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

Answers and explanations
Practice Test 2

Section I: Reading

1. B. Clarifying the confusing term annual angular displacement would help to make the passage easier for a general non-scientific audience to understand, choice B. Choices A and D do not necessarily add clarity; if anything, these choices suggest changes that would make the passage more complex. Choice C addresses concerns about legitimacy, rather than clarity. Choice E suggests eliminating the only portion of the passage that attempts to portray the concept in layman’s terms.

2. B. The position of the pencil appears to shift, depending on which eye is viewing it—that is, according to the point from which it is observed, choice B. Choices A and E incorrectly focus on the identity of the object used in the example, while choice C is not implied by a simple demonstration. Choice D is never suggested.

3. D. Sentence 4 explains that the established military tradition supplied the South with military leaders, choice D. In choice A, the phrase “most of the talent” is too broad a term; this passage deals only with military leaders. Choice B is incorrect because the passage does not hint that the North found any military leaders in the South whatsoever. Choice C is unreasonable; it is not logical to jump from the final sentence of the passage to the idea that the North had no leaders at all. Choice E also displays an unreasonable jump of logic; the passage deals with the beginning of the Civil War, not its outcome.

4. E. Remember not to use your learned knowledge (e.g., knowledge of the Civil War) when answering a question about a subject matter that is familiar. Use only the information that is directly stated or implied in the passage. Of the various advantages held by the North, the passage concentrates on long-term advantages (e.g., superior railroads, industrialization, capital, food production, and population); this ties in directly with the response that the North had the capacity to endure a prolonged conflict, choice E. Choices A and D are contrary to the author’s thoughts about the Civil War. Although the South had seasoned leaders, choice B, the author does not imply that the South was already fighting another war. The North had economic superiority, choice C, but the author does not state or imply that the North had almost all the banks.

5. C. The author describes a misconception about the meaning of Cinco de Mayo, then provides the true background for the holiday, choice C. Choice A erroneously ignores Cinco de Mayo, while choice B is incorrect because no argument is presented. Choice D is incorrect because it ignores the correction of the misconception. Choice E is incorrect in its reference to an ongoing controversy.

6. D. Remember to look for an unstated assumption, rather than finding what is explicitly stated. Read between the lines to choose the correct answer and look for contradictions in the answer choices. The passage makes the point that top European scientists are trying to preserve these paintings, so it follows logically that their restoration is considered important, choice D; if not, why go to the effort? Choice A is incorrect because Sentence 2 describes “. . . vibrant strokes of yellow”; that does not agree with “pale shades of yellow” in choice A. Choices B and C contradict the author’s message: “. . . repel the eye and make the painting less memorable” (choice B) and “A number of paintings . . . are not well-known” (choice C). Choice E also contradicts the facts in the passage in its assertion that the scientists have finally discovered the cause of the damage, when in fact, the passage states otherwise.

7. B. The passage gives emphasis to van Gogh’s “night study.” Therefore, the logical answer is choice B. Choice A is not pertinent to the passage. The author does not discuss the details of the white star in van Gogh’s work. Choices C and D reference daylight paintings, which are irrelevant to the passage. The night paintings are van Gogh’s best-known paintings, eliminating choice E.

8. B. The first sentence of the passage provides a statement of its purpose; the rest of the first paragraph defines the equation, while the second paragraph provides examples of its application, which shows that the passage gives the reader a basic understanding of Einstein’s famous equation, choice B. Choices A, C, and D are secondary points. Choice E is incorrect due to its use of the word mysteries, as the passage focuses on what is already known about the relationship of mass and energy.

9. E. According to the explanation of the equation, c² represents the amount of energy contained in each unit of mass in all matter, as put forth by choice E. Choice A confuses the speed of energy with the speed of light, while choices B, C, and D are not suggested by the passage.

10. D. The first sentence of the passage simplistically defines the doctrine of association as the basis for explaining memories and how one idea leads to another. Sentences 4 and 5 provide two examples of this doctrine. Then, the last sentence adds the idea that things associated with each other are experienced contiguously. Therefore, the author would likely agree that the doctrine itself largely depends on the things happening contiguously, choice D. Choice C flatly contradicts the argument of the passage. Although choices A and B may be true statements, this information is not touched on in the passage. Choice E is weak because associations are not the same for everyone; they depend on each individual’s personal experience.

11. C. Choice C directly contradicts the main point of the passage, that associations are developed through experience. Choices A, D, and E provide examples that actually strengthen the argument in favor of association. In addition, the phrase “very few researchers question the doctrine” in choice B also helps to strengthen the argument because it implies that the vast majority of researchers do agree with the doctrine of association.

12. A. The definition of a political party belongs in a text that explains such organizations and systems—namely, an introductory text on political science, choice A. Choice B is incorrect because it is too vague and does not clarify what special interest the magazine may have. If it were a political magazine, it would be a reasonable response, but if it were a sporting magazine it would not. Choice C, although attractive, is incorrect because it describes existing agencies in government that should already understand the function of a political party. Choice D, campaign literature, is designed to stimulate support for a candidate. Choice E is not relevant to the passage.

13. C. The main idea of the passage is to explore Kermodism, which is the reproduction of white offspring (spirit bears) by black bears. Thus, choice C is the correct answer: “Why Do Black Bears Produce White Offspring?” Choice A is incorrect because white bears, Kermode bears, and spirit bears are all different names for the same animal, so there is no contrast among them. Rule out choice B; while the feeding and hunting habits of black and white bears are explored, this study tries to address the large question of why Kermodism exists. Similarly, choice D is incorrect because the article mentions the ice age theory as one possible explanation of Kermodism, but then dismisses it and seeks an alternate explanation. Finally, eliminate choice E because Kermodism is the only recessive mutation trait that the article explores.

14. C. In Sentence 3 of the second paragraph, the author introduces the glacial bear hypothesis as a possible theory to explain the existence of white bears, but then shoots it down because it fails to explain why white bears continue to flourish in the absence of constant snow and ice. Thus, the correct answer is choice C. Eliminate choice A because the glacial bear theory is not really a secondary theme and, in any case, no reference is made to it earlier. Choice B is incorrect because the second paragraph includes no statistics. Choice D is incorrect because the second paragraph does not claim that the question of why black bears produce white offspring is unanswerable. Choice E incorrectly describes the second paragraph.

15. C. The glacial bear hypothesis is unfounded because it explains how white bears may have emerged during the ice age, but it fails to account for how they have continued to survive since then. Thus, the correct answer is choice C. Choice A is incorrect because the glacial bear hypothesis relates directly to white bears and isn’t intended to explain the behavior of black bears. Choice B is incorrect because ice age survival is irrelevant to the premise. Eliminate choice D because the hypothesis doesn’t focus on fishing or reproduction. Finally, choice E can be ruled out because the hypothesis does not explain the method by which bears are born white.

16. B. The author’s negative assessment suggests an opposing attitude, choice B. Choice A, neutral, suggests an impartial attitude, and is therefore incorrect. Choices C and D can be eliminated because these choices suggest a positive attitude. Choice E is incorrect because the word inconsistent describes the author as shifting from one attitude to another, which does not represent the author’s intention.

17. B. The passage states the correct answer verbatim, On this 100th anniversary of his death, Twain . . . (Sentence 8), choice B. The author does not attempt to sell any books (choice A). The passage does not “exonerate” (to free from blame) Twain's critics, choice C; it disputes their criticisms. Choice D references only a supporting point of the passage. Choice E misrepresents the passage’s focus of dispelling the assertion that Twain was a racist.

18. C. As the passage quotes Twain (Sentence 7), “We have ground the manhood out of them and the shame is ours, not theirs; and we should pay for it.” Choices A, D, and E are never mentioned in the passage, and Twain specifically mentioned that he would not have helped just any student who had asked (Sentence 6), choice B.

19. A. The irony and language used in The Adventures of Huckleberry Finn may have confused some readers and led to a misunderstanding of Twain’s feelings about slavery and issues of race, choice A. Choice B is never discussed, and choice C incorrectly suggests that most readers interpreted the work as racist. Choice D references the wrong book, while choice E presents the opposite of what actually happened.

20. E. Later in the sentence, the author confirms that the term refers to the 100th anniversary of The Adventures of Huckleberry Finn, choice E. Choice A incorrectly characterizes the party as annual, while Choice B attributes the anniversary to the wrong book. Choice C is incorrect because the passage was published on the100th anniversary of Twain’s death, not birth. Choice D is not suggested.

21. E. According to the passage, Pudd’nhead Wilson was an eccentric but clever lawyer (Sentence 4) in one of his novels. Choices A and B represent real people, and choices C and D confuse the character with characters in The Adventures of Huckleberry Finn.

22. D. The point of the passage is that a person’s (or group’s) perception of reality varies according to who experiences it. Most people have varying realities. Choice D is the best example because war is a conflict between two different consensus groups that have two different realities. Choices A and B are not relevant to the main point of the passage. Although choice C is a true statement, it does not provide a supporting example. Choice E contradicts information in the passage because the fans at a baseball game do not have the same reality as the umpires.

23. B. Both choices B and C mention “consensus group,” but choice C says that the members of the group are misled about reality, which contradicts the author’s argument that no view of reality is, strictly speaking, a delusion. Therefore, choice B is correct. In choice A, the word “scientists” is irrelevant. Choice D is incorrect because “reality,” as it is defined in the passage, is not related to a consensus of the majority. Choice E is off topic.

24. C. Once again, the point of the passage is that different people or groups acquire different versions of reality based on their differing experiences. Reality is subjective, not objective, choice C. Choices A, B, and E are contrary to the passage. Reality is never termed a mere figment of one’s imagination, eliminating choice D.

25. D. Choice D is validated by sentences 8 and 9 of the passage. The ideas in the other choices have no corroboration in the passage.

26. E. Choice E correctly paraphrases the author’s point about reality and our perception of it: We cannot know what is “really” real because reality varies with individual perspective. Choice A does not answer this question and is off topic. Choices B, C, and D contradict the passage.

27. C. Sentence 9 serves to explain and summarize the racist and elitist doctrine mentioned in Sentence 8, choice C. Although the author states that social Darwinists expanded Darwin’s theory to society as a whole, the author does not attempt to discredit Darwin (choice A). Choice B is incorrect because the phrase some people in Sentence 9 refers to those who believe some people are superior to others, and does not refer to the author. In choice D, the phrase fair shake is an implausible idea for the author’s purpose. Choice E is incorrect because the phrase modern prominence (meaning “recent importance”) does not fit with the ideas presented in Sentence 9.

28. D. Sentence 5 of the passage focuses on the relevance of Darwin’s theory to human society, and the bulk of the passage develops this connection, choice D. Choice A has no evidence in the passage. Choice B is too strong to be the primary purpose, and the passage does not provide evidence that this answer is an accurate statement about Darwin. Choice C is unreasonable, especially since the author points out that Darwin did not apply his theories to society anyway. Choice E is inaccurate because the passage does not supply any examples of Darwinian evolution.

29. C. Because California is in the American West, it is logical to look for information about an early California dialect under American, Western on pages 263—264, choice C. All of the incorrect choices refer to pages concerning other locations in America, or to vocabulary in other parts of the world.

30. B. The vernacular (dialect of language spoken) of the index is organized by the spoken language of the country of origin, choice B. According to the index, you can find Australian aboriginal (native or indigenous) language on pages 288 and 290—291. None of the other choices are possible.

31. B. By citing the value of planning the presentation of material in an orderly way, the author must assume that organized instruction is beneficial to student learning, choice B. Each of the other choices draws conclusions beyond the scope of the passage.

32. C. Essential, choice C, is one of the meanings of integral. None of the other choices makes good sense when substituted for integral.

33. E. Because Sentence 3 includes the negative phrase not the only problem, any of the three connectives (Yet, However, or But) can be used. The blank in the second paragraph (Sentence 9) calls for a word to introduce a contrast with until recently (Sentence 8). Of the three possibilities, only Now fits. Thus, choice E is correct.

34. B. The shelf life of a product is its durability—how long it will last on the shelf of the market without going stale or spoiling, choice B. This definition is further supported by the phrase fruit that could stand up to shipping and still look good (Sentence 6).

35. E. The main idea in the second paragraph is the race to develop better-looking and better-tasting tomatoes to remain competitive in the future. However, Sentence 10 deals only with varieties available in the past and present, so it is the most expendable line, choice E. All the other sentences directly relate to the paragraph’s main subject.

36. D. Sentence 11 suggests that better-looking and better-tasting tomatoes are what American growers most need, choice D. By comparison, the other choices address what American tomato growers can already produce.

37. E. Although choices A, B, and D are all contributing factors, it is the loss of habitat that is cited as the biggest threat to amphibians, choice E. Choice C is not indicated as a factor in the passage.

38. C. The passage states that such a release would be monumental for amphibians, but not impossible to achieve, as stated in choice C. The passage states that zoos are the best chance for saving amphibians, and after being bred in captivity, the amphibians would be released into the wild.

39. A. Understanding punishment to be a type of negative reinforcement, one may infer that frequent punishment may inhibit learning, choice A. Because the passage focuses on education, the phrase in society at large in choice B leads to its elimination. Choice C is an illogical answer; if negative reinforcement does not work well in school, it will not be useful out of school either. Choice D misstates the author’s intent; a reward should be used instead of punishment, not after it. Choice E is irrelevant to this passage; while it may be true that learning disabilities often lead to emotional problems, this is not addressed in the passage.

40. C. The passage states that budget cuts result in cuts to the teaching staff, so this fact must appear in the correct answer. Only choices C and D specify a staff cut, but choice D is a weak answer; it is unnecessarily specific and possibly not accurate. Therefore, choice C is correct: a teaching staff of fewer than 50 teachers.

41. B. Migratory is the adjectival form of the verb to migrate, which means “to move from one place to another,” or “to move from one place to another with the change of season,” choice B. Choices A, C, and D are not germane to the question. Choice E, accustomed to many habitats, may have distracted you from selecting the correct answer. To help you answer this question, pay attention to the context of the word. Migratory suggests an action (movement), whereas accustomed suggests something fixed, making choice E incorrect.

42. C. Choice C is confirmed in Sentence 5 of the second paragraph, which states, “The best explanation is from well-recognized insect ecologists who have established that the monarchs use the position of the sun to determine their flight direction on long-distance journeys.” Choice A is incorrect because although the winds may help propel the insects, winds do not aid in navigation or direction. Choice B is incorrect because it is not mentioned in the passage. The ideas in choices D and E are mentioned in the passage, but they are presented as theories. Only choice C states that the best explanation is from well-recognized insect ecologists.

43. A. A point underlying this passage is that scientists cannot yet fully explain how a migrating butterfly finds its way (Sentence 9); thus, choice A is the best choice. There is insufficient evidence about butterfly navigation to know whether choice B is true. There is nothing in the passage to either support or refute the ideas in choices C and E. Choice D may or may not be true, but it is not the primary point.

44. E. Sentence 10, choice E, shifts from authoritative theoretical viewpoints about migrating butterflies to the writer’s personal opinion that encourages parents to increase their children’s interest in butterflies. Sentence 6 (choice A) is more of a transitional sentence than an opinion. Sentences 7 (choice B) and 8 (choice C) present theories. Sentence 9 (choice D) restates the point that we still don’t know for sure how these butterflies can navigate over such a long distance.

45. E. The last sentence of the passage defines respiration as a process of releasing energy from food, choice E. Choices A, B, C, and D all present functions that the passage attributes to breathing, rather than respiration.

46. B. The second sentence states that breathing is a function of many multicellular animals. From this it can be inferred that not all multicellular animals breathe, choice B. The passage doesn’t imply that either respiration or breathing is more important than the other. Choices A, C, D, and E are simply incorrect according to the information provided in the passage.

47. D. Choice D offers the true exception; it contradicts the passage because it includes three literature courses not within the same century. All of the other choices contain schedules that could belong to a specialist in The Teaching of Writing.

48. E. The only logical answer is choice E. According to the chart, 10 percent of senior boys are involved in sports, and 10 percent of sophomore boys are also involved in sports; therefore, an equal percentage of senior and sophomore boys participate, NOT a greater percentage of senior boys. All the other answer choices can be derived from the facts in the chart. Choice A is true (senior girls 14 percent; sophomore girls 13 percent). Choice B is true (junior girls 25 percent; senior girls 26 percent). Choice C is true (sophomore girls 53 percent; senior girls 51 percent). Choice D is true (junior girls 20 percent; senior girls 9 percent).

49. C. According to the chart, 63 percent of senior boys are involved in music/drama, the highest of any group/activity combination (choice E); 62 percent of sophomore boys are involved in music/drama, good for second-highest (choice A); and 58 percent of junior boys are involved in music/drama, the third-highest of any group/activity combination, making choice C the correct answer. Choices B (5 percent) and D (26 percent) represent percentages that are too small.

50. D. Junior and senior boys are less involved with newspaper/yearbook than are girls in each respective year, despite being more involved than their female counterparts as sophomores. Therefore, the data supports incentivizing involvement of upperclassman boys with newspaper/yearbook, choice D. The data does not support the program development detailed in choices A, B, C, or E. More girls already play sports than boys in each grade (choice A); more boys than girls participate in music/drama in each year (choice B); involvement in sports is consistent or slightly increases from year to year in each group (choice C); and music/drama already represents the strongest program area in terms of involvement, by far (choice E).

Section II: Mathematics

1. B.To find what number is 15% of 80, multiply:

2. C. Let x represent the price of the pair of shoes before the 40% discount. That is, 100% of x was the original price. Then 100%x — 40%x = $25.50, or 60%x = $25.50.

Now divide $25.50 by the decimal name of 60%, 0.60, to find x: $25.50 ÷ 0.60 = $42.50, choice C.

3. C. Since the figure is a rectangle, its opposite sides are equal. To find its perimeter, first add the two touching sides, 18 and 22, and then double the sum (or double each of the sides and add the results). The perimeter of the rectangle is (18 + 22) × 2 = 80. Since the square has the same perimeter, divide the perimeter by 4 to find the length of each side of the square: 80 ÷ 4 = 20. Finally, square this number to find the area of the square: 20² = 400. These steps are correctly described in choice C: Add 18 and 22, double this sum, divide by 4, then square the quotient.

4. C. Five loads at 15 minutes per load equals 1 hour and 15 minutes. If the washing commences at 3:20 p.m., adding 1:15 results in the work being finished at 4:35 p.m., choice C.

5. C. If six tests average 85%, the sum of all six percentage scores can be determined, choice C: 6 × 85 = 510 total percentage points. None of the other choices can be determined from the information given.

6. E. Simply add the tons shipped for each company: 5 + 7 + 9 + 12 = 33. But remember that the answer must be expressed in millions: 33,000,000, choice E.

7. B. Choices A, C, and E can be eliminated because they are all less than one-half. Now, divide to compare choices B, , and D, :

Choice B, , is the largest in value.

8. B. Method 1: Set up the ratio:

Therefore, 9 pounds of bananas cost $6.03, choice B.

Method 2: Divide $4.69 by 7 to find the cost of 1 pound of bananas and then multiply this result by 9.

$4.69 ÷ 7 = $0.67

$0.67 × 9 = $6.03

9. D. There are three chances out of four of spinning red, yellow, or blue. Thus, the correct answer is , choice D.

10. D. . Now convert to inches: 66 feet × 12 = 792 inches, choice D.

11. C. The easiest way to do this problem is to round $47.93 to $48 and then multiply by 15%.

So, rounded to the nearest dollar, the tip is $7.00, choice C.

12. B. First, notice that choices D and E can be eliminated because they list “square inches.” The answer should be in “inches.” The total length of ribbon equals the ribbon shown plus the ribbon not shown. There are four pieces of ribbon shown. Find the length of these pieces and then multiply by two.

Length shown = 4 inches + 16 inches + 8 inches + 4 inches = 32 inches

Total length = 2 × 32 inches = 64 inches, choice B

13. C. The three passengers will be charged $7.50 each for a total of $22.50. One hour and 45 minutes is hours. Traveling at an average rate of 40 miles per hour for hours, the taxi will have traveled miles. At 6 cents for each quarter of a mile, the charge would be 24 cents a mile. At 24 cents per mile, the cost for traveling 70 miles is ($0.24)(70) = $16.80. The total cost is then $22.50 + $16.80 = $39.30, so choice C is correct.

14. B. The percentile associated with a score represents how many whole percent of all scores lie below that score. Therefore, if a score is in the 85th percentile, this means that 85% of all other scores are below that score. The correct answer is choice B.

15. E. Since D intersects (overlaps) A, B, and C, it must have something in common with each one, choice E.

16. E. Mary worked a total of 24 hours, but you do not know in how many days. Therefore, you can’t derive the number of hours she works each day, choice E. Each of the other choices can be derived from the statements given.

17. D. The total of the five verbal state test scores is 2,635. Dividing that total by 5 (the number of scores) gives 527 as the average, choice D.

18. A. This problem can be solved using simple number replacements or using an algebraic approach.

Method 1: Suppose the original length was 6 and the original width was 4. The original area would be 24. The new length is 12 (double the 6) and the new width is 3 (25% of 4 is 1 and 4 decreased by 1 is 3). The new area is 12 × 3 = 36. Then 36 is 1.5 times more than 24, choice A.

Method 2: If you let l be the original length and w the original width, then lw is the original area. The new length will be 2l and the new width will be 0.75w, making the new area (2l)(0.75w) = 1.5lw. That is, the new area is 1.5 times the original area.

19. B. This question requires that you use a proportion.

20. B. In the 3rd quarter, the profit was $30,000. In the 4th quarter, the profit was $40,000.

21. B. A die has six sides. If it is rolled three times, there are (6)(6)(6) = 216 possible outcomes. Some of these result in all three rolls containing different numbers, and some rolls include duplicate numbers. The probability of rolling different numbers on all three rolls is the quotient between favorable outcomes divided by the total number of outcomes. The first roll can be any of the six sides since it will not match anything. The second roll is limited to five choices since one has already been selected by the previous roll. The third roll is limited to four choices, since the first two rolls have selected two of the choices.

Therefore, the probability of all three rolls resulting in different numbers is , choice B.

22. E. The fraction equals 0.125. Thus, it would lie between (0.111…) and (0.133…), choice E.

23. C. The mean of a set of data is the sum of all its values divided by the number of values. The frequency table indicates how often a value is repeated. This table shows that the number 3 occurs four times, the number 4 occurs eight times, etc. Multiply the number with its frequency and then add these results to find the total of all the numbers. Then add up the numbers in the frequency column to find how many numbers there are.

24. Now you can calculate the mean:

25.

26. B. First, divide $500 by the total budget amount ($4,000) to determine the percent of the total budget that $500 represents: 12.5%. Only two of the expense categories on the graph show a smaller percentage than 12.5%: Tickets and advertising (8%) and Decorations (11%), choice B.

27. E. The only statement that must be true is choice E: The class averages 2 pencils per student. Notice that 30 students could each have 2 pencils, so choices C and D may be false. Likewise, just one of the students could have all 60 pencils; therefore, choices A and B may be false. Only choice E must be true.

28. A. First, find the total length of string needed by multiplying 8 inches by 19:

8 inches × 19 = 152 inches

To determine the amount of string left over from the spool, first convert 5 yards to inches by multiplying 5 by 36 inches = 180 inches. Then, subtract 152 inches from 180 inches:

180 — 152 = 28 inches = 2 feet, 4 inches, choice A

29. C. In this type of question (weighted average), you must multiply the number of students by their respective scores and divide this total by the number of students.

Now divide 2,100 by the number of students in the English class.

2,100 ÷ 25 = 84

Therefore, the average score for all 25 students is 84%, choice C.

30. E. If Tony’s age is y, then Alex’s age is .

If Alex’s age is , then John’s age is , choice E.

31. C. Enlarging each dimension by 20%, the new dimensions would be 4.8 inches and 7.2 inches. Therefore, the new perimeter would be 2(length) + 2(width):

32. B. In order to have the pie graph represent blue-eyed students as 6 out of 24, the piece of the “pie” representing blue-eyed students should be , or . So the blue piece needs to be increased. Likewise, for hazel to represent , its piece of the pie should be slightly less than , so its size should be decreased. Choice B is correct.

33. B. To answer this question, multiply 36 by .

You can also change to 11.5.

36 × 11.5 = 414

34. C. In 2010, 10% of $30,000, or $3,000, was spent on medical expenses. In 2020, 12% of $34,000, or $4,080, was spent on medical expenses. Thus, there was an increase of $1,080, choice C.

35. A. There was an increase from 18% to 22%, or 4%, choice A.

36. D. Using the probability formula, , the chance of choosing a weekday is , choice D.

37. C. 240 out of 800 can be expressed as , which reduces to , or 30%, choice C.

38. E. Simplifying this problem first means changing to 0.2. Next, change 0.02 percent to 0.0002 (that is, 0.02 × 0.01 = 0.0002).

Now that you have simplified the problem, multiply 0.2 × 0.0002, which gives 0.00004, choice E.

39. B. Method 1: The probability of throwing a head in one throw is

Since you are trying to throw a head twice, multiply the probability for the first toss, , by the probability for the second toss, also . Thus, , and is the probability of throwing heads twice in two tosses, choice B.

Method 2: Another way of approaching this problem is to look at the total number of possible outcomes:

There are four different possible outcomes, but there is only one way to throw two heads in two tosses. Thus, the probability of tossing two heads in two tosses is 1 out of 4 total outcomes, or .

40. E. Choice E is the only true statement because is greater than , and is greater than .

41. B. The amount of discount was $120 — $90 = $30. The rate of discount equals , choice B.

42. B. To answer this question, add the mixed numbers and . Find the common denominator:

43. C. First, change 3 miles to feet by simply multiplying 3 by 5,280 (since 5,280 is the number of feet in a mile). This gives you the number of feet in 3 miles. Then multiply this product by 12 since there are 12 inches in each foot. The resulting product is the number of inches in 3 miles, choice C.

44. E. To compute the percentage, simply plug into the formula: .

The problem asks: “The air pressure in the football is approximately what percent of the air pressure in the basketball?” Thus:

(Note: The question asks for an approximate answer.)

45. A. If today Lucy is 14, then last year she was 13. Likewise, if Charlie’s age now is c, then last year he was c — 1. Now put these into an equation.

Transposing the 3 on the right side to the left side gives 13 — 3 = 2(c — 1), choice A.

46. B. The difference in the amounts invested would be 4% — 3%, or 1% of the principal ($1,200) over 3 years.

47. B. The mean of a set of data is the sum of the data values divided by the number of data values.

The median of a set of data values is the middle value when the data is listed from smallest to largest.

Because there is an even number of data values, there are two middle values.

The median becomes the mean of these two values.

The mode of a set of data values is the value repeated most often.

mode = 65

The range of a set of data values is the difference between the largest and smallest values.

range = 82 — 32 = 50

Now, substitute the values into the equation and solve:

(mean — median) × (mode — range)

(60 — 62.5) × (65 — 50) = (—2.5) × (15) = —37.5, choice B

48. B. Use elimination to determine the correct answer. Choice A (0.0028) is less than 0.0036. Choices C, D, and E are all larger than 0.052. Therefore, only choice B, 0.0481, is between 0.0036 and 0.052.

49. D. Since there are four floors, and the construction workers take 4 months to build the house, the average is one floor per month, choice D. The workers may build more or less than four rooms each month. Building four rooms each month, choice A, is only the average. The same is true for how many rooms are on each floor. Having four rooms per floor, choice B, is also an average. Choice C is not necessarily true. Choice E is incorrect; the house averages four rooms per floor, not three rooms.

50. D. To answer this question, multiply the total floor area by the percentage covered.

51. E. Be sure you answer the question. The question asks you to find the cost of the necklace, not the cost of the earrings. This problem can be worked algebraically or by trial and error.

Method 1: To do the problem algebraically, start by either representing the cost of the earrings or the cost of the necklace. Suppose x = the cost of the earrings, and then x + 20 = the cost of the necklace because the necklace costs $20 more than the earrings. The combined cost is $200, so

But x is the cost of the earrings, and the question asks for the cost of the necklace. Because the necklace costs $20 more than the earrings, the answer is $90 + $20 = $110, choice E.

Suppose x = the cost of the necklace, and then x — 20 = cost of the earrings. Then the equation would have been

Since x here represents the cost of the necklace, you have the desired answer.

Method 2: The answer can also be found by trial and error. Remember, the answer choices represent the cost of the necklace.

cost of necklace + cost of earrings = 200 (recall that the necklace is $20 more than the earrings)

Choice A: 70 + 50 = 200 NO

Choice B: 80 + 60 = 200 NO

Choice C: 90 + 70 = 200 NO

Choice D: 100 + 80 = 200 NO

Choice E: 110 + 90 = 200 YES

52. A. Bob is the tallest, choice A. Amir is taller than Ed, who is taller than Sam and Cecil. Since Ricardo is taller than Amir but shorter than Bob, Bob is the tallest.It may be helpful to arrange names on a line from tallest to shortest.

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. 222) to help you take a closer look and understand your scoring range.

Topic 1

Assignment: Identify a particular person or experience that had the greatest impact on your decision to enter the field of education. In an essay to be read by an audience of educated adults, explain why that particular person or experience was significant to you.

Sample Response: A Well-Written Essay

I was really nervous thinking about attending the first day of school. It felt like I was leaping off a high diving board into the unknown waters of a big-city high school. My mother assured me that everything would be fine and that I would meet lots of new friends, but as I contemplated stepping onto the new school grounds, all I felt was terror. My family had just moved to San Jose from a small town and I had fears about what to expect from the community, teachers, and especially my peers.

As a socially awkward 14-year-old boy, I was uncertain about how I would settle into what seemed like another world, especially since most of my peers at my old school thought that I was a little “quirky.” To say that I had a little trepidation about attending the first day of school was an understatement. I was deathly afraid of being ridiculed as the “small town geek.”

It was the first day of school when I met the person who would change my views about the field of education. The person was my sophomore English teacher, Mr. Lewis. On the first day of school, he entered the class with a broad smile. He told us that we all had the tools to learn how to write great stories. Mr. Lewis said that there were specific themes and elements in narrative writing that we could learn. When structured properly, these elements form a creative narrative that capture the readers’ attention—whether written for a short story, novel, script for television, or even a big screen Hollywood blockbuster! He assured the class that each of us had a story to tell. I questioned if this could really be true. Did a person like me really have a story to tell that others might be interested in reading about?

As the school year passed, we wrote many stories and I discovered that writing became one of my greatest passions. Writing gave me an opportunity to express myself and overcome my fears. Mr. Lewis was always enthusiastic and supportive of my writing, even though in retrospect, I now realize that many of these stories couldn’t have been very good. Mr. Lewis always made all of us feel as though our thoughts had value. He offered advice to improve our writing, but reminded us that we were creative and brave individuals for exploring what was in our hearts. This class was more than an English class, it was a lesson in building confidence.

Mr. Lewis’ class helped me to realize, first-hand, the power of mentoring young minds and helping young people feel good about themselves. He was more than a teacher; he nurtured, inspired, and motivated me to succeed in life. Although I didn’t realize it at the time, Mr. Lewis helped me to recognize that teaching can be one on the highest callings that a person can pursue.

Analysis of Topic 1 Response

The writer’s ideas are well-developed and supported with specific examples and details that reinforce the central theme of the essay—the person who had the greatest impact on the decision to become an educator. In this descriptive narrative, the writer initially takes time to explore the setting of the story in detail and explain the reasons for feeling uncertainty about attending a new school (e.g., “I was deathly afraid of being ridiculed”). The writer helps his audience empathize with how intimidated this 14-year-old student felt on the first day of school, and how the subsequent supportive teaching style of his English teacher helped build his confidence. Throughout the essay, the writer stays focused on the topic and organizes the essay by providing reasons why his English teacher was instrumental in changing his attitude about the field of education. This set the stage for the development of his love for learning and eventually, a love for teaching. The narrative effectively explores how one can be artistically inspired to explore one’s inner story.

Topic 2

An important issue in today’s world is improving our environment and preserving the planet. However, some people believe that individual efforts to combat pollution, global warming, and the depletion of natural resources are not likely to make a difference.

Assignment: In an essay to be read by an audience of educated adults, discuss the extent to which you agree or disagree with this observation. Support your opinion with a logical argument and specific reasons.

Sample Response: A Well-Written Essay

Does each of us have a responsibility to the environment and our planet, or are our individual efforts insignificant? I believe that although it is essential for governments to take action to save the planet, each person can make a difference in the way we live our lives. Governments must agree to strict regulations regarding emissions, waste disposal, and preserving resources, but we ourselves must not only adhere to regulations but also go a step further. People can make a difference by buying environmentally friendly products, voting for elected representatives who support environmental issues, and making a daily commitment to preserve our planet.

When we buy environmentally friendly products, manufacturers will respond by making more of them. For example, in the twenty-first century, many people began purchasing hybrid and electric cars; this forced car manufacturers to see the value in making such cars. Now, all car manufacturers sell hybrid and electric cars. This is true with a variety of products, from paper towels to kitchen appliances. These developments would not have occurred without individuals demanding that companies pay more attention to saving the planet. The truth is that the marketplace responds when we as consumers choose to buy “green” products. Our individual actions can become part of a movement, and the more of us who make a commitment, the greater the effects will be. Recycling, for example, has already had an effect on the size of landfills.

Our individual behavior may seem unimportant, but if we can make a commitment to better the world, it may influence legislators and corporation executives who are in a position to make major environmental decisions. In addition, we can vote for government representatives who place environmental issues high on their agendas. Interest groups that work to elect “green” candidates are made up of people, after all. Each of us is responsible for being informed about issues such as global warming so that we can make our decisions about candidates based on facts, not propaganda or campaign slogans.

It is too easy to decide that our individual actions won’t make much difference when it comes to saving the planet, but I believe this is a “cop-out.” In fact, most things of general value to the world are a result of many people coming together to make a difference, and this is certainly true when considering the preservation of our planet and improving our environment. With the information we have today, it is irresponsible, in my opinion, to ignore the importance of our actions.

Analysis of Topic 2 Response

The essay response addresses all of the criteria required to receive a high score on the CBEST. The writer communicates a logical flow of ideas that support the main topic and logically organizes the essay. The opening paragraph begins by asking the reader a critical question about a person’s individual responsibility in changing the environment, “Does each of us have a responsibility to the environment and our planet . . . ?” This question sets up the rest of the essay that describes the writer’s viewpoint.

The last sentence of paragraph one outlines what will be discussed in paragraphs two, three, and four. As the writer continues, he or she stays focused on the topic throughout the essay, and ideas from paragraph one are organized in sequence to help the reader anticipate what should logically follow. The body paragraphs support the writer’s thesis, explaining specifically how an individual’s actions can make a difference in changing the environment. Each paragraph is coherently developed using examples and reasons to support the writer’s opinion. The writer also uses clear transitions from one point to another. The writing is clear and relatively free of spelling and grammatical errors, and the concluding paragraph provides a summary of the writer’s viewpoint of taking important actions to save our environment.