses how the bill was expanded. The correct answer will be consistent with the bill in more recent times. The paragraph indicates that the bill continued to get better, so eliminate (A). The benefits of the bill continue to this day is consistent, so keep (B). G.I.s and their degrees is not consistent, so eliminate (C). The home subsidy is not consistent, so eliminate (D). The correct answer is (B).
33.C
The vocabulary is changing in the answer choices, so this question is testing word choice. Look for a word whose definition is consistent with the other ideas in the sentence. The sentence discusses how the G.I. Bill changed the face of education as we know it, so the word should indicate a substantial change. Good is positive but does not indicate a change, so eliminate (A). Educational means “instructive,” so eliminate (B). Influential means “having a large effect,” so keep (C). Intelligent means “smart,” so eliminate (D). The correct answer is (C).
34.A
Note the question! The question asks for the choice that most effectively supports the ideas in this paragraph, so it’s testing consistency of ideas. The next sentence discusses the fighting, so the answer will be consistent with this idea. The correct answer is (A).
35.D
Apostrophes are changing in the answer choices, so the question is testing apostrophe usage. When used with a noun, the apostrophe indicates possession. In this sentence, the influence belongs to the animal, so the word animal needs an apostrophe. Eliminate (A) and (B). Since one animal is singular, the apostrophe must be before the s. Eliminate (C). The correct answer is (D).
36.B
Note the question! The question asks for the choice that clarifies the information given in the first part of this sentence, so it’s testing consistency of ideas. The part of the sentence that needs clarification is the foreign phrase le détroit. The correct answer will explain what the phrase means. The correct answer is (B).
37.C
The punctuation is changing in the answer choices, so the question is testing STOP and GO punctuation. Use the Vertical Line Test, and identify the ideas as complete or incomplete. Draw the vertical line between the words span and furs. The phrase within a very short span is an incomplete idea and the phrase furs had become the dominant trade items in the region is a complete idea. Therefore, GO punctuation is needed. The period and the semicolon are STOP punctuation, so eliminate (A) and (B). The comma is GO punctuation, so keep (C). The word but is one of the FANBOYS, and a comma plus one of the FANBOYS is STOP punctuation; eliminate (D). The correct answer is (C).
38.C
The word order in the phrases is changing in the answer choices, so the question is testing precision. Select the choice whose word order makes the most sense. Focus on the phrasing and placement of unfortunate. It’s not the popularity that is unfortunate, so eliminate (A). It’s not the resources that are unfortunate, so eliminate (B). Choice (C) makes it clear that the situation of finite resources being popular is unfortunate, so keep (C). Eliminate (D) because it is not as clear as (C) in indicating that the popularity of finite resources is unfortunate. The correct answer is (C).
39.A
Pronouns and verb tenses are changing in the answer choices, so the question is testing consistency. A pronoun must be consistent in number with the noun it is replacing, and a verb must be consistent with the verbs around it. The pronoun here refers to the noun the beaver, which is singular. To be consistent, the pronoun in the answer choice must also be singular. They is plural, so eliminate (C). Although one is singular, it is only consistent with the word one; eliminate (D). It’s is a contraction that means “it is.” Therefore, it’s is in the present tense when the past tense is needed. Eliminate (B). The correct answer is (A).
40.B
Note the question! The question asks whether the phrase should be kept or deleted, so it’s testing precision. The phrase should be deleted unless it is needed to keep the precise meaning of the sentence. In this case, if the phrase by factories were deleted, it would be unclear what is replacing the homes. Therefore, the phrase should be kept. Eliminate (C) and (D). The extinction of the beaver is not consistent with the passage, so eliminate (A). The correct answer is (B).
41.D
The phrases are changing in the answer choices, so the question is testing consistency of ideas. The previous sentences discuss how homes and factories replaced the beaver habitat. The answer will be consistent with the idea that wildlife no longer has a home there. Eliminate (B) and (C) because they are not consistent. Both (A) and (D) are consistent in meaning. However, (D) uses more precise language and is more concise. Eliminate (A). The correct answer is (D).
42.D
Note the question! The question asks for accurate data based on the graph, so it’s testing consistency. First, understand the labels and the data from the graph. The graph shows the population of Detroit over time. Then find the information in the sentence to match. The sentence says that the population of Detroit was reduced by almost half. Between 1990 and 2010 the population dropped from 1,000,000 to 900,000, which is not half; eliminate (A). Throughout the twentieth century, the population rose as well as declined; eliminate (B). Between 1890 and 1950 the population rose, so eliminate (C). From 1950 to 2010 the population dropped from about 1,900,000 to 900,000, which is over half. The correct answer is (D).
43.A
The vocabulary is changing in the answer choices, so the question is testing precision of language. For each phrase, it is only correct to use the verb have, not the preposition of. Eliminate (B) and (C). Using the word would changes the meaning of the sentence, so eliminate (D). The correct answer is (A).
44.B
The phrases are changing in the answer choices, so the question is testing consistency. Each choice uses a comparison word, so the items being compared must be consistent. Both (A) and (D) compare cities to parts, which is not consistent; eliminate (A) and (D). Choice (C) compares parts to parts, but it is unclear what the first parts refers to; eliminate (C). Choice (B) uses the word as to compare actions, so the sentence now compares what happens in other cities to what happened in parts of Detroit (returning to something like a “natural state”). The comparison is consistent. The correct answer is (B).
Section 3—Math (No Calculator)
1.B
The question asks for the solutions to an equation. Although the question asks for a specific value and there are numbers in the answer choices, plugging in the answers could be difficult given the lack of calculator use and the square roots. Instead, solve the equation for x. Start by adding 48 to both sides of the equation to get 3x2 = 48. Next, divide both sides by 3 to get x2 = 16. Then, take the square root of both sides to get x = ± 4. The correct answer is (B).
2.C
The question asks for the function that gives the hectares remaining to be harvested after d days. Translate the information in Bite-Sized Pieces and eliminate after each piece. One piece of information says that the farm workers can harvest 23 hectares a day. Therefore, each day there are 23 fewer hectares remaining to be harvested, so the function must include −23d. Eliminate (A) and (D), which do not contain this term. Compare the remaining choices. Choices (B) and (C) differ by the first term. The question states that the farmers are harvesting a 2.6 square kilometer plot, but the question refers to the function in hectares. The note after the question indicates that there are 100 hectares in 1 square kilometer, so 2.6 square kilometers is equivalent to 2.6 × 100 = 260 hectares. Eliminate (B), which does not contain this number. The correct answer is (C).
3.C
The question asks for the value of x in the equation. Because the question asks for a specific value and the answers contain numbers in increasing order, plug in the answers. Since 16 is divisible by 4 and 8, it is easier to multiply 
and 
by 16 than it is to multiply those fractions by 9, so start with (C). If x = 16, the equation becomes 13 − 
= 
− 5. This becomes 13 − 3(4) = 3(2) − 5, which simplifies to 13 − 12 = 6 − 5 or 1 = 1. This is true. The correct answer is (C).
4.A
The question asks for the value of y that makes the inequality true. Although the question asks for a specific value and there are numbers in the answer choices, plugging in the answers could be difficult given the negative values of some answer choices. Instead, solve the inequality for y. Start by multiplying both sides of the inequality by 4 to eliminate the fraction. The inequality becomes 4y < 3y − 2. Next, subtract 3y from both sides to get y < −2. Because the value of y must be less than −2, (B), (C), and (D) are all too large. The correct answer is (A).
5.B
The question asks for an expression that is equivalent to the one given. There are variables in the question and answer choices, so plug in. Make a = 3 and b = 2. The expression in the question becomes (3)(2)2 − 3(3)(2) + 2(2) − 6, which simplifies to (3)(4) − 18 + 4 − 6 and then to 12 − 20, which is −8. This is the target value; circle it. Now plug a = 3 and b = 2 into the answer choices to see which ones matches the target value. Choice (A) becomes (3 + 2)(2 − 3), which is (5)(−1) or −5. This doesn’t match the target; eliminate (A). Choice (B) becomes [(3)(2) + 2](2 − 3), which is (8)(−1) or −8. This matches the target; keep (B), but check the remaining answer choices just in case. Choice (C) becomes 2(3 + 3)(2 − 3), which is 2(6)(−1) or −12. Eliminate (C). Choice (D) becomes 2[(3)(2) − 3(3)] + 2(2 − 6), which is 2(6 − 9) + 2(-4). This further simplifies to 2(−3) + 2(−4), which becomes −6 − 8 = −14. Eliminate (D). The correct answer is (B).
6.D
The question asks for an equation that represents a graph. To find the best equation, plug points from the graph into the equations in the answer choices. It’s easiest to start with zeroes, but plugging in the origin often makes more than one equation work. Instead, start with (2, 0). In function notation, f(x) = y. Make x = 2 and f(x) = 0 in each answer choice and eliminate any choice that is not true. Choice (A) becomes 0 = (2)(2 + 2), or 0 = (2)(4), which is 0 = 8. Eliminate (A). Choice (B) becomes 0 = (2)(2 − 2), which is 0 = (2)(0) or 0 = 0. Keep (B) but check the remaining answers just in case. Choice (C) becomes 0 = (2)(2 + 2)2, which is 0 = (2)(4)2 or 0 = 32. Eliminate (C). Choice (D) becomes 0 = (2)(2 − 2)2, which is 0 = (2)(0)2 or 0 = 0. Keep (D). Next, plug in another point. It is hard to tell exactly where the line hits when x = 1, but it is positive between x = 0 and x = 2. When x = 1, (B) becomes f(1) = (1)(1 − 2) = (1)(−1) = −1 and (D) becomes f(1) = (1)(1 − 2)2 = (1)(−1)2 = 1. The value of f(1) should be positive, so eliminate (B). The correct answer is (D).
7.A
The question asks for the equation of a line that intersects line a. Because the two lines intersect at 
, that point must be on the second line. Therefore, plug x = 
and y = 2 into each answer choice and eliminate any that is not true. Choice (A) becomes 
− 3(2) = 4, which is 10 − 6 = 4 or 4 = 4. This is true, and no information is given about the line other than the point. Since this equation worked, it must be the equation of the line. The correct answer is (A).
8.D
The question asks for an equivalent form of an expression. There are variables in the answer choices, so plug in. Make x = 2. The expression becomes (2 + 2)(2 − 5) − 18, which is (4)(−3) − 18. This becomes −12 − 18 or −30. This is the target value; circle it. Now plug x = 2 into the answer choices to see which one matches the target value. Choice (A) becomes (2 − 4)(2 + 7), which is (−2)(9) or −18. This does not match the target, so eliminate (A). Choice (B) becomes 22 − 3(2) − 8, which is 4 − 6 − 8 or −10. Eliminate (B). Choice (C) becomes 22 − 3(2) − 25, which is 4 − 6 − 25 or −27. Eliminate (C). Choice (D) becomes (2 − 7)(2 + 4), which is (−5)(6) or −30. This matches the target. The correct answer is (D).
9.B
The question asks for an equivalent form of an expression. There are variables in the answer choices, so plug in. Since y must be greater than 3, make y = 4. The expression becomes 
, which is 
. To subtract fractions, make the denominators the same. One common denominator of 7 and 8 is 56. Multiply the numerator and denominator of 
by 7 to get 
. Multiply the numerator and denominator of 
by 8 to get 
. The expression becomes 
, which is 
. To divide by a fraction, multiply the numerator by the reciprocal of the denominator to get 1 × 
or −56. This is the target value; circle it. Now plug y = 4 into the answer choices to see which one matches the target value. Choice (A) becomes 3 − 4 or −1. This does not match the target, so eliminate (A). Choice (B) becomes 
, which is 
. Multiplying gives 
, which is −56. Keep (B) but check the remaining answer choices just in case. Choice (C) is the reciprocal of (B), so it will equal 
. Eliminate (C). Choice (D) is the numerator of (B), so it will equal 56. Eliminate (D). The correct answer is (B).
10.C
The question asks for the value of n given a function definition. Because the question asks for a specific amount and there are numbers in the answer choices, plug in the answers. 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. Before starting with the answers, find h(−3) because that is what the correct answer will equal. Plug x = −3 into the h function to get h(−3) = 9 −|−3 − 3| = 9 − |−6| = 9 − 6 = 3. The correct answer should give 3 as a value for the function. Start with (B), 3. If n = 3, then h(3) = 9 − |3 − 3| = 9 − |0| = 9. This doesn’t match the result for h(−3), so eliminate (B). It may not be clear if a greater or smaller value of n is needed, so just pick another answer choice to try. Try (A). If n = −6, then h(−6) = 9 − |−6 − 3| = 9 − |-9| = 9 − 9 = 0. This doesn’t match the value for h(−3), so eliminate (A). Try (C). If n = 9, h(9) = 9 − |9 − 3| = 9 − |6| = 9 − 6 = 3. This matches the value of h(−3). The correct answer is (C).
11.B
The question asks for the amount the school is required to spend on curriculum-based activities. Start by reading the final question and translate the information in Bite-Sized Pieces. The question states that the amount spent on curriculum-based activities is represented as x. The school has a monthly discretionary budget of $9,000, and the discretionary budget that month is represented as B, so B = 9,000. Additionally, the school must spend $320 on after-school clubs, and the amount spent on after-school clubs is represented as C, so C = 320. The equation becomes 320 = 0.08(9,000 − x). Solve for x. Start by multiplying both sides by 100 to get rid of the decimal: 32,000 = 8(9,000 − x). Divide both sides by 8 to get 4,000 = 9,000 −x. Subtract 9,000 from both sides to get −5,000 = −x. Multiply both sides by −1 to get x = $5,000. The correct answer is (B).
12.D
The question asks for the meaning of a number in context. Start by reading the final question, which asks for the meaning of the number 135. Then label the parts of the equation with the information given. The variable x is the number of years since the 2010 census, so P must be the population of County Y, in thousands. The equation becomes population (thousands) = 2,500 + 135(years since 2010). Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Choice (A) refers to an increase in population per year, and the 135 is multiplied by years in the equation. This is consistent with the labels, so keep (A) but check the remaining answers just in case. Choices (B) and (C) both refer to the population increasing by a certain amount every 135 years, so these answers are not consistent with the labels. Eliminate (B) and (C). Choice (D) also refers to an increase in population per year, so keep (D). The difference between (A) and (D) is the value of the increase. The equation represents the population in thousands, so 135 should be multiplied by 1,000 to give 135,000 as the actual population increase. Eliminate (A). The correct answer is (D).
13.C
The question asks for the value of b in an equation with exponents. When dealing with questions about exponents, remember the MADSPM rules. The DS part of the acronym indicates that Dividing matching bases means to Subtract the exponents. The bases on the left of the equation do not match, so use fractional exponents to simplify the equation. Radicals can be turned into fractional exponents by the rule power over root. Convert the radicals to fractional exponents to get 
. Next, subtract the exponents to get 
. Multiply the numerator and the denominator of the first fraction by 2 to get a common denominator of 4 on the exponents. The equation becomes 
, which is 
. The bases are the same, so the exponents must be equal. Therefore, b = 
. The correct answer is (C).
14.3
The question asks for the value of s in a system of equation. To find this, look for a way to eliminate the t terms. The t terms have the same coefficient with opposite signs, so stack and add the equations to make t disappear.
Divide both sides by 7 to get s = 3. The correct answer is 3.
15.25
The question asks for the value of x, which is a degree measure on a figure. Use the geometry basic approach. Start by labeling the figure with the given information. Mark that 
RSV is congruent to 
TUV and that 
TUV measures 65°. More information is known about triangle VUT, so look for a way to use that to find x. Opposite angles are equal, so the measure of 
UVT will also be x°. There are 180° in a triangle, so 
is 180 − 90 − 65 = 25°. Therefore, x° also equals 25°. The correct answer is 25.
16.38
The question asks for the number of student tickets that were sold. Use Bite-Sized Pieces to translate from English to math and then solve the resulting system of equations. Let s represent the number of student tickets sold and r represent the number of regular tickets sold. Since the 100-seat theater sold out, s + r = 100. Student tickets are $24, regular admission tickets are $36, and total ticket sales are $3,144, so 24s + 36r = 3,144. The question asks for the number of student tickets sold, so solve for s. Start with the first equation. Subtract s from both sides to get r = 100 − s. Substitute this value of r into the second equation to get 24s + 36(100 − s) = 3,144. Distribute the 36 to get 24s + 3,600 − 36s = 3,144. Combine like terms on the left side by subtracting to get −12s + 3,600 = 3,144. Subtract 3,600 from both sides to get −12s = −456. Divide both sides by −12 to get s = 38. The correct answer is 38.
17.
, .285, or .286
The question asks for the value of an expression. There are related variables in the question, so plug in numbers that make the equation 5x = 7y true. Make x = 7 and y = 5, so the equation becomes 5(7) = 7(5). Next, plug x = 7 and y = 5 into the expression to get 
= 
. The correct answer can be entered as 
, .285, or .286.
Section 4—Math (Calculator)
1.A
The question asks for an equivalent form of the provided expression. Although there are variables in the answer choices, plugging in on this question would be less efficient than simplifying. The expression is not too complicated, though, so simplifying is likely a more efficient approach. Distribute the 2 in front of the parentheses to get 2x − 10 + 3. Combine like terms to get 3x − 7. The correct answer is (A).
2.A
The question asks for the number of teaspoons a glass tube can hold. Begin by reading the question to find information on the glass tube. The question states that a glass tube can hold the 8.50 milliliters of liquid needed and that 1 teaspoon = 4.93 milliliters. Set up a proportion to determine the volume, making sure to match up the units: 
. Cross-multiply to solve for x: 8.50 = 4.93x. Divide both sides of the equation by 4.93 to get x ≈ 1.72 teaspoons. The correct answer is (A).
3.D
The question asks for the number of vials a lab assistant can centrifuge in a certain amount of time. Begin by reading the question to find information on the centrifuge rate. The question states that every fifteen minutes, a lab assistant can centrifuge 3 vials of blood. First, convert hours to minutes. Each hour has 60 minutes, so there are 4(6) = 240 minutes in 4 hours. Set up a proportion to determine the number of vials she can centrifuge in 4 hours, making sure to match up the units: 
. Cross-multiply to solve for x: 15x = 720. Divide both sides of the equation by 15 to get x = 48 vials. The correct answer is (D).
4.D
The question asks for a true statement based on the graph. The graph gives speed on the vertical axis and distance on the horizontal axis. Read each answer choice carefully and use Process of Elimination. Choice (A) refers to the x-intercept, but the graph never touches the horizontal x-axis; eliminate (A). Choice (B) states that the slowest speed is in the last 250 meters, but the slowest speed is at the beginning of the graph; eliminate (B). Choice (C) states that the runner’s speed increases steadily during the first 1,000 meters, but there is a decrease in speed between 250 and 500 meters; eliminate (C). Choice (D) states that the fastest speed is at 750 meters, and the peak of the graph is at that point along the horizontal axis. The correct answer is (D).
5.B
The question asks for the value of an expression given an equation. Start by finding the value of a from the equation. Divide both sides by 10 to get a = 
. Next, substitute 
for a in the expression to get 
. Get a common denominator by multiplying 
by 
. The expression becomes 
. Subtract within the parentheses to get 
. Multiply to get 
or 4. The correct answer is (B).
6.B
The question asks for the value of x that satisfies the equation. Since the question asks for a specific value and the answers contain numbers in increasing order, plug in the answers. Begin by labelling the answers as “x” and start with (B), −1. If x = −1, the equation becomes (−1 − 3)2 = 16. Subtract within the parentheses to get (−4)2 = 16. Square the left side to get 16 = 16. This is true, so stop here. The correct answer is (B).
7.B
The question asks for a probability, which is defined as 
. Read the number of possible outcomes table carefully to find the numbers to make the probability. There are 14 females who indicated volunteering, so that is the # of outcomes that fit requirement. There are 95 total females, so that is the total # of outcomes. Therefore, the probability is 
. The answer choices are expressed as decimals, so divide 14 by 95 to find that this is approximately 0.15. The correct answer is (B).
8.D
The question asks for the number of males that plan to work, relax, or volunteer over the summer, based on the table. Look up the numbers in the table and add them together. There are 17 males who plan to have a summer job, 33 who plan to relax, and 11 who plan to volunteer, for a total of 17 + 33 + 11 = 61 males who plan to do one of those activities. The correct answer is (D).
9.C
The question asks for the predicted number of females in the school who plan to travel based on the table. To calculate this, find the percent of the students surveyed who are females planning to travel and multiply that percent by the total population. There are 25 females who plan to travel out of 200 total students surveyed, so the percent is 
× 100 = 12.5% of the students are female and plan to travel. There are 1,200 students in the school, so there would be 
× 1,200 = 150 females in the school who plan to travel. The correct answer is (C).
10.C
The question asks for the cost of the shoes that Dana purchased. Since the question asks for a specific value and the answers contain numbers in increasing order, plug in the answers. Begin by labelling the answers as “cost of shoes,” and start with (B), $36. If the shoes were $36, then the shirt and purse together were the rest of the bill, or $81 − $36 = $45. However, the shoes cost 25 percent more than the shirt and purse combined, so this cost of the shoes is too low. Eliminate (A) and (B). Try (C), $45. If the shoes were $45, then the shirt and purse together were $81 − $45 = $36. To see if the shoes were 25 percent more than the other two items, find the difference in the costs, which is $45 − $36 = $9. This amount is 25% of $36, so these values fit the requirements of the question. The correct answer is (C).
11.A
The question asks for the percent value used to calculate the shipping charge. To calculate this, first find the cost of the order before shipping. If the shipping cost is $15.65 and the total with shipping is $211.30, then the order cost $211.30 − $15.65 = $195.65 before shipping. The percent becomes 
. The correct answer is (A).
12.C
The question asks for the cost of a frisbee. Since the question asks for a specific amount, plugging in the answers is an option. However, there is a lot of information about the cost of hats and frisbees, so this may get confusing. Instead, start by translating English to math, then solve the resulting system for the price of a frisbee. Let f represent the cost of a frisbee and h represent the cost of a hat. The question says that the total cost of the frisbees and hats is $72, so 5h + 9f = $72. The question also says that the cost of two hats and a frisbee is $14.50, so 2h + f = $14.50. Next, solve for the price of one frisbee, or the value of f One way to solve is to stack the equations and add to eliminate the price of hats. Multiply the equations so the coefficients on the price of hats are the same but with opposite signs. Multiply the first equation by 2 to get 10h + 18f = $144.00. Multiply the second equation by −5 to get −10h − 5f= −$72.50. Stack and add the equations.
Divide both sides by 13 to get f= $5.50. The correct answer is (C).
13.B
The question asks for a true statement given the equations of two lines. Choices (A), (B), and (C) state that the lines are the same line, perpendicular, or parallel, respectively. To determine whether any of these is true, find the slopes of the two lines. The first equation is in standard form: Ax + By = C. The slope of a line in standard form is 
. For this equation, A = 3 and B = 2, so the slope of this line is 
. The second equation is in slope-intercept form: y = mx + b. The slope of a line in slope-intercept form is m, so the slope of the line is 
. The two slopes are negative reciprocals, which means the lines are perpendicular. The correct answer is (B).
14.A
The question asks for the meaning of the constant and coefficient in the equation. Label the parts of the equation with the information given. The question states that m is the number of months since the loan was made, and y is the money, in dollars, that Stephen still owes. Therefore, the equation is the money, in dollars, that Stephen still owes = 1,200 − 75(the number of months since the loan was made). Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Choice (A) states that 75 is the rate of decrease in dollars per month and $1,200 is the original amount of the loan. Since 75 is multiplied by the number of months since the loan was made, and that term is subtracted from 1,200, this is consistent with the labels; keep (A). Choice (B) says that it will take 75 months to pay off the loan, but 75 is multiplied by the number of months. This is not consistent with the labels, so eliminate (B). Choice (C) states that 75 is the rate of increase in the total amount owed, but 75 × months since the loan was made is subtracted from, not added to, the amount owed. Eliminate (C). Choice (D) states that 75 is the rate of increase in the monthly payments, but again, there is not an increase because the equation features subtraction. Eliminate (D). The correct answer is (A).
15.C
The question asks for the average cost of a child’s meal. For averages, use the formula T = AN, in which T is the total, A is the average, and N is the number of things. Read the chart carefully to find the correct numbers to use. In the Children column, there are a total of 1,875 meals for a total cost of $24,750. The formula becomes 24,750 = A(1,875). Divide both sides by 1,875 to find that $13.20 = A. The correct answer is (C).
16.D
The question asks for a probability, which is defined as 
. Read the table carefully to find the numbers to make the probability. There are 1,143 male adults and 1,237 female adults who ordered chicken, so there are 1,143 + 1,237 = 2,380 total adults who ordered chicken. This is the number of outcomes you want. The total possible outcomes includes everyone who ordered chicken. There are also 924 children who ordered chicken, so there are 924 + 2,380 = 3,304 possible outcomes. Therefore, the probability is 
. The answer choices are expressed as decimals, so divide 2,380 by 3,304 to find that this is approximately 0.72. The correct answer is (D).
17.A
The question asks for the answer that is equivalent to two Newtons. Look through the question to find a mention of Newtons. In the equation, R is drag force in Newtons, so the correct answer will make R = 2. The other variables are C as the coefficient of drag and v as velocity in meters per second. Plug the values for C and v in the answer choices into the equation to determine which gives 2 for R. Start with (A). If the coefficient of drag is 1 and velocity in meters per second is 2, then C = 1 and v = 2. Plug those values into the equation to get R = 
, which becomes R = 
or R = 2. This matches the value given in the question, so stop here. The correct answer is (A).
18.A
The question asks for an expression for the amount a customer would pay for two pairs of shoes during a sale. Translate the information in Bite-Sized Pieces and eliminate after each piece. The question states that the tax rate of 6 percent is applied to the whole purchase, so everything should be multiplied by 1.06 to reflect the total (1) plus the additional 6 percent (0.06). Eliminate (C), which only has the 1.06 multiplied by one term, and (D), which does not have 1.06 at all. The question also states that the customer receives a 30 percent discount on a second pair of shoes after purchasing the first at regular price, so the price of the second shoe should be added to the first, not subtracted from it. Eliminate (B). The correct answer is (A).
19.B
The question asks for a true statement based on the data in a histogram. Read the numbered statements carefully and use Process of Elimination. There are various statistical measures in the statements, so start with the easiest to calculate: mode and range. Statement (III) says that the mode is equal to the range. The mode is the most commonly occurring value, so in this case it will be the bar with the most students, which is 5. The range of a list of values is the greatest value minus the least value, so in this case, that is 5 − 0 = 5. Because the mode and range are equal, (III) is true. Eliminate (A) and (C), which do not contain statement (III). Compare the remaining answer choices. Choice (D) includes statement (II), which indicates that the median is equal to the mean. The median is the value in the middle of all the values, when all the values are arranged consecutively. There are 6 students who sold 0 barrels of popcorn, 2 who sold 1 barrel, 3 who sold 2, 3 who sold 3, 7 who sold 4, and 9 who sold 5. Therefore, there are 6 + 2 + 3 + 3 + 7 + 9 = 30 students total. Because there is an even number of students, the median will be average of the 15th and 16th students. Starting from the lower number of barrels of popcorn, there are 6 + 2 + 3 = 11 students who sold 0 to 2 barrels. The next 3 students sold 3 barrels, bringing the list up to 14 students who sold 0 to 3 barrels. Because 7 students sold 4 barrels of popcorn, the 15th and 16th student both sold 4 barrels of popcorn. Therefore, the median is 4. To find the mean or average, use the formula T = AN, in which T is the total, A is the average, and N is the number of things. To find the total number of barrels, multiply the number of students who sold a certain number of barrels by the number of barrels they sold and add up the results. This becomes (6 × 0) + (2 × 1) + (3 × 2) + (3 × 3) + (7 × 4) + (9 × 5), which is 0 + 2 + 6 + 9 + 28 + 45 = 90. Therefore, T = 90 and N = 30 for the number of students. The average formula becomes 90 = A(30). Divide both sides by 30 to get 3 = A. This does not match the median, so statement (II) is false. Eliminate (D) which contains statement (II). The correct answer is (B).
20.D
The question asks for a system of inequalities that models a specific situation. Translate the information in Bite-Sized Pieces and eliminate after each piece. One piece of information says that the tube must contain at least 12 ounces, but no more than 16 ounces. Because the amount in the tube is a + b, the answer should contain 12 ≤ a + b ≤ 16. Eliminate (A) and (B) which do not include this inequality. Compare the remaining answer choices. The difference between (C) and (D) is the third inequality: specifically, whether 0.10 should be multiplied by (a + b). The question states that the product should have a concentration of more than 10% active ingredient. The active ingredient should be more than 10 percent of the total product, so the correct answer must multiply 0.10 by the total product. Eliminate (C) which does not multiply 0.10 by any other term. The correct answer is (D).
21.A
The question asks for the number of pets in the pet shop. Since the question asks for a specific value and the answer choices contain numbers in decreasing order, plug in the answers. Begin by labelling the answers as “total pets” and start with (B), 120. If there are 120 total pets and 40% of those pets are dogs, then 120 × 0.40 = 48 of the pets are dogs. If 25% of those pets are cats, then 120 × 0.25 = 30 of the pets are cats. Therefore, there are 48 − 30 = 18 more dogs than cats. The question states that there are 36 more dogs than cats, so eliminate (B). Since the numbers of cats and dogs were too close together, the total number of pets must be too small; eliminate (C) and (D) as well. If this isn’t obvious, do the calculations on (A), 240. With 240 total pets, there would be 96 dogs and 60 cats, or 36 more dogs than cats. The correct answer is (A).
22.B
The question asks for the equation of h(x) in terms of g(x). The graph of h(x) is the same as the graph of g(x) at every point where y is greater than or equal to 0, but for all the points where y is less than 0 on the graph of g(x), the graph is flipped from below the x-axis to above it on the graph of h(x). The transformation that would cause this would be absolute value, which is (B). Choice (A) would flip all values of g(x) over the x-axis, but only the negative y-values were flipped. Choice (C) would shift g(x) up three units, but the positive values are not shifted, and the negative values are reflected. Choice (D) would shift g(x) to the right three units, but once again the positive values aren’t shifted. The correct answer is (B).
23.C
The question asks for the length of side 
on a figure. Use the geometry basic approach. Start by labeling the figure with the given information. Label NP as 7 and LN as 18. Mark angles NPO and MLN as congruent.
Since the two triangles have a congruent angle and share angle N, the third angles of the triangles will be congruent as well. Therefore, the triangles are similar, with triangle NPO corresponding to triangle NLM. The corresponding sides are difficult to see, since the figure is not drawn to scale and the angle in the lower left of NLM is congruent to the angle at the top of NPO. Redraw the two triangles separately using the description in the question to get the correct scale.
Similar triangles have proportional sides, so set up the proportion with the known sides compared to NO and its corresponding side MN: 
. Plug the information given for the lengths of NP and LN into the proportion to get 
. The question states that the length of 
is 1 unit less than 3 times the length of 
, so translate this into MN = 3(NO) − 1. Put the right side of this equation into the proportion for MN to get 
. To solve for NO, cross-multiply to get 18(NO) = 7[3(NO) − 1] or 18NO = 21NO − 7 Subtract 21NO from both sides to get −3NO = −7, then divide both sides by −3 to get 
. The correct answer is (C).
24.C
The question asks for the relationship between two variables. If the fan group increases by a certain percentage each month, then the actual number of additional members each month increases as the size of the group increases. This is exponential growth, so eliminate (B) and (D), which indicate linear growth. Compare the remaining answer choices. The difference between (A) and (C) is when the higher numbers will occur. Because the size of the group is increasing, later dates will have higher membership numbers; eliminate (A). The correct answer is (C).
25.D
The question asks for the meaning of an expression in context. Start by reading the final question, which asks for the meaning of the expression 
. Then label the parts of the equation with the information given. The question states that x is the length of the sides of the triangular ends and y is the length of the rectangular faces. The equation becomes 
. Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Since the expression 
only includes the sides of the triangular faces as a variable, it doesn’t refer to the rectangular faces; eliminate (B) and (C). Compare the remaining answer choices. The difference between (A) and (D) is the number of triangular faces included. In the equation, the term 
is multiplied by 2, which would result in 
. Therefore, 
must represent both the triangular sides. Eliminate (A). The correct answer is (D).
26.C
The question asks for an equivalent form of an expression. There are variables in the answer choices, so plug in. Make y = 2. The expression becomes (3 − 2)2 − (3 − 2), which is (1)2 − 1 or 0. 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 − 2 or 1. This does not match the target, so eliminate (A). Choice (B) becomes 22 − 7(2) + 6, which is 4 − 14 + 6 or −4; eliminate (B). Choice (C) becomes (3 − 2)(2 − 2), which is (1)(0) or 0; keep (C), but check (D) just in case. Choice (D) becomes 9 − 22, which is 9 − 4 or 5; eliminate (D). The correct answer is (C).
27.B
The question asks for the percent increase from a patient’s actual height to that predicted by the line of best fit. Percent change is defined as 
. The child who is exactly 8 years old is 40 inches tall, and the line of best fit indicates that someone with an age of 8 will have a height of 50 inches. The difference in heights is 50 − 40 = 10 inches. Because the question asks for a percent increase, use the smaller number as the original. The percent change is 
= 25%. The correct answer is (B).
28.396
The question asks for the volume of a box. The dimensions of the box are described in the word problem, so start by translating English to math. The question states that the width is 2 inches more than its length, so w = l + 2. The question also states that the height is 5 inches less than its length, so h = l − 5. The two smallest dimensions would be the length and the height, because l + 2 is greater than l and l − 5. The formula for the area of a rectangle is A = lw. The area of the smallest face is 36, so the formula becomes 36 = l(l − 5). This simplifies to 36 = l2 − 5l Solve by subtracting 36 from both sides to set the quadratic equal to zero to get 0 = l2 − 5l − 36. Factor the quadratic; −9 and 4 add to −5 and multiply to −36, so the quadratic factors to 0 = (l − 9)(l + 4). The values of l are 9 and −4, but a length cannot be negative, so use l = 9. The width is l +2 = 9 + 2 = 11, and the height is l − 5 = 9 − 5 = 4. The formula for the volume of a rectangular box is V = lwh, so plug in the values to determine the volume of the box. The formula becomes V = (9)(11)(4) = 396. The correct answer is 396.
29.1
The question asks for the value of y in a system of equations, so solve the system for y. Look to eliminate the x terms by making the coefficients on x in the two equations the same but with opposite signs. Multiply the first equation by 2 to get 10x − 6y = 14, and multiply the second equation by −5 to get −10x − 5y = −25. Stack and add the equations.
Divide both sides by −11 to get y = 1. The correct answer is 1.
30.56.4 or 56.5
The question asks for the percent of runners completing the marathon in under four hours that were women. The question doesn’t give an actual number for the runners, but percent information about the unknown total is given. Therefore, plug in for the unknown total. Make the total number of runners 1,000. If 45 percent of the runners were men, then 0.45 × 1,000 = 450 of the runners were men. If the rest were women, then 1,000 − 450 = 550 of the runners were women. If 64 percent of the men completed the marathon in under four hours, then 0.64 × 450 = 288 of the men completed the marathon in under four hours. Similarly, if 68 percent of the women completed the marathon in under four hours, then 0.68 × 550 = 374 women completed the marathon in under four hours. The total number of runners who completed the marathon in under four hours is 288 + 374 = 662, so the percent becomes 
percent of the runners who completed the marathon in less than four hours. The correct answer can be expressed as 56.4 or 56.5.
31.66.2
The question asks for the percent of runners who completed the marathon in under four hours. The question doesn’t give an actual number for the runners, but percent information about the unknown total is given. Therefore, plug in for the unknown total. Make the total number of runners 1,000. If 45 percent of the runners were men, then 0.45 × 1,000 = 450 of the runners were men. If the rest were women, then 1,000 − 450 = 550 of the runners were women. If 64 percent of the men completed the marathon in under four hours, then 0.64 × 450 = 288 of the men completed the marathon in under four hours. Similarly, if 68 percent of the women completed the marathon in under four hours, then 0.68 × 550 = 374 women completed the marathon in under four hours. The total number of runners who completed the marathon in under four hours is 288 + 374 = 662, so the percent becomes 
. The correct answer is 66.2.
