PSAT/NMSQT Prep with Practice Tests - Princeton Review 2021

Practice Test 2: Answers and Explanations
Practice Test 2

PRACTICE TEST 2 ANSWER KEY

PRACTICE TEST 2 EXPLANATIONS

Section 1—Reading

1.D

This question asks how to best describe the passage’s point of view. Because this is a general question, it should be done after all the specific questions. In the second paragraph, the narrator refers to John in the third person: He had forgotten and was even more surprised than ashamed. Eliminate (A). In lines 45—47, the narrator says that the blood slowly came to his face, which began to burn with recognition. Since the author is using figurative language here, the point of view of the passage would not be described as a disinterested reporter listing objective facts. Eliminate (B). In the last paragraph, John is described as embarrassed. The narrator is not judging him here but instead is describing his emotions through the course of his conversation with May, so eliminate (C). Choice (D) is a good match because the narrator notes in the last paragraph that it was No wonder they couldn’t have met as if nothing had happened. This line supports the notion that the narrator relates to Marcher’s feelings. The correct answer is (D).

2.B

This question asks how the emotions of John Marcher shift over the course of the passage. Because this is a general question, it should be done after all the specific questions. In the second paragraph, John Marcher is described as being surprised that he had forgotten a conversation with May. In lines 45—47, the text describes a shift in John Marcher’s emotions: Then it was that…a light broke for him…which began to burn with recognition. Incredulity means disbelief, which does not match surprised, and there is no support for begrudging acceptance later in the passage. Eliminate (A). Confusion is a closer match to being surprised and having forgotten, and disconcerted recognition matches the description in lines 45—47, so keep (B). There is no evidence that John Marcher feels disdain nor unrequited love, so eliminate (C). While John Marcher is described as embarrassed (lines 55—56), the word painful is too extreme and isn’t supported by the text, so eliminate (D). The correct answer is (B).

3.C

This question asks about what the passage suggests about John Marcher and May Bertram’s conversation. Because this is the first question in a paired set, it can be done in tandem with Q4. Consider the answers for Q4 first. In the lines for (4A), May Bertram says, “…you told me something I’ve never forgotten…it was that tremendously hot day when we went to Sorrento,” recalling a past conversation with John Marcher. Look to see whether these lines support any of the answers for Q3; they support (3C), which says they are reminiscing about former times and conversations. Draw a line connecting these two answers. The lines for (4B) don’t support any of the answers for Q3, so eliminate (4B). The lines for (4C) discuss John feeling embarrassed and May feeling sorry for him. Choice (3B) is a Could Be True trap answer, since sharing personal information might make someone embarrassed, but John and May are discussing a conversation they had years before, not sharing new information. Therefore, the lines in (4C) don’t support any of the answers in Q3, so eliminate (4C). The lines in (4D) don’t support any of the answers in Q3, so eliminate (4D). Without any support from Q4, (3A), (3B), and (3D) can be eliminated. The correct answers are (3C) and (4A).

4.A

(See explanation above.)

5.C

The question asks what the word claim means in line 12. Go back to the text, find the word claim, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. In line 12, the narrator notes that May was making no claim on John, and contrasts this with the fact that, with another woman, John might have feared the recall…of some imbecile “offer.” Therefore, claim must mean something like “request.” Application and Remark do not match “request,” so eliminate (A) and (B). Appeal matches “request” more closely than Demand, which is too strong. Eliminate (D). The correct answer is (C).

6.A

The question asks what Marcher’s “loss” refers to in line 16. Use the given line reference to find the window. Lines 15—18 state that John was conscious…of a loss and already saw an interest in the matter of her mention. This supports (A), so keep it. Line 13 states that May had made no claim on him of a compliment, but not that Marcher had missed an opportunity to compliment her, so eliminate (B). There’s no discussion of Marcher longing to return to Sorrento, so eliminate (C). There’s no evidence that Marcher’s speech involved declaring love for May, so eliminate (D). The correct answer is (A).

7.D

The question asks what Marcher and May’s conversation suggests Marcher had previously told May. Because this is the first question in a paired set, it can be done in tandem with Q8. Consider the answers for Q8 first. The lines for (8A) don’t mention what Marcher told May, only that he told her something that May has never forgotten. These lines don’t support any of the answers for Q7, so eliminate (8A). The lines for (8B) mention what was not said—neither a compliment or a mistake, but they don’t discuss what March told May. Therefore, these lines don’t support any of the answers for Q7, so eliminate (8B). The lines for (8C) don’t discuss what was said, so they don’t support any of the answers for Q7; eliminate (8C). In the lines for (8D), Marcher talks to May about “…having taken you so far into my confidence.” This suggest that was he told her must have been personal, which supports (7D). Draw a line connecting (7D) and (8D). Without any support from Q8, (7A), (7B), and (7C) can be eliminated. The correct answers are (7D) and (8D).

8.D

(See explanation above.)

9.A

The question asks what the word allusion means in line 57. Go back to the text, find the word allusion, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. In lines 53—54, May asks Marcher “if the thing you then spoke of has ever came to pass?” Lines 55—57 indicate that Marcher feels embarrassed about what May asked, and May feels sorry for him, as if her allusion had been a mistake. Therefore, the word allusion must mean something like “mention” or “remark.” Reference matches “mention,” so keep (A). Image doesn’t match “mention,” so eliminate (B). What May mentioned was not a quotation, so eliminate (C). Apparition means “ghost” or “spirit,” which doesn’t match “mention.” The correct answer is (A).

10.C

The question asks how the focus of the speech changes. Because this is a general question, it should be done after all the specific questions. The passage begins with an explanation of why and how Churchill formed a new government; he begins the description in lines 6—7, On Friday evening last I received His Majesty’s commission to form a new Administration. Then in line 42, Churchill transitions to speaking of one of the greatest battles in history; in the last paragraph, he says the aim of the new government and the country is victory, and he urges the new government and country to go forward together with…united strength. Look for an answer choice that matches this prediction. Choice (A) references both of these topics but lists them in the opposite order; eliminate (A). Choice (B) is too narrow because it focuses only on the formation of the War Cabinet, as opposed to the government as a whole, so eliminate (B). The passage first discusses formation of a new government through appointments and then goes on to rally that government to the shared cause of defeating Germany. This matches (C), so keep it. The passage does accept defeat but rather urges a dedication to victory, so eliminate (D). The correct answer is (C).

11.A

The question asks what the word prosecute means in line 4. Go back to the text, find the word prosecute, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. The text says that there is a united and inflexible resolve of the nation to prosecute the war with Germany to a victorious conclusion. Therefore, to prosecute the war must mean something like “pursue” the war. Litigate and accuse both refer to another meaning of prosecute, “to bring legal action against,” so eliminate (B) and (C). Fight the war matches the prediction of “pursue” the war, so keep (A). Enforce does not mean “pursue,” so eliminate (D). The correct answer is (A).

12.D

The question asks why Churchill claims his administration must be formed more quickly than usual. Notice that this is the first question in a paired set, so it can be done in tandem with Q13. Look at the answer choices for Q13 first. The lines for (13A) say only that Churchill received His Majesty’s commission to form a new Administration, not why that administration needed to be formed. These lines do not support any of the answers to Q12, so eliminate (13A). The lines for (13B) say that It was necessary that this should be done in one single day, on account of the extreme urgency and rigour of events. This information matches (12D), indicating that the current situation requires unusual measures. Draw a line connecting (13B) and (12D). In the lines for (13C), Churchill asks for allowances…for any lack of ceremony due to the quick nature of the political reconstruction. However, these lines do not explain why his actions had to be quick; they don’t support any of the answers to Q12, so eliminate (13C). The lines for (13D) discuss why the British need to prevail in their fight, not why Churchill needed to form his administration quickly. These lines do not support any of the answers for Q12, so eliminate (13D). Without any support in the answers from Q13, (12A), (12B), and (12C) can be eliminated. The correct answers are (12D) and (13B).

13.B

(See explanation above.)

14.D

The question asks what can be inferred about Churchill’s administration. Notice that this is the first question in a paired set, so it can be done in tandem with Q15. Look at the answer choices for Q15 first. The lines for (15A) say that A War Cabinet has been formed of five Members, representing…the unity of the nation. Check the answers for Q13 to see if any of the answers are supported by these lines. At first, they may seem to support (14B), but this is a Mostly Right/Slightly Wrong trap answer: (14B) contains the word all, which is too strong to be supported by the passage. Eliminate (15A) because it does not support any of the answers for Q14. The lines for (15B) state that the appointment of the other Ministers usually takes a little longer, but…when Parliament meets again…the administration will be complete in all respects. This information matches (14D), indicating there are some unfilled positions. Draw a line connecting (15B) and (14D). The lines for (15C) mention that the Speaker took the necessary steps, but say nothing about Churchill’s administration; these lines don’t support any of the answers to Q14, so eliminate (15C). The lines for (15D) state that We have before us many, many long months of struggle and of suffering. This refers to the war with Germany, and doesn’t support any of the answers from Q14. Eliminate (15D). Without any support in the answers from Q15, (14A), (14B), and (14C) can be eliminated. The correct answers are (14D) and (15B).

15.B

(See previous explanation.)

16.A

This question asks why Churchill makes the statement that he has nothing to offer but blood, toil, tears and sweat. Use the given line reference to find the window. In lines 60—65, Churchill states, We have before us an ordeal of the most grievous kind. We have before us many, many long months of struggle and of suffering. You ask, what is our policy? I can say: It is to wage war, by sea, land and air, with all our might and with all the strength that God can give us. His use of physical imagery serves to show the amount of exertion Churchill is willing to expend on fighting the war. Look for an answer choice that matches this prediction. The phrase deep level of commitment to the war effort matches the prediction, so keep (A). Eliminate (B) because it is contradicted by the remainder of the passage, as Churchill strongly speaks of victory. Choice (C) says that there is not much that Churchill can offer, but Churchill emphasizes his dedication; the reference is also not about military resources specifically, so eliminate (C). Choice (D) is a Mostly Right/Slightly Wrong trap answer—Churchill’s statement is about his dedication to the war effort, not to the governing coalition. Eliminate (D). The correct answer is (A).

17.C

The question asks for the rhetorical effect of repeating “victory” and “no survival” in the final paragraph, so read the last paragraph. Lines 67—73 state You ask, what is our aim? I can answer in one word: It is victory, victory at all costs…. for without victory, there is no survival. Let that be realized; no survival for the British Empire, no survival for all that the British Empire has stood for. Churchill’s message is that if Britain does not win the war, the British Empire will fundamentally change, and his repetition of the phrases serves to emphasize that point. Look for an answer choice that matches this prediction. Eliminate (A) because lines 75—76 state that Churchill has hope that their cause will not be suffered to fail. Eliminate (B) because these words are used for emphasis rather than to describe any specific strategy. Keep (C) because it is supported by the text; both of these terms are used to stress the importance of the outcome of the war for the British. Although Churchill ends the speech with optimism, that is not the purpose of these phrases; in these lines, Churchill declares that there would be no survival for Britain without victory; he is emphasizing what is at stake, so eliminate (D). The correct answer is (C).

18.B

The question asks what the word suffered means in line 76. Go back to the text, find the word suffered, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. The text says that mankind will move forward towards its goal. But I take up my task with buoyancy and hope. I feel sure that our cause will not be suffered to fail among men. Therefore, suffered must mean something like “permitted”—Churchill believes that their cause (victory in the war) will not fail. Both endured and tolerated mean “withstood suffering”; these are Could Be True trap answers that do not match “permitted.” Eliminate (A) and (C). Allowed matches “permitted,” so keep (B). Eliminate (D) because endorsed means “approved,” which does not match “permitted” to fail. The correct answer is (B).

19.C

The question asks what the author believes about South Chicago. Notice that this is the first question in a paired set, so it can be done in tandem with Q20. Look at the answer choices for Q20 first. In the lines in (20A), the author describes South Chicago as the city’s most isolated community. Check the answers for Q19 to see if any of the answers are supported by these lines. They support (19C), so draw a line connecting (20A) and (19C). The lines in (20B) mention the aesthetics of the area but do not go as far as to suggest it should be a popular vacation destination like (19A). The lines for (20B) don’t support any of the answers for Q19, so eliminate (20B). Choice (20C) is a Deceptive Language trap answer: the description powerful stench seems to match the phrase smelly nature in (19D), but (19D) says that South Chicago embodies the dirty, smelly nature of American industry in general, and the author does not make this comparison in the passage. Eliminate (20C). The lines for (20D) describe South Chicago as the heart of American industrial might, which does not directly support any answer choice from Q19. Eliminate (20D). Without any support from the answer choices in Q20, (19A), (19B), and (19D) can be eliminated. The correct answers are (19C) and (20A).

20.A

(See explanation above.)

21.A

The question asks why the author includes a list of restaurant names. Use the given line reference to find the window. Lines 19—21 provide examples of small taverns and diners. The author mentions such restaurants as a part of South Chicago’s modest neighborhoods and says, There’s nothing fanciful about this area. Choice (A) matches these lines, so keep (A). Eliminate (B) and (D), as the author does not discuss visitors to the area. Choice (C) can also be eliminated: the author does not discuss the variety of restaurants. The correct answer is (A).

22.B

The question asks what the word suspended means in line 38. Go back to the text, find the word suspended, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. In the text, suspended is used to describe the belts, pipes, and railroad overpasses that go in, out, and over the buildings, therefore, suspended must mean something like “up in the air.” Drooping means “hanging downward,” which doesn’t match “up in the air,” so eliminate (A). Hanging matches “up in the air,” so keep (B). Slumbering means “sleeping;” it doesn’t match “up in the air,” so eliminate (C). Fixed means “securely fastened,” which does not match “up in the air,” so eliminate (D). The correct answer is (B).

23.A

The question asks for what comparison to the image of steel mills is made in the passage. Notice that this is the first question in a paired set, so it can be done in tandem with Q24. Look at the answer choices for Q24 first. The lines in (24A) discuss neighborhoods, and the lines in (24B) describe a highway. Neither of these windows mentions steel mills at all. Therefore, these lines don’t support any of the answers for Q23, so eliminate (24A) and (24B). The lines in (24C) support (23A), describing the steel mills as the man-made equivalent of the Rockies. Draw a line connecting (23A) and (24C). Although these lines also reference a football field, they do not say that the steel mills are like football fields; they only say that some of the mills are three times the size of a football field. These lines also mention aircraft, but this reference is not part of a comparison. Choice (24D) describes the function of the steel mills but does not draw a comparison to any of the answer choices in Q23. Eliminate (24D). Without any support in the answer choices from Q24, (23B), (23C), and (23D) can be eliminated. The correct answers are (23A) and (24C).

24.C

(See explanation above.)

25.B

The question asks what the word consumption means in line 63. Go back to the text, find the word consumption, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. In the text, consumption refers to the use of modern comforts such as the can openers and knives, refrigerators and cars, bridges and skyscrapers produced by steel mills. The correct answer should mean something like “purchase” or “use.” Choice (A) is a Could Be True trap answer: eating is a synonym of consumption, but it does not match “purchase” or “use.” Eliminate (A). Choice (B), expenditure, matches “purchase,” so keep it. Neither corrosion nor burning means “purchase” or “use.” Eliminate (C) and (D). The correct answer is (B).

26.C

The question asks for the primary purpose of the last paragraph in the context of the passage. Read the last paragraph, which discusses how much the local population still depends on the steel mills, and states that there are only 15 million working in the mills now, and describes some of the mills as abandoned and collapsing. The passage as a whole discusses the steel mills of South Chicago, and the final paragraph describes what the mills are like now. Although the author describes the mill owners as complacent, the primary purpose of the paragraph is not to criticize them. Eliminate (A). Although this paragraph describes abandoned factory buildings, the primary purpose is not to lament the abandoned property. Eliminate (B). Choice (C) is supported by the descriptions in this paragraph. Keep (C). Eliminate (D), as the author never proposes specific changes for problems in the industry. The correct answer is (C).

27.D

The question asks for a claim about domestic steel production that is supported by the graph. Work through each answer choice using the graph. Domestic steel production had periods of decrease as well as increase from 1950 to 2000; eliminate (A) and (B). Eliminate (C), as the peak of domestic steel production occurred in the 1970s, not the 1960s, and had a steep decline in the 1980s. Choice (D) is supported by the graph: the domestic steel production was just under 100 million tons in 1950 and just over 100 million tons in 2000, so the net production had increased slightly. The correct answer is (D).

28.B

The question asks for an inference based on both the passage and the graph. First, work through each answer choice using the graph. According to the graph, domestic steel production reached a peak in the mid-1970s, so keep (A). Choice (B) states that U.S. steel production showed growth followed by significant decline. This is supported by the graph, which shows a general increase in steel production to about 1973, followed by a decline. Keep (B). The graph does not directly support any claims about either the size of the steel mill workforces or air pollution, so eliminate (C) and (D). Next, look for support in the passage for (A) or (B). Lines 52—54 mention the 1960s as time when the steel mills employed large numbers, but the passage does not state that the mills reached their greatest productivity in the mid-1970s. Eliminate (A). Lines 45—56 discuss how the first of the mills was built in the 1850s. Within one hundred years, these steel mills produced more steel…than anywhere else in the world. This supports the claim that the steel industry grew from the 1850s to the start of the graph at 1950. The correct answer is (B).

29.C

The question asks what the authors of the passage most likely believe. Because this is a general question, it should be done after all the specific questions. Work backwards from the answers to find evidence in the passage. The text never states that burning should be done semi-annually (which means twice a year), so eliminate (A). According to lines 24—30, late spring burning has been the recommendation since the early 1970s and has maintained the Flint Hills grassland, so eliminate (B). Lines 35—37 state, Burning in late spring…generates more ozone than burning in winter or early spring, and lines 52—54 state, Despite long-standing recommendations that tallgrass prairie be burned only in late spring, the data supporting this policy is equivocal (which means the data could be interpreted in more than one way). These lines support (C), so keep it. The last paragraph states that the historical studies on burning times are inconclusive and then cites a recent study which found that the timing of burning had no significant effect, so eliminate (D). The correct answer is (C).

30.C

The question asks what does NOT influence decisions on the timing of seasonal burns. Because there is no line reference and the entire passage is about the timing of seasonal burns, this question should be done after the other specific questions. Pay attention to the word NOT in the question. Use Process of Elimination to eliminate three answer choices that do influence decisions on the timing of seasonal burning. Eliminate (A) and (B) since lines 4—8 say that biomass production and control of specific plant species do influence when grasslands are burned. According to lines 32—35, Concentrated smoke from grass fires produces particles that facilitate tropospheric ozone production; this is a consequence of en masse burning (many fires burning at once), NOT something that would influence decisions on the timing of seasonal burns, so keep (C). Lines 50—51 say that ranchers often burn in unison when weather conditions are favorable, so eliminate (D). The correct answer is (C).

31.B

The question asks for something that is suggested about the Kansas Flint Hills. Notice that this is the first question in a paired set, so it can be done in tandem with Q32. Look at the answer choices for Q32 first. The lines for (32A) say that for The Flint Hills…frequent burning is integral to its preservation and economic utilization. Check the answers for Q31 to see if any of the answers are supported by those lines. They support (31B), so draw a line connecting (31B) and (32A). Consider the lines for (32B), which say that a good understanding of the consequences of burning at different times of the year is necessary to maintaining the Flint Hills. This answer does suggest an ecologically sensitive area, but it does not describe a need for extreme caution; these lines do not support any of the answers for Q31, so eliminate (32B). The lines for (32C) say that Burning earlier in spring has been regarded as undesirable because it putatively…lowers monthly weight gains of steers compared to burning in late spring, which may seem to support (31D). However, this is a Deceptive Language trap answer. Putatively means “supposedly,” and lines 60—68 suggest that burning grasses in the early spring may support species that are beneficial to the diet of grazers. Therefore, (32C) does not support any of the answers to Q31, so eliminate (32C). The lines for (32D) mention grasses and forbs, but the text does not suggest that these must be studied further. These lines do not support any of the answers for Q31, so eliminate (32D). Without any support in the answers from Q32, (31A), (31C), and (31D) can be eliminated. The correct answers are (31B) and (32A).

32.A

(See explanation above.)

33.A

The question asks what the word practices means in line 49. Go back to the text, find the word practices, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. The text says that burning exclusively in late spring is one of the cultural practices of the Flint hills. Therefore, practices must mean something like “customs.” Traditions matches “customs,” so keep (A). Neither rehearsals, accomplishments, nor chores matches “customs,” so eliminate (B), (C), and (D). The correct answer is (A).

34.D

The question asks what the word equivocal means in line 54. Go back to the text, find the word equivocal, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. The text says that the data supporting burning grassland only in late spring…is equivocal. The rest of the paragraph describes examples of uncertain findings, such as that It was not known if [grass] biomass was reduced by early-spring burning or if the differences were a site effect rather than a treatment effect. Therefore, equivocal must mean something like “uncertain.” Wrong and misleading do not mean “uncertain,” so eliminate (A) and (B). Ambivalent is another possible definition of equivocal, but it does not mean “uncertain;” this is a Could Be True trap answer because it doesn’t match the meaning of the word in this context, so eliminate (C). Unclear matches “uncertain,” so keep (D). The correct answer is (D).

35.B

The question asks what can be inferred about Symphoricarpos orbiculatus. Look for the lead words Symphoricarpos orbiculatus, and read a window around the lines to find the answer in the passage. Lines 68—71 say that Burning in late spring has been considered the most effective time to control invasive shrubs, but Symphoricarpos orbiculatus was the only woody species that declined with repeated late spring burning. Therefore, Symphoricarpos orbiculatus is one of the invasive shrubs. Eliminate (A), (C), and (D), which do not match the prediction. The correct answer is (B).

36.D

This question is the best evidence question in a paired set. Q35 was a specific question, so simply look at the lines used to answer the previous question. The lines used in the prediction were 68—71. The correct answer is (D).

37.C

The question asks which claim about grasses is supported by the graph. Work through each answer choice using the figure. Eliminate (A) because spring burning does not always have a higher biomass than that of autumn or winter burning. Eliminate (B) because biomass increases and decreases similarly over time for areas burned in autumn, winter, or spring. Choice (C) is supported by the graph: the amounts of biomass shown for autumn, winter, and spring burning are similar, so keep (C). Rainfall is not represented in the figure, nor is it clear whether the graph depicts the year 2012, so eliminate (D). The correct answer is (C).

38.C

The question asks why the author of Passage 1 mentions the paper by University of Chicago physicists Sidney Nagel and Thomas Witten. Use the given line reference to find the window. Lines 17—23 state that University of Chicago physicists Sidney Nagel, Thomas Witten, and their colleagues wrote an influential paper about this process in 1997, which focused mainly on suspended spherical particles, but it was not until the Yodh team’s recent experiments that the surprising role played by suspended particle shape was discovered. It’s clear that their paper was influential and that they used spherical particles, and their work preceded that done by Yodh’s team. Look for an answer choice that matches this prediction. The passage doesn’t mention any reason to think that Nagel and Witten could have discovered the impact of ellipsoid particles, so eliminate (A). Eliminate (B) because impediment means “obstacle,” and Passage 1 doesn’t indicate that Nagel and Witten’s work in any way limited other studies. Choice (C) matches the prediction, so keep it. The passage does not state that their research was flawed, so eliminate (D). The correct answer is (C).

39.B

The question refers to Passage 1 and asks what Professor Yodh’s team assumed before they started their experiments. Because this is a general question, it should be done after all the specific questions about Passage 1. Lines 28—30 state that the researchers were surprised at how big an effect particle shape had on the drying phenomenon, so look for an answer about how the researchers didn’t expect particle shape to have much of an effect on drying patterns. Choice (A) is a Deceptive Language trap answer; it looks similar to what is stated in lines 33—34—Spherical particles easily detach from the interface—but this was a discovery in the experiment, not something the researchers assumed before their experiments. Eliminate (A). Choice (B) matches the prediction because they had assumed shape wouldn’t have a major effect; keep it. Lines 26—28 say that the spherical particles could be stretched; the researchers planned this as part of their experiment, so eliminate (C). The passage indicates that the scientists didn’t expect the shape of the particles to have much of an effect, so eliminate (D). The correct answer is (B).

40.B

The question asks for the relationship between Nagel and Witten’s research and Yodh’s research. Use the lead words Nagel and Witten to find the window in Passage 1. Lines 17—23 state that Nagel and Witten wrote an influential paper about this process in 1997, which focused mainly on suspended spherical particles, but it was not until the Yodh team’s recent experiments that the surprising role played by suspended particle shape was discovered. Therefore, Yodh’s research builds on Nagel and Witten’s. Look for an answer choice that matches this prediction. Eliminate (A) because the passage does not indicate that Yodh’s work in any way proved Nagel and Witten’s work wrong. Rather, it indicates that Yodh’s team tried things that the earlier team had not. Choice (B) matches the prediction, so keep it. Choices (C) and (D) contradict the passage—Nagel and Witten’s research came before Yodh’s. The correct answer is (B).

41.D

The question asks what the word undulation means in line 37. Go back to the text, find the word undulation, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. The text says that spherical particles…do not substantially deform the air-water interface. Ellipsoid particles, however, cause substantial undulation of the air-water interface. Therefore, undulation must mean some kind of “change of shape.” Neither attraction, evaporation, nor undertow mean “change of shape,” so eliminate (A), (B), and (C). A Ripple is a “change in shape,” so keep (D). The correct answer is (D).

42.A

The question asks why the author of Passage 2 compares detergents and bacterium. Although this question asks about a specific line reference, it asks about it in relation to the author’s purpose in the passage as a whole. Because this is a general question, it should be done after all the specific questions about Passage 2. Lines 70—74 state, In various industrial applications…the coffee ring effect can be particularly troublesome and scientists have long been seeking ways to counteract it. Then the passage states that researchers have described a solution based on…a particularly promising bacterium, Pseudomonas aeruginosa. Lines 82—91 say that Pseudomonas aeruginosa…produces substances that counteract the coffee ring effect. These surface-tension-disrupting substances are called surfactants. Detergents such as soap are also surfactants. Therefore, the author compares the bacterium and soap as surfactants that may help solve the coffee-ring problem in industrial applications. Look for an answer choice that matches this prediction. Choice (A) mentions research into surfactants and issues in industrial use, so keep it. Eliminate (B) because the passage doesn’t address the dangers of using the bacterium in industrial applications such as paint and varnish; it says it is dangerous in open wounds. Choice (C) is a Deceptive Language trap answer; the passage does mention that soap can help reduce the movement of particles to the edge of a stain, but this doesn’t explain why the author of Passage 2 compares detergents and bacterium. Eliminate (C). The passage does not state that soap is a better surfactant, so eliminate (D). The correct answer is (A).

43.A

The question asks what Passage 2 most strongly suggests about the coffee ring effect. Notice that this is the first question in a paired set, so it can be done in tandem with Q44. Look at the answer choices for Q44 first. The lines for (44A) say that researchers…have now discovered how to counteract coffee rings. Check the answers for Q43; none of the answers are supported by those lines, so eliminate (44A). The lines for (44B) state that the key to the discovery was…a bacterium that counteracts the coffee ring effect; these lines don’t support any of the statements about the coffee-ring effect in Q43, so eliminate (44B). The lines for (44C) say that the coffee-ring effect can also be seen in liquids with particles of other materials such as plastic and wood. These lines don’t provide support for any of the answers in Q43, so eliminate (44C). The lines for (44D) say that the coffee ring effect can be particularly troublesome and scientists have long been seeking ways to counteract it. These lines support (43A). Draw a line connecting (43A) and (44D). Without any support from the answers in Q44, (43B), (43C), and (43D) can be eliminated. The correct answers are (43A) and (44D).

44.D

(See explanation above.)

45.C

The question asks what the word uniform means in line 97. Go back to the text, find the word uniform, and highlight it. Carefully read the surrounding text to determine another word that would fit in its place, based on the context of the passage. This paragraph describes what surfactants such as soap do. Lines 93—98 say that the soap causes a counterflow from the edge back towards the centre of the stain in such a way that the small particles—material or bacteria—end up in a kind of whirlwind. In this way, you get a more uniform distribution of particles as evaporation occurs. Therefore, uniform must mean something like “the same throughout.” Spread thin does not mean “the same throughout,” so eliminate (A). Choice (B) is about similar shape, not distribution, so it doesn’t match the prediction. Eliminate it. Keep (C) because evenly distributed matches “the same throughout.” Eliminate (D) because wiped clean doesn’t mean “the same throughout.” The correct answer is (C).

46.C

The question asks whether the main conclusion of Passage 2 agrees with Passage 1’s description of the properties of the coffee ring effect. Consider one passage at a time. Choice (A) contradicts Passage 1 because lines 52—56 say We were thinking it would be useful if you could just sprinkle in a few of these ellipsoid particles to remove the coffee ring effect…and we found that sometimes this idea works and sometimes it doesn’t. Eliminate (A). Eliminate (D) because Passage 1 does not discuss bacteria. Consider Passage 2 in relationship to (B) and (C). Eliminate (B) because Passage 2 focuses on surfactants and does not discuss the shape of particles. Lines 45—51 in Passage 1 say the researchers added a surfactant and the ellipsoid particles did not get stuck at the interface and flowed freely to the edge. Lines 93—98 of Passage 2 say that soap causes a counterflow from the edge back towards the centre of the stain, and in this way, you get a more uniform distribution of particles as evaporation occurs. This supports (C), so keep it. The correct answer is (C).

47.B

The question asks for a difference between the studies described in the two passages. Consider one passage at a time. In Passage 2, the researchers do not stretch the Pseudomonas aeruginosa bacterium, so eliminate (A). The researchers in Passage 2 use a bacterium—a biological organism—to counteract the coffee ring effect, so keep (B). Choice (C) is a Deceptive Language trap answer because Passage 2 does reference experimenting on nanomaterials, but not in order to breed Pseudomonas aeruginosa. Eliminate (C). Lines 93—98 state, the soap causes a counterflow from the edge back towards the centre of the stain in such a way that the small particles—material or bacteria—end up in a kind of whirlwind. In this way, you get a more uniform distribution of particles as evaporation occurs; these lines support (D), so keep it. Consider (B) and (D) in relation to Passage 1. The researchers in Passage 1 do not use biological organisms, so (B) gives a difference between the passages; keep (B). Eliminate (D) because this statement is true of both studies; the researchers in Passage 1 also experiment with ways to change evaporation and the flow of particles. The correct answer is (B).

Section 2—Writing and Language

1.D

Verbs change in the answer choices, so this question tests consistency of verbs. A verb must be consistent with other verbs in the sentence. Check for other verbs in the surrounding sentences. The verbs in the previous sentence, imagine and go, also refer to the subject you and are in present tense. Therefore, the underlined verb should be in present tense to be consistent. Eliminate (A), (B), and (C) because the verbs are not in present tense. Only (D) contains a present tense verb. The correct answer is (D).

2.C

Punctuation changes in the answer choices, so this question tests STOP, HALF-STOP, and GO punctuation. Use the Vertical Line Test, and identify the ideas as complete or incomplete. Draw the vertical line between the words simple and get. The first part of the sentence, For many, the answer is simple, is a complete idea. The second part of the sentence, get on social media and tell the world, is also a complete idea. To connect two complete ideas, STOP or HALF-STOP punctuation is needed. Eliminate (A), (B), and (D) as commas and no punctuation are GO punctuation. The colon in (C) is HALF-STOP punctuation, which can be used to connect two complete ideas. The correct answer is (C).

3.B

Note the question! The question asks which choice would best maintain the focus of this sentence and paragraph, so it tests consistency. Determine the subject of the sentence and paragraph, and find the answer that is consistent with that idea. The non-underlined part of the sentence discusses telling about the experience on Twitter and Facebook. The following sentences mention these services and Yelp. Look for an answer that is consistent with social media services. Eliminate (A) because there is no mention of social media. Keep (B) because it mentions a consumer-review site, which is consistent with the focus on social media. Eliminate (C) because, although it mentions a phone, it does not mention social media. Eliminate (D) because watching videos of animals is not consistent with the paragraph. The correct answer is (B).

4.A

Note the question! The question asks whether a phrase should be deleted, so it tests consistency. If the content of the phrase is consistent with the ideas surrounding it, it should be kept. If not, it should be deleted. The first two paragraphs of the essay discuss using social media to talk about a restaurant experience. The phrase not just restaurants clarifies that other companies are related to the social media issue discussed in the first paragraph, which only discusses restaurants. The phrase is consistent with the essay and provides a transition between what is true for restaurants and how it is also true for other businesses, so it should be kept; eliminate (C) and (D). Keep (A) because it correctly describes the phrase’s use in the sentence. Eliminate (B) because Chief Listening Officers are not introduced until later in the paragraph and do not provide a reason for keeping the phrase. The correct answer is (A).

5.C

Vocabulary changes in the answer choices, so this question tests precision of word choice. Look for a word or phrase with a definition that is consistent with the other ideas in the sentence. The sentence says that it is more important than ever for companies to “make certain” that they are showing the best possible face to the world on social media, so the correct word or phrase should mean “make certain.” Eliminate (A) because insure means to get insurance, or financial coverage, for something. Eliminate (B) because assure the public means to make people comfortable. Keep (C) because ensure is consistent with “make certain.” Eliminate (D) because make insurance is similar to (A), and both are inconsistent with “make certain.” The correct answer is (C).

6.C

Apostrophes change in the answer choices, so this question tests apostrophe usage. When used with a noun, on the PSAT, an apostrophe indicates possession. In this sentence, the output belongs to a company, so an apostrophe is needed, and because the word a indicates that the noun is singular, the apostrophe should be placed before the s. Eliminate (A) because it does not contain an apostrophe. Eliminate (B) because the sentence is discussing one company, not companies. Keep (C) because it has the apostrophe in the correct place and a singular company. Eliminate (D) because the apostrophe is used incorrectly. The correct answer is (C).

7.D

Phrases change in the answer choices, so this question tests precision of word choice. There is also the option to DELETE; consider this choice carefully as it is often the correct answer. Choices (A), (B), and (C) all contain phrases that mean the same thing in this context. The sentence already says to see if the situation can be remedied, which means “improved,” so there is no need to repeat the idea. The underlined portion should be deleted to make the sentence precise and more concise. The correct answer is (D).

8.B

Vocabulary changes in the answer choices, so this question tests the precision of word choice. Look for a word or phrase with a definition that is consistent with the other ideas in the sentence. The sentence discusses a company “launching” a new advertising campaign, so the correct word or phrase should mean “launches.” Eliminate (A) because unfurls means “unroll” and is used for a physical object such as a piece of cloth. Keep (B) because rolls out means “launches” and need not refer to a physical object. Eliminate (C) because unrolls is similar to unfurls and is not consistent with “launches.” Eliminate (D) because roles refers to “position” and is not consistent with “launches.” The correct answer is (B).

9.B

Phrases change in the answer choices, so this question tests precision and concision. Look for a phrase that is precise in meaning. The sentence says that it is more detailed than market research has ever been before, but the sentence does not clearly indicate what it refers to. Eliminate (A) because the word this does not clarify the word it later on in the sentence. Keep (B) because this kind of “market research” is more precise. It supplies a reference noun for the pronoun it and is consistent with the rest of the sentence. Eliminate (C) because it does not provide what it is. Eliminate (D) because reality does not explain what it refers to. The correct answer is (B).

10.D

Pronouns change in the answer choices, so this question tests consistency of pronouns. A pronoun must be consistent in number with the noun it refers to. The underlined pronoun refers to the noun someone’s, which is singular. Eliminate (A) and (B) because their and they’re are both plural. Eliminate (C) because your is not consistent with someone’s. Keep (D) because his and her are singular pronouns that work with someone’s. The correct answer is (D).

11.A

Note the question! The question asks which choice most directly answers the criticism presented in the previous sentence, so it tests consistency. Eliminate answers that are inconsistent with the purpose stated in the question. The previous sentence says that some criticize the CLO position as a fad and that companies may be overreacting to the power of social media. Look for an answer that responds to that criticism. Keep (A) because it states that CLOs will be needed as long as social media are around, suggesting the potential longevity of CLOs is tied to social media. Eliminate (B) and (D) because they continue the criticism of the previous sentence, and the question asks for a choice that answers the criticism. Eliminate (C) because teachers are not consistent with the previous criticism. The correct answer is (A).

12.A

Note the question! The question asks which choice best maintains the focus of this paragraph, so it tests consistency of ideas. Determine the subject of the paragraph and find the answer that is consistent with that idea. The paragraph says Medical science has created some modern miracles and mentions the Spanish flu and the Philadelphia Yellow Fever Epidemic of 1793. Look for an answer that gives other examples of historical epidemics. Keep (A) because it mentions polio, which is consistent with the other epidemics mentioned. Eliminate (B) and (D) because they give extra and irrelevant details about the Spanish Flu. Eliminate (C) because it discusses the present, while the paragraph is about the past. The correct answer is (A).

13.B

Note the question! The question asks which choice gives information consistent with the chart, so it tests consistency. Read the labels on the table carefully and look for an answer that is consistent with the information given in the graph. Eliminate (A) because the table shows populations in 1790, not populations today, so this information is not supported by the chart. Keep (B) because it correctly states that Philadelphia was the second largest city in 1790 and gives the correct population. Eliminate (C) because, according to the table, Philadelphia had a larger population than Boston. Eliminate (D) because Philadelphia did not have a population higher than that of New York City. The correct answer is (B).

14.D

Vocabulary changes in the answer choices, so this question tests precision of word choice. Look for a word or phrase with a definition that is consistent with the other ideas in the sentence. The sentence says Doctors tried various “cures,” but they were stalled in their inability to figure out both how the disease originated and how it was spreading, so the correct word should mean “cures.” Eliminate (A) because things is imprecise. Eliminate (B) because options is also imprecise. Eliminate (C) because management models is not consistent with the work of doctors. Keep (D) because treatment approaches is consistent with “cures.” The correct answer is (D).

15.B

Verbs change in the answer choices, so this question tests consistency of verbs. A verb must be consistent with its subject and with the other verbs in the sentence. The underlined portion is part of a list of two things doctors were unable to figure out: how the disease originated and something about spreading. To be consistent, the underlined verb must be in the same form as originated, which is in past tense. Choice (A) is in past tense, but spreading is not in the same form as originated, so eliminate it. Keep (B) because spread is in past tense and in the same form as originated. Eliminate (C) because it is in the wrong tense. Eliminate (D) because it changes spread from a verb to a noun, which does not match with originated. The correct answer is (B).

16.C

Vocabulary changes in the answer choices, so this question tests precision of word choice. Look for a phrase consistent in tone with the paragraph. The paragraph discusses medical science, and the first part of the sentence says Medical historians now know that the disease was spread by mosquitoes. The word but indicates a contrast between now and the past, which suggests that the idea was “not proven” until much later. Eliminate (A) because while pretty shady is somewhat similar to “not proven,” it is too casual and thus not consistent with the tone of the passage. Eliminate (B) because stupid idiocy does not match with “not proven” and is also not consistent in tone with the paragraph. Keep (C) because not verified matches with “not proven.” Eliminate (D) because downright wrong incorrectly changes the meaning of the sentence, suggesting that the idea was incorrect until later, whereas it merely wasn’t proven until later. The correct answer is (C).

17.C

Pronouns and nouns change in the answer choices, so this question tests precision. A pronoun can only be used if it is clear what the pronoun refers to. There is no noun in the sentence that indicates who tried to impose, so a pronoun cannot be used; eliminate (A), (B), and (D). Only (C) clearly states who tried to impose. The correct answer is (C).

18.A

Commas and words change in the answer choices, so this question tests the four ways to use a comma and consistency. The sentence contains a list of three things: 1) alcohol, 2) hot sun, and 3) night air. There should be a comma after each item in the list. Eliminate (B) because it is missing a comma after sun. Additionally, all items in a list must be phrased the same way to be consistent with one another. Eliminate (C) because the word also isn’t needed since that’s implied by the word and. Eliminate (D) because it is less concise than (A), and the additional words don’t make the meaning more precise. The correct answer is (A).

19.D

Note the question! The question asks where sentence 7 should be placed, so it tests consistency of ideas. The sentence must be consistent with the ideas that come both before and after it. Sentence 7 mentions blame for something, so it should be placed near other sentences that discuss blame. Sentence 3 says that politicians blamed immigration, so this sentence should go either before or after sentence 3. Since before sentence 3 is not an option, sentence 7 should be placed after sentence 3. The correct answer is (D).

20.C

21.B

Commas change in the answer choices, so this question tests the four ways to use a comma. The underlined portion does not contain unnecessary information, a list, or two ideas that must be connected, so there is no reason to use a comma. Eliminate (A), (C), and (D). The correct answer is (B).

22.A

Transitions change in the answer choices, so this question tests consistency of ideas. A transition must be consistent with the relationship between the ideas it connects. The sentence before the transition states that the Ebola virus in West Africa provides a terrifying reminder of just how deadly certain diseases can be, and the sentence that starts with the transition states that the Yellow Fever Epidemic provides a remarkable instance of a city’s resilience. These are both about examples of deadly diseases, so a same-direction transition is needed; keep (A). Eliminate (B) because it contains an opposite-direction transition. Eliminate (C) and (D) because therefore and thus are used to show a conclusion, which is not consistent with how the ideas connect. Moreover, therefore and thus provide an identical meaning, so there is no reason to choose one over the other, which means they are both wrong. The correct answer is (A).

23.D

Vocabulary changes in the answer choices, so this question tests precision of word choice. There is also the option to DELETE; consider this choice carefully as it is often the correct answer. Choices (A), (B), and (C)—seems doubtful, strikes us as odd, and appears improbable—all mean the same thing in this context. The sentence already says Many people find it difficult to believe, so there’s no need to repeat the idea. The underlined portion should be deleted to make the sentence more concise. The correct answer is (D).

24.C

Note the question! The question asks which choice would most effectively conclude this paragraph by introducing the main subject of the essay as a whole. Determine the subject of the paragraph and find the answer that is consistent with that idea. The paragraph says that the early days of recorded music can be hazy, but there is a treasure trove of recorded music from that era. The next paragraph describes the life of Jimmie Rodgers. The concluding sentence should introduce Jimmie Rodgers. Eliminate (A) and (B) because they do not mention Jimmie Rodgers. Keep (C) because it introduces Jimmie Rodgers. For (D), scan the rest of the passage. It only discusses Jimmie Rodgers and not any of the other musicians mentioned in (D), so mentioning those musicians wouldn’t introduce the main subject of the essay. Eliminate (D). The correct answer is (C).

25.B

Verbs change in the answer choices, so this question tests 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 circumstances, which is plural. To be consistent, the underlined verb must also be plural. Eliminate (A), (C), and (D) because they are singular. The correct answer is (B).

26.C

Phrase length changes in the answer choices, so this question tests precision of word choice. Look for a phrase that is consistent with the ideas in the sentence and is precise. The second part of the sentence is about his father. Eliminate (A) and (B) because for sure and for certain are not precise. Keep (C) because his family is consistent with his father in the latter part of the sentence. Eliminate (D) because his mother, father, and siblings is a less concise way of writing his family. The correct answer is (C).

27.C

Note the question! The question asks which choice would best fulfill the goal of including a detail that provides specific information about Rodgers’s illness, so it tests consistency. Eliminate answers that are inconsistent with the purpose stated in the question. Eliminate (A), (B), and (D) because they do not give specific information about Rodgers’s illness. Only (C) gives the name of the illness. The correct answer is (C).

28.A

Vocabulary changes in the answer choices, so this question tests precision of word choice. Look for a word with a definition that is consistent with the other ideas in the sentence. The sentence says the inability to work was a good thing for Rodgers’s great passion, so the correct word should mean “fortunate.” Keep (A) because fortuitous means “fortunate.” Eliminate (B) because chancy means “risky.” Eliminate (C) because blessed means “holy.” Eliminate (D) because charmed means “unusually lucky” or “privileged,” which goes further than just “fortunate.” The correct answer is (A).

29.A

Punctuation changes in the answer choices, so this question tests STOP, HALF-STOP, and GO punctuation and the four ways to use a comma. Use the Vertical Line Test and identify the ideas as complete or incomplete. Draw the vertical line between the words rails and however. The first part of the sentence, Once Jimmie could no longer work the rails, is an incomplete idea. The second part of the sentence, however, he pursued his musical career in earnest, is a complete idea. To connect an incomplete idea to a complete idea, GO punctuation is needed. A semicolon is STOP punctuation, so eliminate (C). The phrase however is unnecessary information, so it should have commas both before and after it. Keep (A) because it correctly places commas before and after however. Eliminate (B) and (D) because they do not have commas before and after however. The correct answer is (A).

30.C

Note the question! The question asks for the best placement for the underlined portion, so it tests precision. The phrase all the way to New York City should come after the phrase it describes. Eliminate (A), (B), and (D) because the placement of all the way to New York City after sold, year, and copies does not make sense. Keep (C) because chased his dream all the way to New York City provides a precise meaning. The correct answer is (C).

31.A

Punctuation and words change in the answer choices, so this question tests STOP, HALF-STOP, and GO punctuation. The first part of the sentence, By this time, is an incomplete idea. The second part of the sentence, Rodgers had become the famous “Singing Brakeman,” and his influence would be felt for many generations to come, is a complete idea. To connect an incomplete idea to a complete idea, GO punctuation is needed. Keep (A) because a comma is GO punctuation and can be used between an incomplete idea and complete idea. Eliminate (B) and (C) because adding when or as makes the sentence incomplete. Eliminate (D) because a colon is HALF-STOP punctuation and can only be used after a complete idea. The correct answer is (A).

32.B

Words change in the answer choices, so this question tests precision of word choice. The paragraph says This influence would not be felt only in country music either and that blues singer Howlin’ Wolf cited Rodgers as an early influence. Elvis Presley also cited Rodgers as an early influence. Eliminate (A) and (C) because like and similar to are not precise and make the meaning of the sentence unclear (both make it sound like Elvis Presley was an influence, not that he was influenced). Keep (B) because as did makes the meaning of the sentence clear by adding a verb. Eliminate (D) because it is not precise and introduces an unnecessary possessive phrase. The correct answer is (B).

33.D

Note the question! The question asks for a choice that best concludes the essay by reinforcing its main idea, so it’s testing consistency. First, consider the main idea of the passage. The passage introduces Jimmie Rodgers, discusses his early life, explains how he began his country musical career, and evaluates Rodgers’s significance, indicating that his influence would be felt for many generations to come and that his music influenced other non-country artists. Look for an answer choice that is consistent with these ideas. Eliminate (A) because it contradicts the passage’s point that Rodgers was highly influential. Eliminate (B) because his influence on his family is not consistent with the passage’s main idea—the passage focuses on his influence on the music industry. Eliminate (C) because it mentions only his careers and not his influence as a musician, so it’s not consistent with the main idea. Keep (D) because the idea that his influence is still alive and well is consistent with the passage’s main idea. The correct answer is (D).

34.D

Nouns change from singular to plural in the answer choices, so this question tests consistency of nouns. A noun must be consistent in number with the other nouns or pronouns in the sentence. The sentence contains the nouns males and females, which are plural. To be consistent, the underlined noun must also be plural. Eliminate (A), (B), and (C) because they all contain the singular nouns role or distinction. Keep (D) because it contains the plural noun roles. The correct answer is (D).

35.A

Note the question! The question asks which choice gives accurate data based on the graph, so it tests consistency. Read the labels on the graph carefully, and look for an answer that is consistent with the information given in the graph. Keep (A) because it gives information consistent with the graph, which shows that only a small number of species have a post-reproductive life span and that the black-tailed prairie dog is one of them. Eliminate (B) because it is not consistent with the graph as it does not show that most species have a post-reproductive life span, and humans are not on the graph. Eliminate (C) because the common bottlenose dolphin has the longest pre-reproductive life span of any species on the graph. Eliminate (D) because the two rodent species on the graph do have post-reproductive life span. The correct answer is (A).

36.D

Pronouns and nouns change in the answer choices, so this question tests precision. A pronoun can only be used if it is clear what the pronoun refers to. Scientists are not the ones whom evolution has determined should live so much longer, so a pronoun is imprecise; eliminate (A), (B), and (C). Only (D) makes it clear that the female whales are the ones who live so much longer. The correct answer is (D).

37.A

Note the question! The question asks which choice provides the most effective transition from the previous paragraph to this paragraph, so it tests consistency. Determine the subjects of the two paragraphs, and find the answer that is consistent with those ideas. The previous paragraph is about gender differences in the animal kingdom, specifically that many females do not live much beyond menopause. The paragraph ends by stating that Scientists have long wondered why evolution has determined the female whales should live so much longer. The current paragraph says that the social forces that define gender may apply to the animal kingdom and that scientists watched over 750 hours of videos and observed the behaviors of pods of whales. Keep (A) because it acknowledges the question at the end of the previous paragraph and connects to scientists studying whales in the current paragraph. Eliminate (B) and (C) because they do not connect to the information in the previous paragraph. Eliminate (D) because it does not mention whales at all. The correct answer is (A).

38.B

Word order changes in the answer choices, so this question tests precision. Look for the phrase that makes the meaning of the sentence clear. The first part of the sentence says After watching over 750 hours of video and observing the behaviors of pods of whales. The first word after this phrase should indicate who did the watching and observing. The whale grandmothers are not the ones watching and observing, so eliminate (A) and (C). Keep (B) because it makes sense that the scientists are watching and observing. Eliminate (D) because teaching behaviors cannot watch and observe. The correct answer is (B).

39.A

Note the question! The question asks whether a sentence should be added, so it tests consistency. If the content of the new sentence is consistent with the ideas surrounding it, then it should be added. The paragraph discusses scientists studying the teaching behaviors of whale grandmothers. The new sentence states that the older female whales were the most likely to lead younger whales to salmon feeding grounds, which describes a teaching behavior and is consistent with the paragraph. The new sentence should be added, so eliminate (C) and (D). Keep (A) because the sentence clarifies some of the teaching behaviors. Eliminate (B) because the older whales were not ignored in the study. The correct answer is (A).

40.D

Punctuation changes in the answer choices, so this question tests STOP, HALF-STOP, and GO punctuation. Use the Vertical Line Test and identify the ideas as complete or incomplete. Draw the vertical line between the words words and sharpened. The first part of the sentence, The scientists ascribe this behavior to what they refer to as the grandmothers’ roles as “repositories of ecological knowledge” in other words, is an incomplete idea. The second part of the sentence, Sharpened memories and long experience of learned behaviors make the older females extremely valuable to future generations, is a complete idea. To connect an incomplete idea to a complete idea, GO punctuation is needed. STOP punctuation, like periods and semicolons, cannot be used to connect an incomplete idea to a complete idea; eliminate (A) and (B). Repeat the Vertical Line Test, drawing the line between the words knowledge and in. The first part of the sentence becomes a complete idea, and the second part of the sentence remains a complete idea. Only STOP punctuation can be used to connect two complete ideas; eliminate (C). Choice (D) correctly places STOP punctuation between two complete ideas. The correct answer is (D).

41.B

Note the question! The question asks whether the word longevity should be replaced with the word life in the previous sentence, so it tests precision. The previous sentence states The elder females have evolved this longevity because the species, simply put, needs it. The word longevity, which means “living a long time” is more precise than the word life, which doesn’t indicate the long period of time mentioned previously, so it should not be replaced; eliminate (C) and (D). Longevity is more specific, not more formal, than life, so eliminate (A). Longevity specifically refers to “life span,” so keep (B). The correct answer is (B).

42.D

Note the question! The question asks which choice introduces the paragraph most effectively, so it tests consistency of ideas. Determine the subject of the paragraph and find the answer that is consistent with that idea. The paragraph states that the findings also show that societies that value youth and middle age to the detriment of old age may do so at their own peril and that in whale pods as well as human communities, it seems, life may depend on the accrued knowledge of older relatives. Eliminate (A) because gender discrimination is not discussed in the paragraph. Eliminate (B) because there is no discussion of what else whale grandmothers know. Eliminate (C) because Moby Dick is not mentioned in the paragraph at all. Keep (D) because it mentions the study discussed in the previous paragraph and how it connects to society at large. The correct answer is (D).

43.B

Pronouns change in the answer choices, so this question tests consistency of pronouns. A pronoun must be consistent in number with the noun it refers to. The underlined pronoun refers to the noun societies, which is plural. To be consistent, the underlined pronoun must also be plural. Eliminate (C) and (D) because they contain singular pronouns. In addition, the peril belongs to the societies, so the underlined pronoun must also be possessive. Eliminate (A) because there does not show possession. Keep (B) because their is plural and possessive. The correct answer is (B).

44.C

Word order and number changes in the answer choices, so this question tests precision and concision. Look for the phrase that makes the meaning of the sentence clear in a concise way. Eliminate (A) because the phrase is not precise or concise. Eliminate (B) because long lives are long enough is not precise because it doesn’t indicate what their lives are long enough for. Keep (C) because the meaning is clear. Eliminate (D) because the meaning is not clear, and a word is needed between knowledge and the longer-lived people. The correct answer is (C).

Section 3—Math (No Calculator)

1.C

The question asks for the point that satisfies a system of equations. There are specific points in the answers, so use PITA. Test the ordered pairs in both equations from the question and look for a pair that makes both equations true. Start by plugging (A) into the first equation to get 0 = (3) + 3. This becomes 0 = + 3. Since this is not true, eliminate (A). Now plug the point in (B) into the first equation to get 2 = (−2) + 3. This becomes 2 = −1 + 3 or 2 = 2. This is true, but the point must work in both equations. Plugging the point in (B) into the second equation gives −2 = (2)² − 5(2) + 6, which becomes −2 = 4 − 10 + 6 or −2 = 0. Eliminate (B). Plug the point in (C) into the first equation to get 4 = (2) + 3. This becomes 4 = 1 + 3 or 4 = 4. This is true, but test the second equation as well. This gives 2 = (4)² − 5(4) + 6, which becomes 2 = 16 − 20 + 6 or 2 = 2. This is also true. The correct answer is (C).

2.B

The question asks for an equivalent form of an expression. There are variables in the answer choices, so plug in. Make y = 2 and c = 3. The expression becomes 30(2) − 12(3)(2) = 60 − 72 = −12. This is the target value; circle it. Now plug y = 2 and c = 3 into the answer choices to see which one matches the target value. Choice (A) becomes [5 − 2(3)](2) = (5 − 6)(2) = (−1)(2) = −2. This does not match the target, so eliminate (A). Choice (B) becomes [30 − 12(3)](2) = (30 − 36)(2) = (−6)(2) = −12. Keep (B), but check (C) and (D) just in case. Choice (C) becomes (18)[3 − 2(2)] = (18)(3 − 4) = (18)(−1) = −18. Eliminate (C). Choice (D) becomes (18)(3)(2)² = (18)(3)(4), which does not equal −12. Eliminate (D). The correct answer is (B).

3.C

The question asks for an equation in terms of a specific variable. There are two good ways to solve. One is to solve for a. To begin to isolate a, divide both sides of the equation by m to get . Another option is to plug in. Choose easy numbers that fulfill the equation F = ma, such as m = 2, a = 3, and F = 6. Now plug m = 2, a = 3, and F = 6 into the answer choices to see which one contains a true equation. Choice (A) becomes 3 = (6)(2). This is not true, so eliminate (A). Choice (B) becomes 3 = 6 + 2. Eliminate (B). Choice (C) becomes . This is true, so keep (C), but check (D) just in case. Choice (D) becomes , which is not true, so eliminate (D). With either strategy, the correct answer is (C).

4.B

The question asks for the value that satisfies a system of equations. There are specific values in the answers, so plug in the answers. The answer choices represent possible values of j. Test the values in both equations from the question and look for one that makes both equations the same. Start with (B). Plug the value into the first equation to get (−4)(−5) − 10k = 50. This becomes 20 − 10k = 50. Subtract 20 from both sides to get −10k = 30 or k = −3. Then plug the value into the second equation to get (−5) −3k = 4. Add 5 to both sides to get −3k = 9 or k = −3. This is the same as the first equation with this value. The correct answer is (B).

5.D

The question asks about the graph of the data representing a certain situation. Label the parts of the equation to determine what they represent. In this question, y represents the weight of the giant panda and x represents the number of months after the panda was born. The slope of a graph is defined as the change in y over the change in x, so the slope must relate to weight, not time. Eliminate (B) and (C) for this reason. The equation is in y = mx + b form, where m is the slope of a graph, so here the slope is 3,100. Plug and play to determine what gives a value of 3,100. Make m = 0 to get the giant panda’s weight after 0 months, or at birth. This becomes weight = 3,100(0) + 105 or weight = 105. Since the giant panda’s weight at birth is not 3,100, eliminate (A). After one month, the giant panda will have a weight = 3,100(1) + 105 = 3,100 + 105 = 3,205. Therefore, in the first month, the panda gained 3,205 − 105 = 3,100 grams in weight. The correct answer is (D).

6.A

The question asks for a solution to the given equation. Since the question asks for a specific value and the answers contain numbers in increasing order, use PITA. Begin by labeling the answers as b and start with (B), 0. The equation becomes (3)(0)² − (6)(0) = 5 + (4)(0)² or 0 − 0 = 5 + 0. This isn’t true, so eliminate (B). It may be difficult to see whether a larger or smaller number is needed to make the equation true, so just pick either direction. For (A), plug in b = −5 to get (3)(−5)² − (6)(−5) = 5 + (4)(−5)². Simplify this to get (3)(25) + 30 = 5 + (4)(25) or 75 + 30 = 5 + 100. This results in 105 = 105, which is true, so stop here. The correct answer is (A).

7.A

The question asks for a statement that cannot be true about a graph. When given a description of a graph, make a sketch of the graph and use it to eliminate answers. This line crosses the x-axis at 4, so it contains the point (4, 0) as well as the given point (−2, 6). Draw the graph with these points, and then connect them like this:

Now mark each answer as true or false. The slope and the y-intercept are easy to see, so start with those. The slope is negative, so (B) is true, and the y-intercept is positive, so (C) is true. The question asks for a statement that cannot be true, so eliminate (B) and (C). Choice (A) contains a point in the lower left quadrant of the graph, and (D) contains a point in the lower right quadrant. Since the line goes through only the lower right quadrant, only (D) can possibly be true. Eliminate (D). The correct answer is (A).

8.B

The question asks for an inequality that models a specific situation. Translate the question in Bite-Sized Pieces and eliminate after each piece. One piece of information says that each square of fabric must have an area of at least 340 square inches. Since the quilt uses 16 different squares of fabric, multiply 16 by 340 to get the minimum area of fabric needed for the quilt. This results in 5,440, so eliminate (A) and (D), where this minimum value does not appear. Compare the remaining answers. The difference between (B) and (C) is the maximum value. The question states that each square of fabric must have an area of no more than 360 square inches, so multiply 16 by 360 to get the maximum. That value is 5,760, which does not appear in (C), so eliminate it. The correct answer is (B).

9.D

The question asks for an equation that models a specific situation. Translate the question in Bite-Sized Pieces and eliminate after each piece. One piece of information says that a 15% discount will be applied. A 15% discount would be calculated with a multiplier of 0.85 (1—0.15), so eliminate (A) and (C), which multiply by 1.15 (an increase of 15%) instead. Compare the remaining answers. The difference between (B) and (D) is where the 15% discount is being applied. The question states that x is the total cost in dollars. The discount should be applied to the original purchase price of the dishes and bowls, so eliminate (B). The correct answer is (D).

10.C

The question asks for the value of a constant that appears as part of a fractional exponent. When dealing with questions about exponents, remember the MADSPM rules. The MA part of the acronym indicates that Multiplying matching bases means to Add the exponents. The PM part of the acronym indicates that raising a base with an exponent to another Power means to Multiply the exponents. Use the order of operations to apply the exponents outside the parentheses to the bases inside by multiplying the exponents to get . Although it is possible to reduce some of these exponents, the next step will be to add them together, since the bases are multiplied. Leave the exponents in fractional form to make that easier, getting . According to the equation, this is equal to , so k must equal 7. The correct answer is (C).

11.C

The question asks for a system of inequalities that models a specific situation. Translate the question in Bite-Sized Pieces and eliminate after each piece. One piece of information says that the baker needs to buy at least 2 containers of flour. Since f represents the number of containers of flour, one inequality should say f ≥ 2, so eliminate (B) and (D), where this does not appear. Compare the remaining answers. The difference between (A) and (C) is the direction of the inequality sign. The question states that the baker has $75 dollars with which to purchase ingredients. Since the baker cannot spend more than this amount, the inequality should say that the total cost is ≤ 75. This does not appear in (A), so eliminate it. The correct answer is (C).

12.A

The question asks for the y-coordinate of a parabola’s vertex. The question gives the equation of a parabola in factored form, which makes it easy to determine the solutions, or y-intercepts in this case. Because parabolas are symmetrical about a central axis that runs through the vertex, the y-coordinate of the vertex will be halfway between the two y-intercepts. If x = 0, then the equation becomes 0 = (y + 5)(y − 15). Set each binomial equal to 0 to get y + 5 = 0 and y − 15 = 0, so y = − 5 or 15. Eliminate (C) and (D), which aren’t between the intercepts at all. To find the midpoint, average the y-intercepts to get . Ine correct answer is (A).

13.D

The question asks for a pair of congruent angles in a figure containing triangles. When given two or more triangles and information about the ratios of the sides, look for similar triangles. Sides FJ and FH are both on the smallest triangle, while FG and GH are both on the largest triangle. Redraw the two triangles side-by-side to better see the similarities. Start with triangle FHJ, redrawing it by itself with the same orientation it currently has, labeling the vertices. Then draw a bigger triangle next to it with the same shape as triangle FHJ, like this:

Since the ratio of is equal to , label the sides of this new triangle correspondingly. Make sure to keep ∠FGH as the smaller angle and ∠GFH as the larger one, like this:

Now it is easier to check corresponding angles. Choice (A) gives the angles on the lower left of the big triangle and the lower right of the small triangle. These are not necessarily congruent, so eliminate (A). Choice (B) gives an angle that does not appear on either triangle and the angle at the top of the small triangle. These are not necessarily congruent, so eliminate (B). Choice (C) gives an angle that does not appear on either triangle and the angle on the lower left of the small triangle. These are not necessarily congruent, so eliminate (C). Choice (D) gives the angles at the tops of both triangles, so these angles are congruent. The correct answer is (D).

14.36

The question asks for a measurement and gives conflicting units. Begin by reading the question to find information on the measurement. The question states that Monica made a total of 3 pounds and 6 ounces of jam on Wednesday and Thursday. There are 16 ounces in a pound, so set up a proportion to determine how many ounces of jam she made in total: . Cross-multiply to solve for x: 48 = x. Add the remaining 6 ounces to get the total for both days: 48 + 6 = 54 ounces in all. The question says she made half as many ounces of jam on Wednesday as she did on Thursday. The question asks how many ounces she made on Thursday alone, so set up an equation to find the answer, where x represents the ounces of jam Monica made on Thursday: 54 = x + x. Add x + x to get 54 = x. Then multiply both sides by to get 36 = x. The correct answer is 36.

15.3

The question asks for the value of z for which the provided equation will have an infinite number of solutions. First, isolate z. Distribute the 6 to get 12y + 6z = 12y +18. Subtract 12y from both sides to get 6z = 18. Then divide both sides by 6 to get z = 3. If z is set equal to 3, the equation will have infinitely many solutions, because the y terms will always be eliminated. The correct answer is 3.

16.24

The question asks about the product of two coefficients within a pair of binomials. When given a quadratic in factored form, it is often necessary to use FOIL to multiply the factors out to the standard form ax² + bx + c to solve the question. The expression becomes 6gx⁴ + ghx²y² − 3Ax²y¹ − 4hy⁴. It might be tempting to try to figure out what the values of g and h are, given the information that they have a difference of 5. However, make sure to read the full question, which asks for the value of gh, not g or h separately. The gh appears as the coefficient of one of the x²y² terms, and the question states that the coefficient on that term when like terms are collected is zero. The second x²y² term has a coefficient of −24, so the first one must have a coefficient of 24 in order to equal 0 when the two terms are combined. Thus, gh must equal 24. The correct answer is 24.

17.2

The question asks for the value of one of the coefficients in a quadratic. When given a quadratic in standard form, which is ax² + bx + c, it is often necessary to factor it to solve the question. Here, the question supplies one of the factors, so use that to find the other factor. If (2y − 3) is a factor, then the first part of the second factor must multiply by 2y to result in 8y². Divide 8y² by 2y to get 4y as the first term in the second factor. Similarly, the second term in the second factor must multiply by −3 to get −15. Divide −15 by −3 to get 5 as the second term of the second factor. Therefore, the second factor must be (4y + 5). Now use FOIL on the two factors to both verify that these numbers give you 8y² and −15 and to determine the coefficient on the y term, which will be the value of d. The expression becomes (2y − 3)(4y + 5) = 8y² + 10y − 12y − 15 or 8y² − 2y − 15. Therefore, d = 2. The correct answer is 2.

Section 4—Math (Calculator Allowed)

1.C

The question asks for the profit the store makes for selling 20 pencils. Because profits increase as pencils sold increase, set up a proportion: . Cross-multiply to get 12x = $15. Divide both sides by 12 to get x = $1.25. The correct answer is (C).

2.A

The question asks for the period that shows the least decrease. Ballpark to find the answer. Choice (A) has a decrease of about one interval between horizontal gridlines. Choice (B) has a decrease of about more than two full intervals. Choice (C) has a decrease of about 4 intervals. Choice (D) has a decrease of about 2 intervals. Therefore, the correct answer is (A).

3.D

The question asks for the meaning of a piece of an equation in context. Start by reading the full question, which asks for the meaning of the number 870. Then label the parts of the equation with the information given. The question states that A represents the remaining amount she owes and w represents the number of weeks since she borrowed the money. Because the number 870 is used to calculate A, the remaining amount owed, it must have something to do with money. Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Choice (A) describes the total amount Sydney has repaid. However, the amount will change over time, so it cannot be represented by a constant. Eliminate (A). Choice (C) describes w and not 870, so eliminate (C). To check (B) and (D), plug in some numbers. If w = 1, then A = 870 − 30(1) = 840, so after 1 week, $840 remains to be paid. If w = 2, then A = 870 − 30(2) = 810, so after 2 weeks, $810 remains to be paid. Therefore, between week 1 and week 2, 840 − 810 = 30 was repaid. Thus, 30 represents the amount Sydney repays each week, so eliminate (B). Only one choice remains. To confirm (D), note that the original amount that Sydney owes is the amount that she owes after 0 weeks. If w = 0, then A = 870 − 30(0) = 870. The correct answer is (D).

4.A

The question asks for the relationship between years of ownership and selling price. Look at the graph. There is clearly a downward trend in both the scatterplot and the line of best fit. Therefore, this is a negative correlation: as one variable increases, the other variable decreases. Eliminate (B), (C), and (D), which do not describe such a relationship. The correct answer is (A).

5.B

The question asks how much more the actual selling price was compared to that predicted by the line of best fit for the car that was sold after it was owned for exactly 7 years. Find 7 on the horizontal axis and trace up to the point and the line of best fit. They lie between two gridlines on the vertical axis. Since each interval is $2,000, the difference must be less than $2,000. Eliminate (C) and (D). Since the difference makes up more than half the interval, the difference must be more than $1,000. Eliminate (A). The correct answer is (B).

6.D

The question asks for the value of b in the equation when graphed and provides a point on the graph. Plug the point into the equation. Plug x = 3 and y = −1 into y = 2x − b to get −1 = 2(3) − b. Simplify the right side to get −1 = 6 − b. Subtract 6 to both sides to get −7 = −b. Divide both sides by −1 to get b = 7. The correct answer is (D).

7.A

The question asks for the model that best fits the data. Compare the answer choices. Two choices describe a linear decrease, which is a decrease by the same amount each month, and two choices describe an exponential increase, which is an increase by the same percent each month. Because linear decreases are easier to work with, first determine whether the relationship is linear with a consistent decrease. From month 0 to month 1, the decrease is $1,400 − $1,344 = $56. Eliminate (C), which indicates a decrease of $47. From month 1 to month 2, the decrease is $1,344 − $1,290 = $54. Eliminate (D), since the decrease is not always $56. Therefore, the decrease must be exponential. To find the percent change between months, use the formula . From month 0 to month 1, the percent decrease is . The correct answer is (A).

8.A

The question asks for the rate of the snail in centimeters per hour. Begin by reading the question to find information on the snail’s pace. The question states that the snail moves at a rate of 700 millimeters per second. Convert the 700 millimeters into centimeters. Since there are 10 millimeters in 1 centimeter, set up the proportion . Cross-multiply to get 10x = 700. Divide both sides by 10 to get x = 70. Therefore, the snail moves at a rate of 70 centimeters per minute. Determine the number of centimeters travelled in 1 hour. Since there are 60 minutes in 1 hour, set up the proportion . Cross-multiply to get y = 4,200. Therefore, the snail moves at a rate of 4,200 centimeters per hour. The correct answer is (A).

9.C

The question asks about the solutions to the equation. Two of the choices include numbers, and the other two are infinitely many solutions and no solutions. Plug in the easier of the choices with numbers. Plug in y = 10 to get . The equation becomes 5(5 + 5) = 20 + 5 + 25 or 5(10) = 50. Since this is true, y = 10 is a solution. Eliminate (A), since y = 1 cannot be the only solution, and eliminate (D), since there is at least one solution. It is still possible that there are infinitely many solutions. To test, plug in any other number. To make the math as easy as possible, plug in y = 0 to get . The equation becomes 5(0 + 5) = 0 + 0 + 25 or 5(5) = 25. Therefore, y = 0 is also a solution. Since y = 10 is not the only solution, eliminate (B). The correct answer is (C).

10.D

The question asks for the difference of polynomials, so simplify and combine like terms. Do this in Bite-Sized Pieces. Find like terms, such as 2ab² in the first polynomial and 2ab² in the second polynomial. Subtract to get 2ab² − 2ab² = 0. Therefore, the correct answer must not have an ab² term. Eliminate (B) and (C). Now, look at the a² terms. Subtract −3a² from 5a² to get 5a² − (−3a²) = 8a². Eliminate (A), which does not include this term. Only one choice remains. The correct answer is (D).

11.B

The question asks for a percent based on data. Set it up, then find the numbers on the table. The question asks what percent of the athletes in the school are right-handed varsity athletes, so the percent is . The table indicates that there are 98 right-handed varsity athletes, and the question states that there are 270 athletes in the school. Plug the two values into the percent to get . The question says approximately, so select the closest choice. The correct answer is (B).

12.D

The question asks for the difference between the maximum weight that Helen can lift and the median, so find the median. The median of a list of numbers is the middle number when all values are arranged in order. In lists with an even number of items, the median is the average of the middle two numbers. Put the maximum weights in order from least to greatest: 30, 40, 60, 70, 110, 130, 170, 230. Find the middle number by crossing out numbers in pairs starting from the outside. Cross out 30 and 230. Cross out the next least and next greatest: 40 and 170. Cross out the next least and next greatest: 60 and 130. Only 70 and 110 remain. Since there is no single middle number, find the average of the middle two to get as the median. Find the difference between this value and the maximum weight that Helen can lift. The maximum weight that Helen can lift is 170 pounds, so the difference is 170 − 90 = 80. The correct answer is (D).

13.A

The question asks which statement is true, and the statements refer to mode and range. Begin with the easier statistic, which is mode. By definition, the mode of a list of numbers is the number that appears the most often. For the Physics class, 25 is the only number that appears more than once, so 25 is the mode. Similarly, for the Biology class, 32 in the only number that appears more than once, so 32 is the mode. Since the mode for Physics is less than the mode for Biology, eliminate (B) and (D). Now check the range, which is, by definition, the difference between the greatest and least number in a list. For the Physics class, the range is 31 − 23 = 8. For the Biology class, the range is 32 − 21 = 11. Since the range for the Physics class is less than the range for the Biology class, eliminate (C). The correct answer is (A).

14.C

The question asks how many cars the factory can produce in 540 hours. The rate is given in minutes, so convert the 540 hours into minutes, using the proportion . Cross-multiply to get x = 32,400. Since the factory can produce 1 car in 1,080 minutes, set up the proportion . Cross-multiply to get 1,080y = 32,400. Divide both sides by 1,080 to get y = 30. The correct answer is (C).

15.A

The question asks for the difference between the percentage of patients in the experimental physical therapy with a recovery time of more than 6 months and the percentage of patients in the conventional physical therapy with a recovery time of more than 6 months. Find both percentages. There was a total of 82 + 112 = 194 patients in the experimental physical therapy, 112 of whom had a recovery time of more than 6 months. Therefore, the percentage is . There was a total of 151 + 140 = 291 patients in the conventional physical therapy, 140 of whom had a recovery time of more than 6 months. Therefore, that percentage is . To find the difference, subtract to get 57.731 − 48.11 = 9.621. The question asks for the difference rounded to the nearest percent, so the correct answer is (A).

16.D

The question asks for the number of patients who had both knees replaced. The ratio of those who had one knee replaced to those who had both knees replaced is 3:7. Add the parts of the ratio together to determine the number of people in one group, which is 3 + 7 = 10. Now use the chart to determine the actual number of people. The question only refers to those in conventional physical therapy. According to the chart, there is a total of 151 + 140 = 291 patients in the conventional physical therapy. If there are 10 people in a group and 291 people total, divide 291 by 10 to find that there are 29.1 groups. This multiplier can be applied to both parts of the ratio to find the actual numbers. The question asks about those with both knees replaced, which is the 7 in the ratio. Multiply the ratio by the multiplier to find that there were 7 × 29.1 = 203.7 people in conventional therapy that had both knees replaced. The question asks for the best approximation of this number, so round the number to 204. The correct answer is (D).

17.C

The question asks for the probability a patient in the study selected at random will have a recovery time of more than 6 months. Probability is defined as . Read the table carefully to find the right numbers to set up the probability. Because the question states that a patient in the study is selected at random, the total # of possible outcomes is the total number of patients in the study, which is 485. Because the question asks for the probability that the patient will have a recovery time of more than 6 months, the # of outcomes that fit the requirement is the total number of patients with a recovery time of more than 6 months. Make sure to include both those in experimental physical therapy and those in conventional physical therapy to get a total of 112 + 140 = 252. Therefore, the probability is . The question says is closest to, so select the closest choice. The correct answer is (C).

18.D

The question asks for the equation of a circle. The equation of a circle can be written in the form (x − h)² + (y − k)² = r², where (h, k) is the center of the circle and r is the radius of the circle. Eliminate (A) and (C), which have subtraction between the binomials instead of addition. Look at the two remaining choices. The choices differ both in the center and in the radius, so eliminate one choice using any of this information. Since the center is (−3, 5), h = −3 and (x − h) = (x + 3). Also, since the radius is 4, r² = 16. Using either of those pieces, eliminate (B). The correct answer is (D).

19.A

The question asks how many additional hours a performance will need to be for the piano player to charge an additional dollar. Although there are numbers in the answer choices, plugging in the answers is not the ideal approach here because they represent the difference rather than a value in the equation. Instead, since there is a relationship between the two variables, this can be solved using Plugging In. Let t = 2. If t = 2, then C = 100(2) + 50 = 250. The question asks about the piano player charging an additional dollar. Since the amount charged is C, let C = 250 + 1 = 251. Plug C = 251 into the equation to get 251 = 100t + 50. Solve for t. Subtract 50 from both sides to get 201 =100t. Divide both sides by 100 to get 2.01 = t. The question asks for the additional hours, so subtract the two values of t to get 2.01 − 2 = 0.01. This is equivalent to , so the correct answer is (A).

20.B

The question asks how many yards of fencing are needed to surround each area. There are numbers in the answer choices, so plug in the answers. Start with one of the middle choices. Try (B). If 40 yards of fencing are needed for each area, then the perimeter of each area is 40 yards. Begin with the square area. If the perimeter of a square area is 40 yards, then each side is 40 ÷ 4 = 10 yards. The side of the octagon is 5 yards shorter than this, which is 10 − 5 = 5. The perimeter of the octagon must match the perimeter of the square, so find the perimeter of the octagon, which is 8 × 5 = 40. Since this is equal to the perimeter of the square area, the correct answer is (B).

21.B

The question asks for the value of k, which is the x-coordinate of one of the x-intercepts. According to the question, the graph of f is a parabola, which means it has vertical symmetry. In a parabola, the axis of symmetry goes through the vertex. Since the vertex is at (5, −3), the axis of symmetry is x = 5. Since one of the x-intercepts is (3, 0), the other must be equidistant from the axis of symmetry. Since the distance from 3 to 5 is 2, the distance from 5 to k must also be 2. Therefore, k = 5 + 2 = 7. The correct answer is (B).

22.D

The question asks for an equivalent form of the function that displays values not included in the domain as constants or coefficients. Determine what is not in the domain. In a rational function, a value of x is not in the domain if it makes the denominator equal to 0. To find these values, set the denominator equal to 0 to get 3x² − 3x − 18 = 0. To get the roots of the quadratic, put the quadratic in factored form. Therefore, the correct answer must have the denominator written in factored form. Factor 3 from 3x² − 3x − 18 to get 3(x² − x − 6). Now factor (x² − x − 6) to get 3(x − 3)(x + 2). Therefore, the denominator must be written in the form 3(x − 3)(x + 2). Eliminate (A), (B), and (C), which don’t include this. The correct answer is (D).

23.B

The question asks how many times larger the surface area of the volleyball is compared to the surface area of the tennis ball. Because the question does not ask for either surface area but only for the relationship between the two, this can be solved by plugging in. Plug in the radius of the tennis ball as 2. If r = 2, then SA = 4πr² = 4π(2)² = 16π for the tennis ball. The radius of the volleyball is three time the radius of the tennis ball, so, for the volleyball, plug in r = 3 × 2 = 6. If r = 6, then SA = 4πr² = 4π(6)² = 144π for the volleyball. Translate the question into an equation. The term how many translates to the variable. Use y. The word times translates to “multiplication.” The term the surface area of the tennis ball translates to 16π. The word is translates to “equals.” The term the surface area of a volleyball translates to 144π. Solve the equation y × 16π = 144π. Divide both sides by 16π to get y = 9. The correct answer is (B).

24.B

The question asks for the velocity, in terms of t. There are variables in the answer choices, so plug in. According to the question, the particle accelerates from 20 to 50 meters per second in 10 seconds, so when t = 10, the velocity is 50. Let 50 be the target number, and plug t = 10 into each of the choices, eliminating any that are not equal to 50. Choice (A) is V = −50 + 3(10) = −20, so eliminate (A). Choice (B) is V = 20 + 3(10) = 50, so keep (B), but check the other answers just in case. Choice (C) is V = −20 − 3(10) = −50, so eliminate (C). Choice (D) is 50 − 3(10) = 20, so eliminate (D). The correct answer is (B).

25.C

The question asks for h(x + 3). There are variables in the answer choices, so plug in. Let x = 2. If x = 2, then h(x + 3) = h(2 + 3) = h(5) = 2(5)² − 7(5) − 3 = 2(25) − 35 − 3 = 50 − 38 = 12. Therefore, the target is 12. Plug x = 2 into each choice and eliminate any for which h(5) is not equal to 12. In (A), h(2 + 3) = 2(2²) − 7(2), so h(5) = 2(4) − 14 = 8 − 14 = −6. Eliminate (A). In (B), h(2 + 3) = 2(2²) − 7(2) −6, so h(5) = 2(4) − 14 − 6 = 8 − 20 = −12. Eliminate (B). In (C), h(2 + 3) = 2(2²) + 5(2) − 6, so h(5) = 2(4) + 10 − 6 = 8 + 4 = 12. Keep (C). In (D), h(2 + 3) = 2(2²) − 23(2) + 15, so h(5) = 2(4) − 46 + 15 = 8 − 31 = −23. Eliminate (D). The correct answer is (C).

26.A

The question asks for the point of intersection, which is the point that satisfies both equations. There are specific points in the answers, so plug in the answers. Test the ordered pairs in both equations from the question and look for a pair that makes both equations true. Start with the simpler equation. Plug in each choice into the second equation. For (A), (8) = 2, so keep (A). For (B), (16) = 4, so keep (B). For (C), (24) = 6, so keep (C). For (D), (32) = 8, so keep (D). Since all four choices are solutions to the second equation, plug them into the first equation. For (A), the equation becomes 10(8) − 62 = 9(2). This simplifies to 80 − 62 = 18 or 18 = 18. This is true, so keep (A). Since the coordinates in (A) work in both equations, (A) must contain the intersection of the two lines. The correct answer is (A).

27.C

The question asks for the model that best describes the decay of the amount of carbon-14 over time. Compare the answer choices. Two of the choices describe linear decay and two describe exponential decay. Linear decay describes a relationship in which the decrease is by a constant amount. Exponential decay describes a relationship in which the decrease is by a constant factor or percent. Eliminate (A) and (D), which reverse the definitions. According to the question, the amount of carbon-14 halves every 5,730 years. This is a reduction by the same factor. To better see this, plug in. If there are 100 grams of carbon-14 to start, then in 5,730 years, there will be 50 grams. In another 5,730 years, there will be 25 grams. Since the amount of the decrease was not constant, eliminate (B). The correct answer is (C).

28.2 or 18

The question asks for the sum of x and y and provides a system of equations. Since both equations are set equal to the same value, setting the right sides of the two equations equal will be the best method to solve the system for x. The new equation becomes x + 8 = x² − x − 7. Because this is a quadratic equation, get one side equal to 0. Subtract 8 from both sides to get x = x² − x − 15, and subtract x from both sides to get 0 = x² − 2x − 15. Factor the right side. Find two numbers with a product of −15 and a sum of −2. These are 3 and −5. Therefore, the equation can be written as 0 = (x + 3)(x − 5). Set each factor equal to 0 to get x + 3 = 0 and x − 5 = 0. The question asks for one possible sum of x and y, so it is necessary to get only one value of x. Therefore, one possible solution is to subtract 3 from both sides of x + 3 = 0 to get x = − 3. Plug this value of x into the first equation to get y = −3 + 8 = 5. Therefore, one possible sum of x and y is −3 + 5 = 2. Alternatively, to get the other possible solution, add 5 to both sides of x − 5 = 0 to get x = 5. Plug this value of x into the first equation to get y =5 + 8 = 13. Therefore, the other possible sum of x and y is 5 + 13 = 18. The correct answer is either 2 or 18.

29.20

The question asks for the least number of boxes of platinum that the jeweler can order to satisfy the requirements. Translate the English into math in Bite-Sized Pieces. Let the number of gold boxes purchased be g and the number of platinum boxes purchases be p. Since there are two ounces of gold per box, the total weight of the gold purchased is 2g. Since there are five ounces of platinum per box, the total weight of the platinum is 5p. Therefore, the total weight of the metal is 2g + 5p. The jeweler wants to purchase at least 90 ounces of metal, so 2g + 5p ≥ 90. Similarly, a box of gold costs $2,500, so the total cost, in dollars, of the gold is 2,500g. A box of platinum costs $7,500, so the total cost, in dollars, of the platinum is 7,500p. Therefore, the total cost of the metal is 2,500g + 7,500p. This must be at least $170,000, so 2,500g + 7,500p ≥ 170,000. According to the question, the jeweler already ordered 10 boxes of gold, so plug in g = 10 to get 2(10) + 5p ≥ 90 or 20 + 5p ≥ 90 for the first inequality and 2,500(10) + 7,500p ≥ 170,000 or 25,000 + 7,500p ≥ 170,000 for the second inequality. Solve each inequality. Subtract 20 from both sides of 20 + 5p ≥ 90 to get 5p ≥ 70. Divide both sides by 5 to get p ≥ 14. Now look at the other inequality. Subtract 25,000 from both sides of 25,000 + 7,500p ≥ 170,000 to get 7,500p ≥ 145,000. Divide both sides by 7,500 to get p ≥ 19.3. The least value of p that satisfies both inequalities is p = 20. The correct answer is 20.

30.160

The question asks for the value of h, which is the number of hours jogged during the month of December. The question says that the total distance jogged each of the two months was the same. Find the distance jogged in November. The question says that Robert jogged at an average pace of 8 miles per hour, and the chart says that he jogged for 140 hours. To find the total distance, multiply the rate by the time to get 8 × 140 = 1,120 miles. In December, the rate is 7 miles per hour and the total distance is also 1,120. To find the time, set up the equation 1,120 = 7h. Divide both sides by 7 to get h = 160. The correct answer is 160.

31.636

The question asks for the total distance jogged during June. According to the graph, Robert spent 120 hours jogging. The question says that Robert spent 70% his jogging time at the slower pace, which was 5 miles per hour. Therefore, he spent hours at 5 miles per hour. To find the distance, multiply the rate by the time to get 84 × 5 = 420 miles. He spent the rest of the time at the faster pace. The remaining time is 120 − 84 = 36, so he spent 36 hours at 6 miles per hour for a distance of 36 × 6 = 216. Thus, the total distance traveled for the month is 420 + 216 = 636 miles. The correct answer is 636.

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PSAT/NMSQT Prep with Practice Tests - Princeton Review 2021

Practice Test 2: Answers and ExplanationsPractice Test 2

Practice Test 2: Answers and Explanations
Practice Test 2