CliffsNotes CBEST - BTPS TESTING Ph.D., Jerry Bobrow Ph.D. & 8 more 2021

Answers and explanations
Practice Test 3

Section I: Reading

1. D. If you read the entry for infinitive, you find all of the answer choices except choice D, subjunctive.

2. C. Under the entry “in,” you find a reference to its use “after a superlative.” Since words like best and worst are superlatives, the correct answer is choice C, page 126.

3. A. The specific concerns raised by the author about hydroelectric power relate to 1) unstable employment caused by inconsistent hydroelectric power production and 2) the shutdown of wind power plants. Selling excess power to other energy providers in regions of need, choice A, helps alleviate these concerns by providing a way to eliminate this surplus energy in a beneficial manner. Choice B does not address the unstable conditions for employment, while choice C does not address the hydroelectric-specific concern mentioned in the question. Choice D addresses low-output years, rather than surplus years, and choice E is irrelevant to the author’s concerns.

4. D. The author’s entire argument and conclusion are based on recent studies indicating a downward trend in aptitude test scores. The author must assume these test scores are accurate, choice D, to have faith in the conclusion that a student needs changes in both home environment and mindset. Choice A does not offer an assumption; rather, it offers a new fact (that previous studies were overturned), which is irrelevant to this question. Choice B offers an assumption, but it relates to heredity and thus is irrelevant to an argument about environment and mindset. Choice C is unreasonable; the argument offers no rationale to believe that the ongoing decline in test scores will stop declining soon. Choice E is simply inaccurate; the argument offers nothing to indicate that more out-of-school activities are available.

5. A. Choice A is the best option because the writer’s primary purpose focuses on the contrast between Dickinson’s perceived life and her talent; she was perceived as an eccentric, almost reclusive woman (Sentence 1) who wrote poetry that was either unappreciated by the public or unknown because she did not publish much. The lack of appreciation for her poetry during her life is contrasted with the fact that Now, in our time, she is one of America’s most celebrated poets (Sentence 5). Choice B does not address the question; the passage does mention that she did not receive recognition for her talent during her life, but it is not developed enough to be the writer’s primary purpose. Choice C contradicts the passage, and choice D is only a minor point in the passage. Choice E is never addressed.

6. E. The reference is made to create an analogy between Cinderella’s transformation into a princess and Dickinson’s transformation into a cultural icon after her death, which makes choice E the correct answer. Choice A is incorrect, as Dickinson never experienced riches in her lifetime. Choice B is incorrect in that it characterizes the passage in an overly negative fashion. Choice C is incorrect because Dickinson’s poetry did not change her life. Choice D is incorrect because the author does not focus on women succeeding outside of the social hierarchy.

7. B. Choice B correctly identifies Sentence 3 as the least important line because the overall subject of the paragraph is the increased availability of herbs, not the increased popularity of the Internet. This third sentence could be deleted without diminishing the message. In contrast, all the other sentences are relevant and focused on the topic.

8. C. Because Sentence 5 introduces the idea of several reasons and Sentence 6 begins with the phrase One is, it is logical to expect the seventh sentence to begin with a phrase like A second is or And another is. Choice C, A second is that more doctors are recommending herbal remedies to their patients, is the best fit. The four other choices do not fit nearly as well. In addition, each one has stylistic flaws or inconsistencies. Choice A uses the slang phrase turned on; choice B introduces the pronoun you, which has not been used elsewhere in the paragraph. Choice D is redundant terminology (doctors = medical practitioners, and larger = greater). Choice E is a sentence fragment; it lacks a subject.

9. D. Sentence 12 should begin with a word that signals a contrast, like however, since the passage is moving to the other side of the argument—the case in favor of herbs. The next part of the sentence gives a second example, so it should begin with a word or phrase like furthermore or additionally. Choices A, B, and C all begin with an incorrect transition, one that shows continuation of an idea, not a contrast. Choice E begins with a transition that will work in the first blank, but its second word, however, is the opposite of what’s needed in the second blank. Therefore, however and furthermore, choice D, best fit the blanks in Sentence 12.

10. A. Choices A and D each give an adequate summary of the first paragraph, but only choice A correctly refers to both the pros and cons of herbs given in the second paragraph. In choice B, the paragraph two information is also incorrect; the second paragraph does not address guarding against ineffective herbal medicines. In choice C, the statement for paragraph one is too vague, and the statement for paragraph two is inaccurate; the second paragraph does not discuss traditional medicines. In choice E, the first idea is too vague and the second is not addressed.

11. D. Since all five choices begin with however, we know that the answer must provide a counterargument to the idea that electric bicycle sales should continue to increase due to the anticipated rises in both fuel prices and population. Choice D undermines this argument by implying that a rise in fuel prices would not necessarily result in increased sales of electric bicycles because studies have shown that most electric bicycles are not very fuel-efficient. Choice A is incorrect because it merely states a minor geographic exception based on the premise that avoiding sweating is the main point of the purchase. Choices B and E support rather than weaken the idea that sales will increase by implying that American demand for electric bicycles may soon increase, and choice C is irrelevant to the author’s argument.

12. C. The passage is concerned with the current market for electric bicycles, along with their prospect for future growth and sales, choice C. Choice A incorrectly characterizes the passage as an overview of the actual vehicle, rather than its market prospects. Choice B is incorrect because no such potential roadblocks are discussed, while choice D incorrectly focuses on the past. Choice E incorrectly suggests that the author is trying to sell something to the reader.

13. D. As is often the case, the first sentence states the main idea of the passage, choice D. Choice A is incorrect, both because it is too narrow and because the passage tells the reader only that cat litter is made from clay and does not tell how it is produced. Choice B is also too narrow and does not address the author’s purpose. Choice C is incorrect because only one sentence mentions this fact; it cannot be the overall purpose. Choice E is incorrect because the article does not describe a method for preventing fires.

14. B. The Mine Safety and Health Administration claims that clay excavation is subject to the same rules that govern other excavations, such as coal mines. If the clay excavation sites are indeed as deep as coal mines, as stated in choice B, then MSHA’s position would be stronger because they could pose the same safety risks to workers. Choices A, C, and D are all irrelevant. The distance between the clay excavation site and the company (choice A) does not affect the depth of the excavations. Whatever material Southern Clay uses in their cat litter does not affect the MSHA position about excavations (choice C). Whether or not clay is found in coal mines does not affect MSHA’s position (choice D). Choice E may be mathematically correct from the Southern Clay standpoint, but it does not strengthen MSHA’s position.

15. D. The best definition of paraphernalia is equipment, choice D. The rest of the passage describes the two pieces of equipment that are needed. All other answer options neither fit the context of the passage nor the basic definition of paraphernalia, which refers to the miscellaneous articles, especially equipment, associated with a particular activity.

16. B. The passage recommends identification in the field where additional specimens . . . are available (Sentence 5), choice B. While it may be reasonable to assume that one would prefer to avoid transporting specimens (choice A) and possibly exposing them to deterioration (choice C), these objections are not the main reason it is preferable to make identifications in the field. Choices D and E are unreasonable ideas that are not supported in the passage.

17. E. The passage states that if one uses a substitute for a vasculum (a metal box to transport plants), it needs to be “fairly airtight” (Sentence 7), choice E, which is an attribute of a resealable plastic bag. None of the ideas in the other answer choices are stated in the passage.

18. D. The tone of the author concerning Antonio Vieira is certainly positive, but not spiritual (choice A) or idolatrous (worshiping idols), choice B. Therefore, admiring, choice D, is the best choice. Choice C, indifferent, describes someone who is uninterested, which is contrary to the author’s writing. Choice E, critical, has a negative, not a positive, tone.

19. B. The study in choice B would underscore the importance of a minimum calorie requirement, and thus weaken Dr. Orton’s argument that calorie requirements are outdated and less important than healthy menu items. Choices A and C are irrelevant to Dr. Orton’s argument that children would benefit from healthy food more than a required calorie threshold, and choices D and E actually support the doctor’s position.

20. A. The passage does not describe the author’s personal opinion, choice A. The passage underscores logic and reason by presenting authoritative sources and examples (e.g., School Nutrition Dietary Assessment Study, USDA), choices B, D, and E. The passage also presents a specific argument, choice C, by introducing an expert, Dr. Orton, who states that the calorie standard is out of date and that it is more important to make sure kids eat healthy food than it is for them to have a certain number of calories.

21. C. Since the lower number of accidents has not resulted in lower premiums, one suggestion of the passage is that the insurance companies are pocketing the savings rather than passing them on to the consumer. Thus, the author implies that insurance companies are taking advantage of drivers, choice C. Choice A confuses two ideas from the passage; the passage implies that the insurance companies are being unfair, not that the 65-mile-per-hour speed limit is somehow unfair. Choice B cannot reasonably be concluded because the argument does not mention auto manufacturers. The passage implies no greater or lesser importance to saving lives or lowering premiums, so choice D cannot be accurate. Choice E can be eliminated because there is nothing in the passage implying that driving skills have improved greatly.

22. C. Choice C is correct; the passage describes the invention of the first printing press and explains why it was one of the most revolutionary inventions known in human history. Choice A incorrectly frames the passage within the context of Johannes Gutenberg’s achievements; the passage does not state if the printing press was Gutenberg’s most famous (i.e., “crowning”) achievement. Although choices B and E may be correct historical statements, they are incorrect answers. Remember that you should not use your knowledge of history to answer the question; only use the information provided in the passage. Choice B (providing background for the intellectual renaissance in Europe) and choice E (describing the effect of the printing press on the class structure of Europe) are not mentioned in the passage. Choice D describes a secondary purpose of the passage.

23. B. To answer this question, you must identify the answer that is not presented as having been improved by the invention of the printing press. Choices A, D, and E are all presented as improvements in the final sentence of the passage (the diffusion of knowledge), as is choice C, albeit more subtly. Choice B is the correct answer; the passage claims the invention had a profound and immediate impact on the political, economic, and social structure of Europe, but it does not assert a positive change in political oppression.

24. B. According to the chart, the largest “bonus discount” for Extra Firm mattresses is $75.00, choice B. Do not be fooled by choice C; while a $90.00 discount is larger, it applies to a Royal Satin mattress set, not the Extra Firm mattress specified in this question.

25. C. According to the chart, the sale price of both the Regal King and the Royal Satin Queen is $699.00.

26. A. At first, it seems the young male would have no incentive to assist the older male in the elaborate mating dance; after all, the young male apparently receives no reward. However, look for a long-term incentive for a young male bird to assist in the mating dance. Being the lead bird in a mating dance significantly increases the likelihood that the courtship will lead to mating. Therefore, a logical explanation could be that assisting in the dance increases a young male bird’s likelihood of finding his own assistant when the time comes, choice A. Rule out choice B, as the presence of a second female would be irrelevant to the presence of a second, younger male and would not help resolve the paradox. Choice C is incorrect because being more likely to die of hunger would be a disincentive to being an assistant rather than an incentive. Choice D is incorrect because the greater strength and agility of a bird before becoming an assistant would not help to explain why it becomes an assistant. Eliminate choice E because the health and livelihood of the dancing bird’s future offspring provide no incentive for the unrelated, younger bird to participate.

27. D. The idea in choice D, optimistic and uplifting, is backed up by Sentence 6: There is life, not death . . . love, not bitterness, in the paintings. . . . Choices A and C contradict the passage; Chagall left the interpretation to the art historians and critics (Sentence 14) and he painted with technical mastery (Sentence 15), that was well beyond primitive skills. Choice B is unreasonable; the passage does explain how Chagall’s work can be understood and offers no evidence that the artist himself did not understand his own work. The negative tone in choice E contradicts the positive interpretation of Chagall’s works.

28. C. The phrases enduring themes [in his paintings] (Sentence 7) and through Chagall’s paintings that dreams . . . survive (Sentence 16) indicate choice C. The passage states that Chagall was a Jew from Russia, but it does not suggest that his famous collection of paintings is now held in a Russian museum, choice A. The passage offers no information about any increase (or decrease) in the value and popularity of Chagall’s work, making choice B incorrect. Choice D is unreasonable and contradicts the thrust of the passage’s praise for Chagall’s art. Choice E is not implied in the passage. In fact, the overall tone of the passage suggests that Chagall’s paintings are popular today.

29. D. Since Sentence 2 states This is how Marc Chagal painted himself, the presence of the Eiffel Tower in the painting possibly intimates the artist once lived in Paris, choice D. All other choices misread the description of Chagall’s self-portrait in the first paragraph or misinterpret information found elsewhere in the passage.

30. E. According to the graph, Boston had almost all night-game attendance (about 90 percent) compared with very small day-game attendance (about 10 percent), choice E.

31. A. Choice A is correct, as the passage suggests that Californians were anxious to escape from Mexico’s reign, yet states that Spain had been no better in terms of its emphasis on the territory’s development. Choice B is never implied by the passage, and while the passage suggests that some Californians favored annexation by the U.S., it does not mention a majority (choice C). The passage’s reference to landowners as the real power brokers contradicts choice D, and the desire for California to pursue a plan of independence is not mentioned in the passage (choice E).

32. C. The focus of the entire passage is on describing the situation in which Californians found themselves under Mexican reign, choice C. Choice A is incorrect, as the United States is only mentioned in the final sentence, and choices B and E provide only secondary purposes discussed in one to two sentences each. Choice D is an overreach that is only touched on by the reference to the power held by landowners.

33. B. By stating that nitrogen is essential for life (Sentence 4) and that bacteria are required to convert the nitrogen into useable forms (Sentence 3), the conclusion must be that bacteria must also be essential for life, choice B. Choice A is incorrect because the author makes no reference to the importance of oxygen, and choice C is incorrect because the author does not imply that plants retain the nitrogen they use for growth. Choice D incorrectly interprets the passage as claiming that there are no other building blocks for life, and choice E is incorrect because the author does not mention non-atmospheric nitrogen.

34. D. The term assistance (Sentence 2) refers to the points in the nitrogen cycle during which bacteria help convert the nitrogen into useable forms (Sentence 3), choice D. Choices A and B incorrectly assume that the word refers to nitrogen’s assistance in the production of life, while choice C is never mentioned in the passage. Choice E is incorrect because the passage does not mention what causes the nitrogen cycle to begin.

35. C. According to the passage, the auroras occur because solar wind pushes against Earth’s magnetic field, causing an electrical power supply (Sentence 5), choice C. The word unnatural in choice A is inaccurate. In choice B, the phrase caused by makes the choice incorrect. Choice D confuses Earth’s tail with the aurora borealis and aurora australis. Choice E is inaccurate because physicist Lou Frank studied recent satellite photos of the auroras; he was not the first to photograph them.

36. D. Sentence 7, Their colors are mostly green, and sometimes red, choice D, is the least relevant to the passage since the aurora colors are already mentioned in Sentence 4, These colorful displays of green and red. . . . It is unnecessary and redundant to repeat the colors later in the passage. The other choices are relevant in supporting the detailed description of the auroras.

37. D. Because Earth’s tail must be similar to those of comets (Sentence 1), they are probably also composed of electrically charged particles (Sentence 2), choice D. Choice A is a complete misread; the passage states that the auroras are visible in the northern and southern hemispheres, not at the equator. Choice B is an illogical and far-fetched conclusion to draw from the passage. Choice C is also unreasonable, especially since the passage claims the tail is invisible and never mentions high-powered telescopes. Choice E also misreads the passage; the auroras do not race from the sun; rather, it is the solar wind that does (Sentence 5).

38. B. The author presents the argument for abolishing grades with the reasoning that grades are not a good indicator of intellectual ability. To accept this argument, the author must presume that there are viable, superior alternatives, choice B. Choices A and C are overextensions of the argument’s implications, while choice D is irrelevant to the argument. Choice E is incorrect because the author does not present grades as the only current issue in education.

39. B. The author argues that the abolition of grades would increase student interest in subject matter, choice B, and uses this argument in support of the abolition of grades. The author then explicitly states that motivational factors such as subject matter are more important than . . . a letter on a transcript, thus emphasizing its value. Choices A and C are incorrect because the author does not argue that grade point average is a motivator or that grading criteria should be more important. Choices D and E are not mentioned in the passage.

40. D. The use of us in the last sentence (when discussing evaluation and instruction) indicates that the writer is likely a teacher speaking to other teachers, choice D. It would not make sense for politicians (choice A), parents (choice B), students (choice C), or civic leaders (choice E) to concentrate on evaluation or instruction.

41. C. The second sentence of the passage confirms that Diego Rivera’s primary political intention was to energize the Indian population and direct it toward the future, choice C. Choice A confuses Rivera with Orozco. Although choices B, D, and E may have been of interest to Rivera, the passage makes it clear that revitalizing the Indian population was the purpose of his mural.

42. A. Choice A best summarizes the passage, citing two supporting points for the main idea—that California’s roads have deteriorated. Choice B has no support in the passage for its phrase second in the nation, and is too narrow a choice to summarize the entire passage. Choice C presents an idea that is not in the passage, the concept of how much wear and tear fuel-efficient cars cause to roads. Choice D is not a summarization of the passage and exaggerates the passage’s point with the absolute word every. Choice E is incomplete and the over three-quarters phrase is correct only in reference to the state’s country roads.

43. E. A demand for new highways, choice E, is not a problem stated in the passage. The facts cited in all the other choices are mentioned in the passage.

44. D. In promoting the spending of state funds to advertise California’s tourist attractions, the author assumes such tourism will result in more income for the state, choice D. Choice A is unreasonable because of the word never. Choice B is incorrect because, while increased tourism may increase revenue, it cannot be assumed that such an increase will decrease the competition from other states. Choice C cannot be assumed by the author; tax revenues could never come from tourism alone. Choice E is irrelevant.

45. A. Implied by the passage is the belief that the campaign, if effective, will bring in many times the tourist revenue than what the advertising initially cost, so the $100-million price tag will be a bargain, choice A. Nothing in the passage suggests choice B, about monitoring advertising campaigns, or choice C, about opposing the advertising campaign. Choice D is contradicted in the passage, which implies that Hollywood is no longer the tourist draw it once was. Choice E is illogical and certainly not implied in the passage.

46. D. Sentence 4 makes the main point of the passage: that 1906 was the first time the United States fielded a real Olympic team, choice D. Choices A, B, and C are secondary points; choice A is only discussed in the first sentence to provide an introduction, and choices B and C are only briefly mentioned in the last sentence (Sentence 5) as interesting asides. There is no criticism in the passage, as suggested by choice E.

47. C. From the context, it is clear that purists refers to those who insist that because an Olympiad occurs once every 4 years, the 1906 games in Athens cannot be considered Olympic Games; in other words, purists most nearly means people who strictly adhere to a definition, choice C. Remember, you are looking for the “best” answer from the choices listed. Choices A, B, D, and E do not make sense in the context of the sentence.

48. A. The 1906 Olympics occurred despite the lack of an Olympiad (4 years) having passed since the 1904 games. Therefore, those who put on the 1906 games must not have believed that such a passing was necessary, choice A. Choices B and E provide unsubstantiated speculation about their motives, while choices C and D confuse the Olympic organizers with the American Olympic committee.

49. C. Although their reaction didn’t last long, the author explicitly states in Sentence 1 that intellectuals were initially hopeful in the aftermath of the stock market Great Crash, choice C. This hopefulness is not emphasized in the passage because it quickly disappeared. Restrained (choice A) is never mentioned. Choices B, D, and E describe characteristics likely taken on by intellectuals further into the Depression; it is important when taking the CBEST that you do not use your outside knowledge to answer the question. Use only the information presented in the passage.

50. C. The passage uses the word bulwark (supporter; defender) in the context of describing how the middle class was failing and desperate, in contrast to its traditional role as the stronghold of society. This suggests that foundation, choice C, would be a good synonym for its traditional role. Choices A and B portray meanings contrary to the intended use of the word. Choices D and E, peak and apex (meaning greatest), are the opposite of foundation. They are overly positive descriptions of the middle class.

Section II: Mathematics

1. C. Method 1: One way to solve this problem is to set up a ratio: 10 kilometers is to 6.2 miles as 45 kilometers is to how many miles? This is expressed in mathematical terms as:

Cross-multiplying gives:

Dividing both sides by 10 gives:

Method 2: Another method is to realize that 45 kilometers is exactly times 10 kilometers. Therefore, the number of miles in 45 kilometers must be times the number of miles in 10 kilometers, or times 6.2. Thus, 4.5 × 6.2 = 27.9.

2. C. Add the amount paid to the real estate agent and the amount the family received to arrive at the sale price:

3. E. Since the chart does not distinguish how many houses are 3 years old vs. 4 years old, the number cannot be determined from the information given, choice E.

4. D. There are two methods to solve this problem: (1) arithmetic logic and (2) algebra computation.

Method 1: Determine the ratio of the differences between the balance point (average) of $1.80 and both endpoints ($2.10 and $1.30). The differences are $0.30 and $0.50. Their ratio is 3 to 5. Divide the 8 pounds into two numbers that are in that same ratio. Clearly, that is 3 pounds and 5 pounds. Since the balance point (average) of $1.80 is closer to the $2.10, the larger weight must be assigned there; thus, the 5-pound weight is assigned to the $2.10 nuts, choice D.

Method 2: Let x be what we are looking for, that is the number of pounds of the $2.10 nuts. Set up an equation and solve for x.

Therefore, x = 5 pounds of nuts that cost $2.10 per pound.

5. A. The four listed items total $1,740. Therefore, by subtracting from the listed total of $2,220, you can see that the missing item must have cost $480: $2,220 — $1,740 = $480, choice A.

6. D. . Cross-multiplying gives 2q = 27. Dividing both sides by 2 gives:

Remember to check for this answer (in improper fraction form) in the choices before automatically changing to a mixed number .

7. B. The total of the five math state test scores is 2,570. Dividing that total by 5 (the number of scores) gives 514 as the average, choice B.

8. D. By plugging in the value of 5 for x into the equation, you can find y.

9. C. The mean of a set of data is found by finding the sum of all the data values and dividing by how many data values there are. Using the frequency table, we find the sum of the data as follows:

(3)(4) + (4)(1) + (5)(2) + (8)(3) = 12 + 4 + 10 + 24 = 50

Since there are 10 data values, the mean .

The median of a set of data is the middle value when the values are listed from least to greatest. From the frequency column, we see that there are 10 data values (4 + 1 + 2 + 3 = 10). The median is then the average (arithmetic mean) between the 5th and 6th scores. Listed in order, the scores are as follows:

3, 3, 3, 3, 4, 5, 5, 8, 8, 8

The 5th score is 4, and the 6th score is 5. The median then is found by finding the sum of 4 and 5 and dividing it by 2. The median .

Since the mean is 5, and the median is , choice C is the correct answer.

10. B. If each student drinks of a gallon of lemonade, 1 gallon is consumed by 8 students. Since 28 students are in attendance, , which is a number between 3 and 4, choice B.

11. C. To determine what percent was left after household and credit card expenditures, add up these two expenditures and subtract the total from 100% (because the chart represents 100%).

Now subtracting gives:

So 46% was left, choice C.

12. C. Since the figure is a rectangle, its opposite sides are equal. To find its perimeter, first add the two touching sides, 10 and 16, and then double the sum (or double each of the sides and add the results). The perimeter of the rectangle is (10 + 16) × 2 = 52. Since the square has the same perimeter, divide the perimeter by 4 to find the length of each side of the square: 52 ÷ 4 = 13. Finally, square this number to find the area of the square: 13² = 169. These steps are correctly described in choice C: Add 10 and 16, double this sum, divide by 4, and then square the quotient.

13. C. Sam walks 5 miles each day. Since he walks 5 days each week, he walks 25 miles each week. In 5 weeks, he would walk 5 × 25, or 125 miles, choice C.

14. D. If Jason is 4 years older than Emily, and if you call Emily’s age x, then Jason’s age must be x + 4. Since the total of their ages is 24, Emily’s age + Jason’s age = 24. Therefore, x + (x + 4) = 24, choice D.

15. D. If 8 pairs of shoes cost $360, then one pair of shoes costs . To find the cost of 12 pairs of shoes, multiply: 12 × $45 = $540, choice D.

16. A. Note that since there is a mark between +7 and +9, that mark equals +8. Thus, each mark equals 1. Counting back, point Q is at +5. Therefore, 15 units to the left of +5 would be +5 —15 = —10, choice A.

17. D. Twenty percent of 250 may be written as 0.20 × 250 or . Note that reduces to : , choice D.

18. D. Only choice D uses the correct meaning of percentile. It is the only accurate answer that compares Daniel’s score to that of other test-takers. Choice A is incorrect because a score of 55% incorrectly assumes that there were a total of 100 questions, but the number of questions is unknown. Choice B is incorrect because 18%, not 45% (percentile), did better than Daniel. Choice C is incorrect because 82% (again, use percentile) did worse than Daniel. Choice E is incorrect because we don’t know the percentage of correctly answered questions.

19. B. To purchase 12 DVDs, Andres must buy six packages. At $2.98 per package, he spends $17.88. His change from a $20 bill will be $20.00 — $17.88 = $2.12, choice B.

20. B. Note that all choices except choice B are greater than . Choice B, , is less than , and is, therefore, the smallest.

21. A. If all 200 decks were sold at a price yielding a 15% profit, the price per deck would be (1.15)($2.20) = $2.53. Total revenue would be (200)($2.53) = $506. If Gavin sold each deck at a price yielding a 25% profit, the price per deck would be (1.25)($2.20) = $2.75. Total revenue would be (200)($2.75) = $550. Only choice A, $540, yields a revenue between $506 and $550.

22. B. This problem can be solved using a Venn diagram. Draw three intersecting circles representing the three movies.

Since three people saw all three movies, place a 3 in the intersection of all three circles. Then because four people saw exactly two movies, but we don’t know which two, distribute the four friends into the three parts of the diagram that are inside exactly two of the circles. It does not matter how you distribute them. In this case, we put a 2 in one of these regions and two 1s in the other two. (You could put 3 in one region, 1 in another, and 0 in the third.) Now fill in the remaining regions of the diagram.

Since eight people saw a drama, we put a 2 in the region in the drama circle that is not inside either of the other two. This gives a total of 8 in the drama circle. Repeat for the comedy circle and the action circle.

Adding all the numbers inside at least one of the circles gives a total of 11. This means that one person did not see any of the three movies, choice B.

23. E. Assume that the length of each side of each square is 1. To determine the perimeter of each diagram, add up all of the sides. Mark off the starting point.

The diagram in choice A has a perimeter of 14.

The diagram in choice B has a perimeter of 10.

The diagram in choice C has a perimeter of 10.

The diagram in choice D has a perimeter of 14.

The diagram in choice E has a perimeter of 24; diagram E has the greatest perimeter.

24. A. Rounding 0.14739 to the nearest thousandth means first looking at the digit one place to the right of the thousandths place: 0.14739. Since that digit is 4 or less, simply drop it. (There is no need to replace it with zeros because they are not required to the right of a decimal point.) The correct answer is 0.147, choice A.

25. A. Note that 12 can be expressed as (10 + 2). Therefore, another way to compute 12 × 1.60 is 10(1.60) + 2(1.60), choice A.

26. B.

Cross-multiplying:

The correct answer is choice B.

27. A. Sixteen out of 400 may be expressed as a percent, as . Dividing 16 by 400 gives 0.04, or 4%, choice A.

28. B. Maya budgeted 10% for air travel. She spent 20% more, or another 2%, bringing the amount for air travel to 12%. She budgeted 60% for the cruise fare. She spent 10% less than this amount, or 6%, bringing the amount for the cruise fare down to 54%. She budgeted 20% for on-board expenses. She spent 20% more than budgeted, or another 4%, bringing the amount for on-board expenses to 24%. She budgeted 10% for gifts. She spent 20% less than budgeted, or 2%, bringing the amount she spent on gifts to 8%. Adding the actual percentages, gives 12% + 54% + 24% + 8% = 98%. She spent approximately 98% of her budgeted amount on her cruise vacation, choice B.

29. C. Method 1: To calculate the answer, you could multiply 7 by $1.00 and 7 by $1.25 and then add the results:

It cost Sara $15.75 to wash and dry seven loads of laundry, choice C.

Method 2: The other possible method to calculate the answer is to add the washer and dryer costs together and then multiply the total by 7.

30. C. Using the probability formula, , the chance of choosing a weekend day is , choice C.

31. C. To answer this question, set up a fraction. The number of shaded boxes is the numerator and the number of total boxes is the denominator. Thus, shaded boxes, choice C.

32. C. Note that only choice C raises one of the numbers by 5 while it lowers the other number by 5. This gives the best approximation of the five choices.

33. E. Since each cluster of symbols represents 10 stars, clusters must equal 95 stars, choice E.

34. C. Use the definition of probability to determine the answer. Probability of taking a green or purple gumball:

Remember to decrease the number of purple gumballs by 1 because Trang already took one purple gumball and chewed it.

35. B. Thirty percent off the original price equals a discount of (0.30)($8,000) = $2,400. Therefore, the new selling price is $8,000 — $2,400 = $5,600, choice B.

36. D. Since Araceli’s hybrid car averages 35 miles for each gallon of gas, on 12 gallons he’ll be able to drive 12 × 35, or 420 miles, choice D.

37. B. Note that if there were an equal number of adults and children, then there would be 75 of each. Since there are more adults than children, the number of children must be lower than 75. Since choice A, a decimal number, is an unreasonable answer, of the choices given, only choice B could be the number of children.

38. D. Use this formula when solving percent change problems.

Amount spent for food in February was 20 and in March it was 30.

The percent change becomes , choice D.

39. D. Note that, for example, as the temperature decreased from —10° to —15°, the average amount of snowfall per hour increased from 2 to 2.5 inches. (Watch out for the minus sign, which means the temperature drops when it goes from —20° to —25°.) This relationship exists throughout the chart. Therefore, choice D is correct.

40. C. To determine the number of dry erase markers costing 82¢ each that can be made for $75, simply divide: $75.00 ÷ 0.82 ≈ 91.46.

Note that since you cannot have a fractional answer in this case, 91 is the answer, choice C.

41. A. Determine the percent of the school population that did not attend graduation: . Dividing 35 by 280 gives 0.125, or 12.5%, choice A.

42. E. There are several quick methods of solving this problem.

Method 1: A ratio can be set up.

Method 2: Alternatively, determining Fatima’s hourly rate (5 pages per hour) tells you that she will need 10 hours to proofread 50 pages.

43. B. If team B’s victories are called x, then team A must have 2x victories, team C must have (2x — 5) victories, and team D must have (x + 4) victories. All together, these total 6x — 1. The problem states that the total equals 29 victories. Thus,

Therefore, team D has (x + 4) victories, or (5 + 4) = 9, choice B.

44. D. The new dimensions are:

Note: Perimeter is the distance around. Think perimeter (rim). Simply add the sides (10 + 8 + 10 + 8) = 36 inches. Or apply the perimeter formula:

45. E. So far, George has averaged 80% on each of three tests. Therefore, his total points scored equal 3 times 80, or 240 points. In order to average 85% for four tests, George needs a total point score of 4 times 85, or 340 points. Since George presently is 100 points short of 340, he needs to get 100 points, or 100%, on the fourth test, choice E.

46. B. Solving for p, first subtract 9 from both sides.

Now divide both sides by 7:

47. E. Method 1: (You don’t know this, so represent it as x.) Shortcut—These are equivalent fractions.

Since 5 × 9 = 45, then 12 × 9 = 108 (which is x). Now divide by 60:

Method 2: You can also solve this mathematically as follows, by first cross-multiplying:

To solve for x, divide both sides by 5.

48. B. Note that, on the graph, a 35-degree drop in temperature on the line correlates with a 20% attendance drop (the fourth slash up the graph), choice B.

49. D. First add the value of one of each coin:

$1.00 + $0.50 + $0.25 + $0.10 + $0.05 + $0.01 = $1.91

That leaves $9.15 — $1.91, or $7.24, for the rest of the quarters:

Remember that you already counted one quarter when you added each circled coin above. Now, add the 28 additional quarters to the 1 original quarter. Thus, 29 is the largest number of quarters she can have, choice D.

50. A. The probability of two independent events is the product of their individual probabilities. The probability of spinning a 3 is , and the probability of spinning a blue is . Therefore, , choice A.

Section III: Writing

To help you evaluate your essay writing skills, review the two examples of written responses for Topic 1 and Topic 2. Compare your essay response to these examples and use the checklist (p. 264) to help you take a closer look and understand your scoring range.

Topic 1

All people have significant events in their life that influence their future, whether favorably or unfavorably. Sometimes it is a seemingly minor event, sometimes a major one.

Assignment: In an essay to be read by an audience of educated adults, identify and describe an event in your life that influenced you and explain what effect it had on your future.

Sample Response: A Well-Written Essay

My dad, the son of Serbians who immigrated to the U.S., was the ultimate “Walk It Off” man. If anything bad ever happened, we kids simply had to buck-it-up and keep moving forward, even when it hurt. Let me illustrate: We went on our first family backpacking trip along with another family, encompassing four adults and six children. In typical dad-fashion, this somehow grew and expanded into a Serbian Forced March. This was not a simple weekend excursion, not a local jaunt, but rather a 52-mile trek through King’s Canyon. I was all of five years old, and the only girl of all the children. Granted, dad wasn’t that hard a taskmaster. He kindly hired burros to carry our heavy canvas tents, sleeping bags and other provisions, plus a spare burrow for the six children to take turns riding so we would not have to walk every step. Well, the first day we stopped at Mist Falls to rest while the two dads went scouting ahead. Being fascinated by the beasts of burden, I wanted to go pet the pretty one, named Terrapin, that we children shared. I foolishly ignored the adults’ advice, and as I quietly stepped up behind him to pet his rear, he reared up and kicked me in the rear, sending me flying several feet through the air. Naturally, I was traumatized; I screamed at the top of my lungs as a huge bruise quickly developed on my hip. My mom, not knowing what else to do in the wilderness, got a sleeping bag for me to curl up in as I calmed down. The men returned shortly thereafter, and I recall whimpering up at Dad who appeared about fourteen feet tall as he looked down at me in the sleeping bag on the ground. I bet you all know what he said . . . “Well, you’ll just have to walk it off!” And indeed I did. The swelling and bruising eventually declined, and I walked the trail for the rest of the trip, singing some silly childhood song over and over and over again, surely annoying everyone else.

The lesson is obvious, and I am better today for knowing how to walk it off. The burro incident in my life and its aftermath taught me that I can get over hardship, that I can conquer anything I set my mind to, and that a kick in the butt can eventually make me stronger. We kids used to tease my dad for telling us to walk it off so often, but he hammered resilience into his children, and today I’m proud of my ability to face adversity of any kind and know that if I keep my sights on my goal, I will succeed. As I look back on this incident, it was indeed a minor one in the big picture, but I never forgot that day when I learned I would not be babied by others, and that I’d have to do my own walking.

Analysis of Topic 1 Response

This writer addresses the topic by describing a childhood incident that, although physically painful at the time, helped her grow and become resilient. The description is clear and the action easy to follow. She begins by setting up how her father’s “Walk it off” saying illustrates the incident she uses to address the topic. Her five-year-old experience of getting kicked by a burro that she had naively hoped to pet is almost comic in her retelling, and instead of stressing how painful the incident was, she stresses how much it helped her mature in life. The incident itself works well for this topic and the writer demonstrates the ability to communicate with clarity and precision.

Topic 2

Some American public schools have removed the “A” to “F” grading system and substituted a “Pass-Fail” grading system, with the instructor adding a written statement about the student’s progress.

Assignment: In an essay to be read by an audience of educated adults, state the pros and cons of removing the “A” to “F” grading system. Support your position with logical arguments and specific examples.

Sample Response: A Well-Written Essay

Evaluating a student’s progress is a concern among most teachers. Although it would be agreeable to say that grades “don’t matter” as much as students’ subject-matter improvement, that simply isn’t true. Traditionally, the measurement of students’ progress has been a letter grade, but some public schools have adopted the “pass-fail” grading system with a written statement describing each student’s progress. Although letter grades provide a measurement of a student’s performance that is universally understood, “pass-fail” grading places less stress on students, removes negative stigmas, encourages motivation, and encourages students to take more academic risks.

Letter grades are a more definitive reflection of a student’s progress. If a student receives a “C,” he is ranked as average compared to other students. If he receives an “A,” he is among the top students, and a grade of “D” reflects that the student may be in danger of failing. The “pass-fail” system, on the other hand, does not show equivalent letter grades. For example, if a student passes a subject, it is unclear precisely where the student ranks compared to other students. Even a teacher’s comment may be open to interpretation. A student may choose to interpret a teacher’s comment as favorable, when in fact the teacher may have intended to show that the student’s progress was simply adequate.

Letter grades are also universally understood by all teachers and schools. If a student has a “B” average, other teachers and schools know where that student stands in relation to others. However, it is also common for different teachers and different schools to have distinct grading standards. For example, a teacher in my high school was notorious for giving students no higher than a “B,” no matter the circumstances. Research studies have shown that students with similar academic skills can be ranked differently by different teachers. Another problem with evaluating students with letter grades is that students may feel pigeon-holed and the letter grades may influence motivation and attitude.

The “pass-fail” system has numerous benefits. It places less stress on students and removes negative stigmas that are carried by letter grades. A teacher’s statement, along with the pass-fail designation, can be very helpful in motivating students, but perhaps the best argument for a “pass-fail” system is the emphasis is on learning, not on “getting an “A.” Too often students struggle to achieve high grades by memorizing material, rather than trying to understand what is being taught. The best argument against “pass-fail” is that it can be too vague and can make it difficult for a student to understand where he stands.

Each grading system has its advantages and disadvantages. With a “pass-fail” system students, teachers, and schools may ultimately translate teachers’ “pass-fail” comments to an equivalent letter grade. In my opinion, the better option for evaluation might be a combination of the letter grade system with a written statement used in the “pass-fail” system.

Analysis of Topic 2 Response

This essay is well organized and is free from unwarranted conclusions. The writer stays focused on the topic and logically organizes the advantages and disadvantages of the two grading systems. In addition, the writer offers evidence and examples to support his or her ideas. Notice that the topic does not require the writer to take a stand on which system is better, though this writer does offer an opinion in the summary of the concluding paragraph. The writer’s opinion is stated at the end of the essay after discussing the pros and cons throughout the essay. A particular strength of this essay is that the paragraphs are well developed (except perhaps for the last one), and the writer uses varied sentence structure intended for an audience of educated adults, offering smooth transitions (for example, on the other hand, however) throughout the essay. In addition, the writing is presented clearly with minimal grammatical errors.