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

Answers and explanations
Practice Test 1

Section I: Reading

1.   D. Information about subjective complements is listed under Complement, subjective, with linking verb, 188—190, choice D. The pages listed in choice A (pp. 184—186) address compound subjects; choice B

(pp. 186—198) addresses complements (not subjective complements); choice C (pp. 187—188) addresses intransitive verb complements; choice E (pp. 214—216) addresses compound sentences.

2.   A. The entry under Comparison in essay based on, 54—57 is the best place to look for information about organizing an essay that would compare the two planets, choice A. The pages listed in choice B (pp. 92—98) give information about conclusions in essays. Choices C (pp. 186—198), D (pp. 255—256), and E (pp. 347—348) address grammar-related information, not essay (theme) writing information.

3.   C. The adjective versatile means “adaptable in many areas, able to turn easily from one subject to another, capable of many accomplishments,” choice C. The word comes from the Latin verb vertere, “to turn.” This definition focuses on the multifaceted aspects of the paragraph’s content—that Jackie Robinson achieved success in many areas. Although choices A (famous) and B (fiercely competitive) are accurate descriptions of Robinson, they are not the best definitions for “versatile.” Choices D and E are not related to “versatile” and do not address Robinson’s multitalented resourcefulness.

4.   B. Choice B is the only sentence that is consistent with the rest of the paragraph in both style and the writer’s purpose. The content in choice A is irrelevant to the passage; additionally, you should eliminate choice A because it uses the first person (I), whereas the rest of the passage uses only the third person (he). Similarly, choice C can be eliminated because of its use of the second person (you). Choice D can be eliminated because of its off-topic information and its careless use of slang, big deal. Choice D also presents no information about Robinson. Choice E can be eliminated because the language is not consistent with the writer’s tone of the passage.

5.   B. The passage moves forward in time and is organized chronologically, from Robinson’s becoming a Major League player in 1947 to his life after baseball and his 1962 election to the Hall of Fame, choice B. The other four options are simply untrue; all of them misrepresent the true structure of the passage.

6.   E. The first blank requires a transition indicating a contrast between the ancients and the more modern. Of the five choices offered for this first transition, the only ones that are possible choices are C, “Meanwhile,” and E, “However.” The second transition should point to a similarity between the more modern and the 1990s. Choice C can be eliminated because the second word, “Consequently,” does not fit well in the second space. Choice E is correct because “Similarly” does fit well. Choices A, B, and D do not logically fit the information and organization of the paragraph.

7.   A. Arbitrary means “random, whim, or chance.” The best of the five choices is “based on whim; capricious,” choice A. Capricious means “impulsive or unpredictable.” The passage does not specifically suggest that modern man is lacking in judgment, choice B. The definition in choice C, “conveying a truth,” actually contradicts the intended meaning of arbitrary, as the passage continues with has no special significance. The definition offered by choice D is too strong. The passage does not imply that naming a date in time is totally useless; indeed, the last sentence states that names and dates were created to make relationships easier to grasp. Finally, choice E does not fit into the overall meaning of the passage; nothing alludes to two meanings of names.

8.   E. The sentence in choice E opens with the comparison Like the names of the stars, which links the subject of the first paragraph (the arbitrary names people give to stars) with the useful terms called numbers, choice E. The point of the passage is that both are fictions created by humans, not eternal natural truths; therefore, choices A, B, C, and D can be eliminated.

9.   B. This author indicates that the starry constellations in Earth’s skies are merely useful fictions; they are patterns created by humans that would make no sense if viewed from any other point in the universe, and our names for them simply reflect the times in which they were created. Therefore, even if the author is an expert on stars, he is a skeptic overall, so it is NOT reasonable to conclude that he would trust astrology. Rather, it is much more reasonable to infer that the author would tend to be skeptical of astrology, making choice B correct. The author does not believe in astrology, choice A. Choice C contradicts the passage; the author explicitly says that the millennium has no special significance in the . . . natural world. There is no support in the passage for choice D; nothing indicates whether the author approves or disapproves of comics and cartoons. Finally, the claim made in choice E, that people can have absolutely no influence on the events of the natural world, is not the point of this author, who merely indicates that some things, such as dates or names, have no effect on nature.

10.  D. The correct answer is choice D because in the natural sciences, the lowest percentage is in physics (8%); in the social sciences, the lowest is in sociology (4%); in the humanities, the lowest is in French (5%). Choices A, B, C, and E are incorrect.

11.  E. The combined percentage representing humanities courses (30%) is smaller than the percentage for both natural sciences (38%) and social sciences (32%), which means that there are fewer students enrolled in humanities classes than in social sciences or natural sciences classes. The graph’s title also informs the viewer that the chart represents all classes at Kennedy High School; therefore, choice E can safely be concluded. The chart contradicts choices A and B, while choice C is an overreach (the chart does not mention national student preferences). Choice D is not implied by the graph.

12.  C. The passage serves to define social psychology. Choice C provides an accurate and comprehensive summary of the author’s main point about social psychology. Remember to look for the best choice among the answer choices listed. Choice A can be eliminated because it combines social scientists with social influences. Choice B incorrectly focuses on the influence of an individual on behavior, rather than varying influences. Choices D and E overreach and are not implied by the passage.

13.  D. Choice D is directly supported by Sentence 4, What impacts one child can impact the entire class. The phrase free to talk in Sentence 5 implies that teachers should not necessarily persuade quiet children to talk, choice A, nor allow them to fade out of the group dynamic, choice B. Choice C is incorrect because cooperative peer groups are not mentioned in the passage, nor are the higher test scores suggested by choice E.

14.  C. The passage puts forth that the classroom is a microcosm within a larger context that influences child development, which is rephrased by choice C. Choices A, B, and E misinterpret the definition of the word microcosm, while choice D erroneously refers to a specific classroom; the passage only discusses learning dynamics in general terms.

15.  B. By stating that the new type of citizen will not be intimidated by ending careers, the author presumes that present citizens are intimidated, choice B. Choice D is incorrect because it states an implication rather than an assumption; remember that an assumption addresses what the author believes before writing, and an implication addresses what the reader can reasonably conclude after reading the passage. Choices A, C, and E all draw conclusions that are beyond the scope of the passage.

16.  D. The final sentence of the passage expresses a somewhat skeptical, qualified view of the ultimate value of technology; the point in choice D is too upbeat for this author. On the other hand, each of the other choices is consistent with the author’s views about humanity; therefore, you can eliminate choices A, B, C, and E.

17.  D. Nevertheless in Sentence 3 suggests that Nightingale pursued her interest despite social attitudes, suggesting that she was dissatisfied with a woman’s usual role, choice D. Nothing in the passage supports choice A. She convinced her family to allow her to do something that was considered off-limits for a woman of her class; they did not sponsor her studies, choice B. Nightingale’s religious feelings are not addressed, choice C. In spite of her putting splints on her dog’s paws, there is no indication in the rest of the paragraph that she wanted to be a veterinarian, choice E.

18.  B. The author cites the reduction in the hospital death rate immediately after stating that Nightingale took a team of nurses to Turkey, choice B. The reader has no way of determining whether choice A is true. Choice C is irrelevant because the passage deals with Nightingale’s becoming a nurse, not a physician. Choice D might seem correct, but the emphasis is on the reduction in the death rate, not on the horrible conditions in hospitals. Choice E might also seem possible, but this detail is used specifically to dramatize the effect of the nurses, which is not the main idea of the paragraph.

19.  B. Choice B correctly concludes that if people retire earlier in the future and face the financial burdens of retirement in their middle ages, they will need more money to support themselves for the rest of their lives. Choices A and C state conclusions that are neither expressed nor implied in the passage. The passage portrays early retirement as an unattractive, problematic occurrence that will affect many; choices D and E contradict these unattractive connotations of early retirement.

20.  C. The primary assets of the tropical waters are that they are warmer, shallower, and provide more protection for mothers and calves, making them more conducive to breeding, choice C. Choice A is accurate, but it is not cited as the main reason for the whales’ migration. No parallel is drawn between whale migration and bird migration, choice B. The reason the humpback whales mate and calve in warmer waters is physical, not biological, choice D. Food supply in colder waters is not mentioned, choice E.

21.  E. Choice E is the most comprehensive choice, describing the overall purpose of the passage rather than secondary purposes and implications. Choice A states the case too strongly; it does not really address the author’s overall purpose, and a widespread lack of self-expression is never specifically mentioned. Addressing anxiety, choice B, is not discussed in the passage. Choice C is irrelevant because the passage’s purpose is not to place any value judgment on good literature. Encouraging creative writing, choice D, may be something the author would like, but it is not his or her primary purpose in writing this passage.

22.  C. Remember that a negative question reverses the meaning. Search for the false statement among the choices because the question asks you to select the least likely. A discussion of creative writing is relevant to English and psychology, and therefore, it is possible to appear in choices A, B, D, and E. Creative writing is the opposite of technical writing. Therefore, choice C is the only possible answer.

23.  C. The passage states that dormant emotions may be released through the revealing of a deep, inner thought; choice C correctly restates this idea. Choice A is incorrect because the passage does not imply that creative writing will necessarily be autobiographical. Choice B is an irrelevant response that does not follow from the question. Choices D and E are not supported by information in the passage.

24.  C. This question is another negative question. Look for the “false” answer among the choices. Spelling is the one characteristic the author neither expresses nor implies as relevant to creative writing, choice C. Choices A, B, D, and E are important to creative writing.

25.  C. The passage explicitly states that creative writing is above all . . . a means of self-expression, choice C. The ideas in all the other choices (A, B, D, and E) are included in the passage, but none of them encapsulates the most important idea.

26.  B. The passage stresses changing the social studies curriculum, thus designating its audience as those who can effect such changes—teachers, choice B. Since the passage focuses on educating teachers and instituting a proper curriculum rather than urging students to choose certain existing classes, choice A is incorrect. Historians and politicians, as mentioned by choices C and D, are not referenced in the passage. The passage never mentions the role of parents, as posited by choice E, which would make them a secondary audience, at best.

27.  E. Among the choices listed, Futuristics, as an academic area . . . (Sentence 8) is the only sentence that presents factual information, choice E. Although choices A and B (sentences 4 and 5) present information that is most likely true, these sentences are not based on facts (e.g., Sentence 4, . . . such fascination has taken on a very practical dimension, and Sentence 5, . . . greater numbers of people are demanding a role in planning the future). Choices C and D (sentences 6 and 7) are the author’s opinions and are not based on facts.

28.  C. By advocating the addition of futurism to the social studies curriculum, the author must assume that futurism is not adequately acknowledged at this time, choice C. Without that assumption, the author would have no reason to make that argument. Choices A and E exaggerate the author’s stance, and the author does not suggest that students know little about the past, eliminating choice B. Choice D may be an implication of the passage, but the argument does not require the underlying assumption that historical figures are equal to modern-day fortune-tellers.

29.  E. By distinguishing global from national in the passage, the author suggests that a global society is larger and more inclusive than any national one, as put forth by choice E. Choices A and B are overly specific and not suggested. Choice C seems like an acceptable answer within the context of the overall passage, but ignores the global/national distinction in its containing sentence. The author does not suggest that global society should include outer space, as in choice D.

30.  B. Choice B weakens the passage by calling into question the usefulness and value of futurists of the past, and thus raises questions about the importance of the pursuit. Choices A and E are irrelevant to the strength or weakness of the argument. Choices C and D would strengthen the argument of the value of futurism.

31.  D. The overall stress on changes in education indicates the author is most likely an educator, choice D. Although choice A may seem like a good answer because of the historical examples presented, the focus on the future rather than the past runs contrary to the conclusions of choices A and B. The author makes no scientific arguments (as suggested by choice C). Choice E is never implied; the passage offers no support for the idea that the author would be a pacifist.

32.  A. The author claims that futuristics is already being taught at many major universities in an attempt to lend extra credibility and legitimacy to his argument that futuristics should be more significantly incorporated into learning curriculums, choice A. Choice B is incorrect because no previous claim was made regarding current university implementation, and the sentence does not summarize the author’s arguments, provide a conclusion, or look into the future as implied by choices C, D, and E.

33.  C. Choice C is the only possible choice because it mentions the critical role of listening in oral communication. Choices A, B, and D are incorrect because they either mention a secondary rather than a primary point, or assign a purpose (for example, to urge readers); thus, they go beyond the scope of the passage. Choice E contradicts the passage.

34.  E. In Sentence 2, the author states that approximately eight million children in the United States can be classified as learning disabled. The sentence adds that many more function ineffectually throughout their entire lives; therefore, choice E is correct. Choices A, B, and C are contradicted in the passage. Choice D is too slight because of the phrase “slightly over.”

35.  D. All the choices, except choice D, are unreasonable. The passage explicitly addresses auditory processing and learning disabilities, choice D, and is not so technical that it would be intended for practicing audiologists—Choice E.

36.  D. The second paragraph generally supports the author’s point that poor reading may be a learning disability related to auditory processing skills, choice D. Therefore, placing this statement at the beginning of the second paragraph forms a logical flow of ideas to connect paragraphs one and two. Choices A and B contradict the author’s main purpose. Choices C and E are not relevant to paragraph two.

37.  C. Choice C is the most comprehensive statement. The other choices express secondary rather than primary purposes—as in choice B—or are simply not evidenced in the passage, choices A, D, and E.

38.  A. The final statement of the passage (Sentence 8) explicitly stresses the complexity of auditory processing related to reading, indicating that reading difficulty may not have a simple cause, choice A. It does not restrict this complexity to only five causes, so choices B and C are incorrect. Choices D and E are irrelevant to the final statement.

39.  B. The first sentence states that learning disabilities are among the most frequently occurring of all childhood developmental disorders, thus implying that other disorders exist as well, choice B. Choice A is too strong to be implied by Sentence 1. Choices C, D, and E are not supported by Sentence 1.

40.  C. Choice C accurately expresses the primary point of the passage. Choices A, B, D, and E go beyond the scope of the passage.

41.  A. The author would agree that cartoons have some creative value and should not be banned, choice A. Choice B should be eliminated because it makes cartoons a primary source of inspiration. Choices C and E are not mentioned in the passage, and are therefore incorrect. Choice D contradicts the passage (the parents’ contribution is said to be beneficial).

42.  C. This question asks you to look for the answer that would most weaken the argument. Choice C decreases the emphasis on early childhood as a time of rapid change by saying that midlife may be a time of rapid change. Choices A and B are irrelevant and are not supported in the passage. Choice D is an underlying assumption that may be true; therefore, it would strengthen the passage. Choice E is a correct statement that supports the argument; it does not weaken the argument.

43.  B. Display means “to show or place where it can be easily seen in a prominent place.” It is the correct word choice for the first blank because it follows the writer’s line of reasoning that less academic students should have an opportunity to show off their skills. Work is the correct word choice for the second blank because teachers will have an opportunity to see the overall accomplishments of their students’ efforts in the classroom. Therefore, choice B is correct. Choice A, boast, means “to brag,” and grades suggests “scores” or “evaluations” of students. These words do not accurately depict the writer’s intention (i.e., physical proficiencies, rather than academic proficiencies). Choices C (give; sports), D (relate; exercise), and E (explain; games) do not fit the meaning of the sentences.

44.  A. The main theme of the passage is that physical education is beneficial to elementary school students, especially those students whose self-esteem is enhanced through physical movements, choice A. Choices B and C may be true statements, but do not address the importance of a good athletic program. Choice D is incorrect because it opposes the writer’s ideas. Although choice E may have some merit, it is not the best choice because it is not addressed in the passage.

45.  B. According to Virginia Woolf, financial independence was a crucial first step toward all other forms of independence for women, choice B. The Married Women’s Property Act of 1882 gave women some degree of financial independence—but not full rights (choice A). Choices C and D, while both true, are not why the Married Women’s Property Act was important. Nothing in the passage suggests that it was concerned with women’s rights to inherit businesses (choice E).

46.  D. By relating a series of school situations in which students are discouraged from self-expression, the author implies that attending school may cause children to become inhibited, choice D. Choice A is not a reasonable inference that readers can draw from the passage. Although choice B may be a true statement, it is not implied in this question. Choices C and E are neither inferred nor addressed in the passage.

47.  C. The overall suggestion in the passage is that students are inhibited by being harshly criticized or corrected in the classroom. Therefore, the correct interpretation for chopped off is being “severely criticized,” choice C. Choices A and B are similar terms; put out means to “place something outside or remove it.” Both terms are not focused on the writer’s argument. Although choice D sounds like a logical answer, the term misunderstood means “misinterpreted,” and is not consistent with the punitive meaning of chopped off. Choice E, cut back, is not consistent with the writer’s overall tone.

48.  A. The author repeatedly addresses the reader with what are presumed to be common experiences, using phrases such as Possibly everyone and Perhaps some, choice A. However, the passage offers no educational theory, so choice B is incorrect. The anecdotes that the author provides are not illogical, choice C. The passage does not contain a story, choice D, or any reference to the writer’s teaching experience, choice E.

49.  B. The author cites a number of negative situations, leaving no question that he or she is critical of the classroom practices described, choice B. The words in choices A and D have positive connotations, and thus they are contradicted by the author’s tone. The word skeptical, choice C, means “to doubt,” which does not accurately describe the author’s attitude. Choice E, affected, means “to influence or pretend,” which is also inaccurate.

50.  D. Choice D accurately restates the author’s overall point. Choices A, B, and C contradict the argument of the passage. Choice E may contradict the implied argument; because the meaning of assist is not made clear, it may suggest the teacher should supply words for the student.

Section II: Mathematics

1.   A. To determine the answer, you will notice that 500 or above rounds up to the next highest thousand. 499 or below rounds down to the previous thousand. Thus, 342,499 rounds down to 342,000. Note that choices B, C, and E could have been quickly eliminated, since they were rounded to nearest hundreds, not thousands.

2.   B. To determine the largest value, convert all the answer choices to decimals.

A. 0.09, B. 0.0909, C. 0.085, D. 0.084, E. 0.077

Now you can visually see that 0.0909 (choice B) is the largest value among the other answer choices, eliminating choices A, C, D, and E.

3.   B. This arithmetic word problem is straightforward. Simply convert the words into math equations. Of the 48 students, three-fourths are male, or . Therefore, there are 36 males and 12 females in the class. Of the 12 females, one-third of them are less than 6 feet tall, or . Therefore, 12 — 4 = 8, or 12 total females minus 4 females that are less than 6 feet tall equals 8 females that are at least 6 feet tall. Therefore, 8 females are 6 feet tall or taller, choice B.

4.   C. First, add all distances:

To find the average, divide the total (22) by the number of distances you added (4):

5.   C. The maximum number of squares (1 inch by 1 inch), is 4 × 4 = 16, choice C. The image below will help you visualize the answer.

6.   E. The highest temperature is 22°, and the lowest temperature is —12°. The difference is

22° — (—12°) = 22° + 12° = 34°, choice E

7.   E. Since there are 8 red gumballs in the bowl, picking just 8 could result in all 8 being red and therefore, not choosing one of each. Since there are 8 red and 7 white, picking 15 gumballs could result in getting only red and white gumballs. Therefore, at least 16 must be chosen to be sure of getting at least one of each color, choice E.

8.   D. Let’s examine Figure R and Figure S.

Remember to read the question carefully. You are looking for the “shaded” area of Figure R and the “unshaded” area of Figure S. Notice that Figure R has 2 of 3 parts shaded, so it represents the fraction . Figure S has 5 of 8 parts unshaded, so it represents the fraction . The word sum means “addition.” Therefore, , choice D.

9.   C. Plugging in the values for x and y into the expression gives you:

10.  C. Step 1. Calculate the profit from Stock A and Stock B.

Stock A was purchased at $16.50 per share and sold at $20 per share, a profit of $3.50 per share. Stock B was purchased at $19.50 per share and sold at $20 per share, a profit of $0.50 per share.

Step 2. Multiply the number of shares by the profit.

Stock A has 200 shares. Therefore, the profit is (200)($3.50) = $700.

Stock B has 500 shares. Therefore, the profit is (500)($0.50) = $250.

Step 3. To find Stock B’s percent of the combined profits, divide the combined profits of both stocks by Stock B.

11.  C. This problem can be solved by using math reasoning or math proportion.

Method 1: Using math reasoning with the visual graphic.

The first step is to divide the total distance, 26 inches, by the distance that the tortoise travels.

The graph below will help you visualize the distance and answer the question using math logic.

It will take the tortoise hours to move 26 inches, choice C.

Method 2: Using a math proportion equation.

12.  E. To find the number of different combinations possible, simply multiply the number of varieties of lettuce (3) by the number of varieties of tomatoes (3) by the number of varieties of beans (4).

3 × 3 × 4 = 36 different combinations, choice E

13.  A. To solve this problem, first find 12% of 250: 0.12 × 250 = 30, which means that 30 sailors are between 20 to 25 years old. The remaining sailors are ages 26 to 35, which represents 10 age groups. Since there are 250 sailors total and 30 sailors are 25 years old and younger, then 220 sailors are 26 to 35 years old. Knowing that the remaining sailors are evenly distributed, divide the 220 by the 10 age groups remaining: 220 ÷ 10 = 22, choice A.

14.  A. Solving the equation:

Substitute for y and solve:

15.  A. First change 2 feet, 6 inches to feet.

Next, since there are 30 students, multiply , but first change the mixed number to an improper fraction, . Now, the equation reads , choice A.

Remember, when multiplying fractions, cross-canceling can save you time, as follows:

Note: Choices D and E are unrealistic and can be quickly eliminated.

16.  B. Start by finding the sum of the sales of regular unleaded gasoline and diesel fuel.

Next, find the difference between the total sales and the sum of regular and diesel fuel to calculate the total sales of premium unleaded gasoline.

Divide $742 by the amount sold to arrive at the price per gallon of premium unleaded gasoline, 742 ÷ 200 = $3.71.

The formula for percentage change .

The change from $3.50 to $3.71 is $0.21. The starting amount was $3.50.

17.  E. If the flat-screen television is marked down 20%, then its current price is 80% of its original price. Thus, 0.80P = $320, choice E.

18.  B. Hazel rounds to the nearest thousand and then adds up the values:

$45,000 + $57,000 + $73,000 = $175,000

Ivan rounds to the nearest ten and then adds up the values:

$45,260 + $57,250 + $72,980 = $175,490

The difference between these amounts is $175,490 — $175,000 = $490, choice B.

19.  D. Since Wei-Jen can run 8 miles in one day, she ran an average of 160 miles each month. So the most miles she could have run this year, choice D, is 12 × 160, or 1,920 miles.

20.  C. Method 1: You can set the problem up as follows:

Fifteen is 25% of 60, choice C.

Method 2: You can set up a proportion and solve as follows:

21.  E. Since the bus stops four times each mile, the total number of stops will equal the number of miles times 4. Thus, 8 miles multiplied by 4 stops each mile = 32 total stops, choice E.

22.  C. Choices A, B, and E are incorrect; in order to be correct, they need to read “Divide b into a, move the decimal point two places to the right, and add a percent sign.” Choice D is also incorrect; in order to be correct, it needs to read “Solve the proportion and add a percent sign to the value of x.”

Multiplying a number by 100 and adding a percent sign will not change its value but will express it as a percentage. The correct answer is choice C.

23.  D. Method 1: One way to solve this problem is to set up a ratio: 3 tests is to 9 minutes as 30 tests is to how many minutes?

Cross-multiplying gives:

Method 2: Another method to solve this problem is to use math reasoning. That is, 30 tests is exactly 10 times 3 tests. Therefore, the time it takes to correct 30 tests is exactly 10 times 9 minutes. Thus 10 × 9 = 90 minutes = 1 hour, 30 minutes.

24.  E. The perimeter is the sum of the lengths of the four sides of the tablecloth.

25.  D. Only choice D shows the correct meaning of stanine score. A stanine test score of 4, 5, or 6 shows that Julian’s score is average and that he performed at the same level as other students who took the test. Choice A is incorrect because answering 80% of the questions correctly makes an assumption that there were a total of 100 questions. The test could have consisted of any number of questions. Choice B is incorrect since raw scores and percentile scores are different, and this question is about stanine scores. Choice C is incorrect because Julian achieved a (percentile) score that is higher than 75% of the other students who took the test. Choice E is incorrect because we don’t know the percentage of correctly answered questions.

26.  C. The word of means multiply. Thus, 90% of 80% of 70% is (0.90)(0.80)(0.70) = 0.504, or approximately 50%, choice C.

27.  D. Since each bus carries a maximum of 42 children, it will take three buses to carry all 98 children, choice D. Remember, the answer must be reasonable. A fractional bus (for example, bus) is not a logical answer.

28.  D. If two numbers average to 5x, the sum of the two numbers must be 10x, since 10x divided by the two numbers gives 5x for an average. Therefore,

Therefore, the other number is 10x — 3, choice D.

29.  B. The top of the pyramid has 1 sugar cube. The second layer has 2 sugar cubes per side to form a square, or 4 sugar cubes. The layer below that forms a square with 3 sugar cubes per side, so it contains 9 sugar cubes. Keep adding these square numbers together until the total is 55: 1 + 4 + 9 + 16 + 25 = 55. Hence, 5 layers of sugar cubes make up the pyramid, choice B.

30.  D. The state requires no more than 50% asphalt. So 50% of 200 square feet is 100 square feet of asphalt maximum. Notice that this maximum limit eliminates choices A and E. The other requirement is no less than 20% grass. So 20% of 200 is 40 square feet of grass as a minimum. This eliminates choices B and C. Only choice D provides no more than 50% asphalt and no less than 20% grass.

31.  C. First, find the selling price for a dozen at three for $0.85: 3 × 4 = 12 = one dozen and $0.85 × 4 = $3.40. Hence, six dozen will yield $3.40 × 6 = $20.40. The cost for six dozen at $1.80 per dozen is $1.80 × 6 = $10.80. Hence, the profit on six dozen of these items will be $20.40 — $10.80 = $9.60, choice C.

32.  E. Since his scores were all between 72% and 94%, Adrian’s average for the eight tests must fall between the highest and lowest scores, choice E. The average for all eight tests, however, does not necessarily have to be 83%, the average of only the highest and lowest scores, so choice A is incorrect.

33.  D. Price today = $100

In 1 year = $100 + 5% of 100 = $105

In 2 years = $105 + 5% of 105 = $110.25

In 3 years = $110.25 + 5% of 110.25 = $115.7625

Rounded to the nearest hundredth, the cost of the headphones in 3 years will be $115.76, choice D.

34.  B. This problem can be easily solved using proportions.

The container weighs approximately 100 kilograms, choice B.

35.  C. Since there are a total of 160 voters polled (84 + 65 + 11 = 160) with 84 voters favoring candidate x, the fraction of those polled who favored candidate x is

36.  D. To find the answer, add and .

The total amount of fabric purchased was yards, choice D.

Note: The square yards given in the original information is not needed to find the answer.

37.  C. To solve an addition problem containing fractions with different denominators, a common denominator must be found. Both 90 (choice A) and 30 (choice C) are common denominators, but only 30 is the lowest common denominator. Using 30 for the denominator eliminates the necessity of reducing your final answer and also minimizes the size of the numbers in your computations, choice C.

38.  A. There are 36 possible combinations of two dice. Of these 36 combinations, only 6 combinations total 7. Group in pairs: 1 and 6; 2 and 5; 3 and 4; 4 and 3; 5 and 2; 6 and 1. Thus, 6 out of 36 equals , or , choice A.

39.  D. According to the graph, the tallest “B” (before) bar is county 4, choice D.

40.  E. To determine a 25% increase, find the county in which the increase in the number of sightings equals of the original number of sightings, choice E.

Note that merely approximating the size of the bars does not work because the bars do not begin at 0 (they begin at 200).

41.  A. Problems of distance, speed, and time can be solved using d = rt, where d is distance, r is rate or speed, and t is time. Therefore,

Thus, hour, or 15 minutes, choice A.

42.  B. The fastest method to solve this problem is to divide the amount of commission by $6.80 to get the number of $50 sales:

Thus, Sofia’s total sales were 23 × $50 = $1,150, choice B.

43.  C. Since of the students are boys, there are boys in the class. Out of the 24 boys in the class, are under 6 feet tall, or boys under 6 feet tall, choice C.

44.  E. To solve, divide the astronaut’s weight on Venus by his or her weight on Earth:

45.  D. The fastest method to solve this problem is to add all of the quizzes at 70%, then add all of the quizzes at 80%.

46.  The average is determined by dividing the total points by the number of quizzes:

47.  1,120 ÷ 15 = 74.67%, or , choice D

48.  E. Since of the seniors take physics, of the seniors do not take physics. Now multiply by the total number of seniors (you may want to do some canceling):

49.  E. Since Daniel’s four paychecks total $2,520, the average of the four paychecks is $630 (choice A). If the largest is $300 more than the average, the largest paycheck is $930 (choice B), and if the largest is $600 more than the smallest, the smallest paycheck must be $330 (choice C). You can also determine the sum of the largest and smallest paychecks (choice D): $930 + $330 = $1,260. However, you cannot determine the second-largest paycheck, so choice E is the correct answer.

50.  C. In order to find the median of a set of data, first list the numbers from least to greatest.

14, 16, 19, 21, 23

Before adding any number, we can see that 19 is the median (the middle number). If we add 19 to the set, it still remains the middle number. Also by adding 19, it now becomes the mode (the most occurring number) because it occurs twice, choice C.

51.  D. There were 4 days (July 10, 11, 14, and 15) on which the maximum temperature exceeded the average. Thus, is approximately 57%, choice D.

52.  C. The maximum temperature rose from 86° to 94° from July 13 to July 14, choice C. This was the greatest increase.

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

Topic 1

The twelve years that students spend in elementary and secondary school, plus any time spent in college, provide them with opportunities to learn new material, master social skills, and make lifelong friends.

Assignment: In an essay to be read by an audience of educated adults, identify and describe one of these areas that you personally recall, and discuss how the school setting affected your experience.

Sample Response: A Well-Written Essay

When I was in high school, I discovered my calling. I attended school in a district that did not have grade-specific classes, like 9th grade, 10th grade, 11th grade, and 12th grade English, but instead offered a variety of electives that students could choose from to meet the graduation requirements. Naturally, we had to take classes in English, science, math, social studies, and physical education, but we had a great deal of leeway in choosing most classes within those subjects. I recall a few exceptions, such as required classes in U.S. History and Civics, but it was the freedom to choose that eventually led me to my desire to become an English teacher.

I have always been an avid reader. In elementary school, I adored going to the library and getting as many books as possible, only to devour them quickly. Biographies about famous people like Abraham Lincoln and Helen Keller fascinated me, but I also loved fiction, like the Beezus and Ramona series, Nancy Drew stories and delightful books like Stuart Little and Charlotte’s Web. So, when high school offered an assortment of English classes, I dove right in. Yes, I did complete the basic requirements, like algebra, biology, and history, but I remember very little from them. Instead, I adored all my English classes and the teachers; this is my big take-away from high school.

I was able to take linguistics (a baby-version, introductory class), American Literature, British Literature, World Literature, and Contemporary Literature. In these classes, I thrived. I learned to love exploring character, to appreciate quality writing, to analyze literary theme, and, of course, to relish a well-told story. These skills I carry with me today. I was thrilled to discover that all British Literature fascinated me, from Anglo-Saxon tales like Beowulf to modern poets such as Dylan Thomas. I also adored the Contemporary Literature class where we studied works like Brave New World and Catch-22, novels that changed and shaped who I am today.

Although I came to the English classroom ready, willing, and able to learn, my English teachers were a major reason that I fell so deeply in love with the subject. I still remember their names, their enthusiasm, and their passion for the written word. How has that affected me? I became an English major in college, specializing in British Literature, and hope to foster my former teachers’ enthusiasm and knowledge to help me become the best English teacher I can be. If I can inspire a few students as my teachers did, I will consider myself successful.

Analysis of Topic 1 Response

This is a well-written and well-organized descriptive essay that clearly addresses all parts of the topic. The writer identifies which part of the prompt she will address (learning new material), then describes it with ample detail from her schooling. By discussing how her English teachers spread enthusiasm for their subject, the writer also addresses how the school setting affected her experience.

The writer begins by describing the fact that her high school allowed elective classes, as long as the student completed basic graduation requirements. Then the writer makes it more personal by explaining her lifelong love of books, and how this love grew substantially throughout high school because the system allowed for elective choices, and that she had inspiring teachers. The writer provides specific detail to make the experience come alive, such as naming favorite classes and pieces of literature. The writer then transcends her earlier years by establishing how the high school experience “changed and shaped who I am today,” and that that becoming “the best English teacher I can be” is her primary goal. The writing quality is sophisticated, and the chronological organizational scheme works well for a personal experience essay.

Topic 2

One of the current trends in education is the use of computers in the classroom. While proponents cite numerous instructional advantages, opponents cite the disadvantages of overusing computers in the classroom.

Assignment: In an essay to be read by an audience of educated adults, discuss whether you agree or disagree with using computers for classroom instruction. Support your argument with specific examples from your personal experience, readings, or general knowledge.

Sample Response: A Well-Written Essay

While many educators and students are enthusiastic about the growing use of computers for instruction, I believe that computers in the classroom are a real “double-edged sword.” The decision to utilize computers in the classroom brings both advantages and challenges.

On the positive side, computers help to lessen one of the greatest frustrations that teachers experience. Teachers often find it difficult to teach a classroom of students who have a wide range of learning needs. Teachers are often compelled to teach subjects to the “middle learner,” rather than focus on the diverse needs of each student. With well-structured software, however, slower students can progress at their own pace and not feel left behind. Advanced students can progress at a faster pace and not feel bored by a slower-paced class. The structure of the software is also ideal for students who are absent and need to catch up to the rest of the class, possibly requiring less individual attention from the teacher.

In addition, computer software programs are frequently designed with visual graphics and colorful animation, which helps visually oriented students who might otherwise have trouble focusing their attention on complex tasks. Furthermore, using computers in a classroom allows students and parents to monitor the status of completed homework assignments and grades. This allows students to feel more responsible for their own work, and ultimately encourages a meaningful learning experience. The use of computers also allows students in danger of failing to have more chances to identify problem areas and make the necessary corrections to improve grades.

On the negative side, computer-assisted instruction can never substitute for in-person classroom instruction. Students don’t have the opportunity to personally engage with teachers, and teachers don’t have the opportunity to observe and assess students. In addition, when students are asked to spend hours of time staring at a computer screen, instruction has the risk of becoming one-dimensional and may stop holding the students’ attention. If the software has recurring stimulation, students may expect the same stimulation for in-person instruction. This may cause inattention issues. Students may develop an inability to focus their concentration on a teacher’s classroom instruction material. Scientific research has concluded that prolonged computer screen time has contributed to feelings of isolation from peers and causes a decline in verbal communication skills. Studies show that overexposure can also contribute to “screen addiction.”

In conclusion, computer instruction in the classroom certainly has some real advantages, but as responsible educators, we must also take into account some of the serious risks of excessive computer use.

Analysis of Topic 2 Response

The thesis statement in the introductory paragraph effectively describes what to expect in the essay and lets the reader know the direction of the essay. The issue of computer use in classrooms is a “double-edged sword,” and has both advantages and challenges.

The writer organizes the topic from both sides of the issue by showing the positive and negative aspects of overusing computers in a classroom. In paragraphs two and three, the writer lays out the argument on the positive side, and in paragraph four, the writer proceeds by addressing the dangers of excessive use of computers in a classroom. In paragraph four, the writer further demonstrates the contradictions of computer use with a clear statement, computer-assisted instruction can never substitute for in-person classroom instruction.

The writer’s ideas are well-developed and provide specific supporting examples and evidence on both sides of the issue. The response is logically organized and clearly addresses four advantages and four disadvantages of extensive computer use as well as cites research about the warning of excessive computer use. This serves to grab the readers’ attention. The writer’s reasons are plausible, and the writer uses varied vocabulary that demonstrates a command of English. In addition, the writer uses transitional words (e.g., in addition, furthermore, and in conclusion) to guide the reader smoothly from point to point.