QUANTITATIVE SECTION 37 QUESTIONS • 75 MINUTES Directions for Problem Solving Questions: (These directions will appear on your screen before your first Problem Solving question.) Solve this problem and indicate the best of the answer choices given. Numbers: All numbers used are real numbers. Figures: A figure accompanying a Problem Solving question is intended to provide infor- mation useful in solving the problem. Figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. Straight lines may sometimes appear jagged. All figures lie on a plane unless otherwise indicated. To review these directions for subsequent questions of this type, click on HELP. Directions for Data Sufficiency Questions: (These directions will appear on your screen before your first Data Sufficiency question.) This Data Sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether: (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked; (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked; (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient; (D) EACH statement ALONE is sufficient to answer the question asked; (E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. Numbers: All numbers used are real numbers. Figures: A figure accompanying a Data Sufficiency problem will conform to the information given in the question, but will not necessarily conform to the additional information in statements (1) and (2). Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight. You may assume that positions of points, angles, regions, etc., exist in the order shown and that angle measures are greater than zero. All figures lie in a plane unless otherwise indicated. Note: In Data Sufficiency problems that ask you for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity. To review these directions for subsequent questions of this type, click on HELP. practice test Practice Test 3 473 www.petersons.com 1. If a b • b c • c d • d e • x 5 1, then x 5 (A) a e (B) e a (C) e (D) 1 a (E) be a 2. Three of four women—A, B, C, and D—are to be selected randomly to serve on a certain committee. Two of three men—X, Y, and Z—are to be selected randomly to serve on the same committee. What is the prob- ability that the committee will consist of B, C, D, Y, and Z ? (A) 1 12 (B) 1 9 (C) 1 6 (D) 3 16 (E) 2 9 3. Who takes less time to drive to work, Maria or Lupe? (1) Maria drives to work in 20 minutes. (2) Lupe and Maria drive the same distance to work. 4. The arithmetic mean (average) of two numbers is P 3 Q. If the first number is Q, what is the other number? (A) 2PQ 2 Q (B) PQ 2 2Q (C) 2PQ 2 P (D) P (E) PQ 2 Q 5. What is the minimum value of |a 1 b|? (1) |a| 5 3 (2) |a 2 b| 5 1 6. W RG B In the simple light show pictured above, a light starts at the center (white) at time zero and moves once every second in the following pattern: from white (W)toblue(B), back to white, then to green (G), back to white, then to red (R), and back to white—in a counterclockwise direc- tion. If the light continues to move in this way, what will be the color sequence from the 208th second to the 209th second? (A) White to green (B) White to blue (C) White to red (D) Red to white (E) Green to white 7. What is the value of x? (1) x . 0 (2) x 2 2 6x 1 9 5 0 474 PART VI: Five Practice Tests www.petersons.com 8. If b u c 5 u 2 2 u , what is the value of b 2 3 c 1 b 2 2 3 c? (A) 2 2 3 (B) 0 (C) 2 3 (D) 4 9 (E) 8 9 9. In the figure above, if AB i CD, then x 5 (A) 40 (B) 50 (C) 60 (D) 70 (E) 80 10. Kirk sent $54 to the newspaper dealer for whom he delivers papers after deducting a 10% commission for himself. If newspapers sell for 40 cents each, how many papers did Kirk deliver? (A) 135 (B) 150 (C) 160 (D) 540 (E) 600 11. If x 1 y 5 a, and if x 2 y 5 b, then x 5 (A) 1 2 (a 1 b) (B) a 1 b (C) a 2 b (D) 1 2 ab (E) 1 2 (a 2 b) 12. Four of the five interior angles of a pentagon measure 110°, 60°, 120°, and 100°. What is the measure of the fifth interior angle? (A) 100° (B) 110° (C) 125° (D) 135° (E) 150° 13. A certain animal shelter houses two different types of animals—dogs and cats. If d represents the number of dogs and c the number of cats, which of the following expresses the portion of animals at the shelter that are dogs? (A) d c 1 d (B) c c 1 d (C) c d (D) c d (E) d 1 c d practice test Practice Test 3 475 www.petersons.com 14. HARVESTED CROP REVENUES (YEAR X) (Percent of total revenue among four counties) nonsub- sidized farms sub- sidized farms Willot County 7% Tilson County 12% Stanton County Osher County 8% (Total Percentages) 30% Based on the table above, if the total harvested crop revenues for Willot and Tilson counties combined equaled those for Stanton and Osher counties combined, then Stanton County’s subsidized farm revenues accounted for what percentage of the total harvested crop revenues for all four counties? (1) During year X, Osher County’s total harvested crop revenues totaled twice those of Tilson County. (2) During year X, Tilson County’s farms contributed 18% of all harvested crop revenues for the four counties. 15. In the figure above, the centers of all three circles lie on the same line. The radius of the middle-sized circle is twice that of the smallest circle. If the radius of the smallest circle is 1, what is the length of the boundary of the shaded region? (A) 9 (B) 3p (C) 12 (D) 6p (E) 12p 16. If a m 5 b n , and if a Þ b Þ m Þ n, what is the value of a 1 b 1 m 1 n? (1) a, b, m, and n are all non- negative integers less than 10. (2) b n 5 81. 17. M college students agree to rent an apartment for D dollars per month, sharing the rent equally. If the rent is increased by $100, what amount must each student contribute? (A) D 1 100 M (B) D M 1 100 (C) D M (D) M D 1 100 (E) M 1 100 D 476 PART VI: Five Practice Tests www.petersons.com 18. If n is a positive even integer, and if n 4 3 results in a quotient with a remainder of 1, which of the follow- ing expressions is NOT divisible by 3? (A) n 1 2 (B) n 1 5 (C) n 2 1 (D) n 3 2 (E) n 3 3 19. Î a 2 b 2 1 a 2 b 2 5 (A) a 2 b 2 (B) a b (C) a 4 b 4 (D) a b Î a b (E) |a| = 2 |b| 20. Is it true that = 3 a , a? (1) a , 0 (2) a .21 21. A certain purse contains 30 coins. Each coin is either a nickel or a quarter. If the total value of all coins in the purse is $4.70, how many nickels does the purse contain? (A) 12 (B) 14 (C) 16 (D) 20 (E) 22 22. Once a month, a crop duster sprays a triangular area defined by three farm houses—A, B, and C—as indicated in the figure above. Farmhouse B lies due west of Farmhouse C. Given the compass directions and distances (in miles) indicated in the figure, what is the total area that the crop duster sprays? (1) Farmhouse C is located 4 miles further south than farmhouse A. (2) Farmhouse C is located 10 miles further east than farmhouse A. 23. Each computer system in a graphic- arts classroom is equipped with a scanner or a printer or both. What percentage of the computer systems are equipped with scanners but not printers? (1) 20 percent of the computer systems are equipped with both scanners and printers. (2) 25 percent of the computer systems are equipped with printers but not with scanners. 24. Daniel, Carl, and Todd working together can load a moving van in 8 hours. How long would it take Daniel working alone to load the van? (1) Working alone, Carl can load the van in 15 hours. (2) Carl and Todd working together can load the van in 12 hours. practice test Practice Test 3 477 www.petersons.com 25. What is the unit area of circle O on the standard xy-coordinate plane? (1) Point R(7,23) and point S(7,7) both lie along the circumference of circle O. (2) R and S are the endpoints of the longest possible chord of circle O. 26. If A and B denote the digits of a three-digit number BAB, is BAB divisible by 4? (1) The product of A and B is divisible by 4. (2) The sum of B, A, and B is divisible by 4. 27. If a total of 55 books were sold at a community book fair and if each book was either hardback or paperback, how many hardback books were sold at the book fair? (1) The proceeds from the sale of paperback books, each of which was sold for 75 cents, totaled $19.50. (2) The proceeds from the book fair totaled $48.50. QUESTIONS 28–29 REFER TO THE FOLLOWING FIGURE: 28. According to the graph, the two age groups, other than the group that spent the greatest number of hours per week watching sports on televi- sion, accounted for approximately what percent of the total hours spent watching television among all three age groups? (A) 27 (B) 36 (C) 60 (D) 76 (E) 85 29. Which of the following is the approxi- mate ratio of the average number of hours per week that the youngest age group spent watching entertainment on television to the average number of hours that the other two groups combined spent watching the same type of programming? (A) 3:4 (B) 1:1 (C) 5:4 (D) 4:3 (E) 5:3 478 PART VI: Five Practice Tests www.petersons.com 30. If a portion of $10,000 is invested at 6% and the remaining portion is invested at 5%, and if x represents the amount invested at 6%, what is the annual income in dollars from the 5% investment? (A) 0.05(10,000 2 x) (B) 0.05(x 1 10,000) (C) 5(x 2 10,000) (D) 5(10,000 2 x) (E) 0.05(x 2 10,000) 31. In a geometric series, each term is a constant multiple of the preceding one. If the first three terms in a geometric series are 22, x, and 28, which of the following could be the sixth term in the series? (A) 2128 (B) 217 (C) 64 (D) 256 (E) 512 32. What is the maximum number of rectangular boxes, each measuring 2 inches by 3 inches by 5 inches, that can be packed into a rectangular packing box measuring 18 inches by 19 inches by 35 inches, if all of the smaller boxes are aligned in the same direction? (A) 296 (B) 356 (C) 378 (D) 412 (E) 424 33. If J is a set of six integers, what is the median value of those integers? (1) The difference between the least and greatest integers in set J is 40. (2) The arithmetic mean (average) of the six integers in set J is 15. 34. In the circle with center O above, is the area of the shaded region less than the combined area of the two triangles? (1) x 5 60. (2) The length of chord AB equals the circle’s radius. 35. Two buses are 515 miles apart. At 9:30 a.m., they start traveling toward each other at rates of 48 and 55 miles per hour. At what time will they pass each other? (A) 1:30 p.m. (B) 2:00 p.m. (C) 2:30 p.m. (D) 3:00 p.m. (E) 3:30 p.m. 36. 7 77 2 7 76 6 5 (A) 7 (B) 7 77 76 (C) 49 (D) 7 75 (E) 7 76 37. An investor can sell her MicroTron stock for $36 per share and her Dynaco stock for $52 per share. If she sells 300 shares altogether, some of each stock, at an average price per share of $40, how many shares of Dynaco stock has she sold? (A) 52 (B) 75 (C) 92 (D) 136 (E) 184 practice test Practice Test 3 479 www.petersons.com VERBAL SECTION 41 QUESTIONS • 75 MINUTES Directions for Sentence Correction Questions: (These directions will appear on your screen before your first Sentence Correction question.) This question presents a sentence, all or part of which is underlined. Beneath the sentence you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise choose one of the others. This question tests correctness and effectiveness of expression. In choosing your answer, follow the requirements of Standard Written English; that is, pay attention to grammar, choice of words, and sentence construction. Choose the answer that produces the most effective sentence; this answer should be clear and exact, without awkwardness, ambiguity, redundancy, or grammatical error. Directions for Critical Reasoning Questions: (These directions will appear on your screen before your first Critical Reasoning question.) For this question, select the best of the answer choices given. Directions for Reading Comprehension Questions: (These directions will appear on your screen before your first group of Reading Comprehension questions.) The questions in this group are based on the content of a passage. After reading the passage, choose the best answer to each question. Answer all the questions following the passage on the basis of what is stated or implied in the passage. 1. Not only smoking cigarettes but also cigar smoking has been banned now from many public places. (A) Not only smoking cigarettes but also cigar smoking has been banned now (B) Cigarette smoking and cigar smoking are both banned now (C) Not only has smoking cigarettes been banned but so has cigar smoking (D) Both smoking cigarettes and cigar smoking is now banned (E) Smoking cigarettes as well as cigars is now banned 2. The Reluctant Monarch, which Francis Craig wrote as her third in a series of books about the British Monarchy. (A) The Reluctant Monarch, which Francis Craig wrote as her third (B) The Reluctant Monarch is the third book written by Francis Craig (C) Written by Francis Craig, The Reluctant Monarch, which is her third book (D) Francis Craig wrote The Reluctant Monarch, which book is her third (E) The Reluctant Monarch, written by Francis Craig, is her third 480 PART VI: Five Practice Tests www.petersons.com 3. Some varieties of parrots live as long as the age of one hundred years. (A) as long as the age of one hundred years (B) as long as one hundred (C) as long as one hundred years old (D) as long as one hundred years (E) to be one hundred years old in age 4. Two years ago, a court found a certain cigarette manufacturer legally liable for the deaths of several thousand people who smoked the company’s cigarettes and ordered the company to pay a large sum to the families of those victims. The next year, the company’s profits increased to record levels. The lesson for other large corporations is clear: Produce products that are unsafe or un- healthy for consumers and your company will become more profitable. Which of the following, if true, would provide the best reason for rejecting the conclusion drawn in the last sentence above? (A) Publicity resulting from court judgments against large businesses often affects their profitability. (B) Manufacturers of potentially unsafe or unhealthy products are required by law to provide appropriate warnings to consumers. (C) Manufacturers of dangerous products are often held liable for injuries to consumers resulting from the use of those products. (D) The risks involved in using any product are just one of many types of factors consumers con- sider when buying a product. (E) Compared to cigarettes, most consumer products pose insig- nificant risks to the health or safety of those who use them. 5. John: If a person believes in the inevitability of success, then that person will surely succeed. Jolanda: I disagree. According to a recent magazine article entitled “The 100 Most Successful Women in History,” most of these 100 women did not believe they would ever become successful. Which of the following would be John’s most logically convincing response to Jolanda’s counter- argument above? (A) Success does not depend on whether a person believes in its inevitability. (B) Successful people are often viewed by others as unsuccess- ful. (C) Success is inevitable for some people but not for others. (D) Society’s definition of success might have changed throughout history. (E) None of the successful people listed in the magazine article were men. QUESTIONS 6–8 ARE BASED ON THE FOLLOWING PASSAGE: Line The decline of the Iroquois Indian nations began during the American Revolution of 1776, when disagreement among them as to whether they should become involved in the war began to divide the Iroquois. Because of the success of the revolutionaries and the encroachment upon Iroquois lands that followed, many Iroquois resettled in Canada, while those who remained behind lost the respect they had enjoyed among other Indian nations. The introduction of distilled spirits resulted in widespread alcoholism, leading in turn to the rapid decline of both the culture and population. The influence of the Quakers impeded, yet in another sense contributed, to this decline. By establishing schools for the Iroquois and by introducing them to modern technology for agriculture and practice test Practice Test 3 481 5 10 15 20 www.petersons.com husbandry, the Quakers instilled in the Iroquois some hope for the future yet undermined the Iroquois’ sense of national identity. Ironically, it was Handsome Lake who can be credited with reviving the Iroquois culture. Lake, the alcoholic half-brother of Seneca Cornplanter, perhaps the most outspoken proponent among the Iroquois for assimilation of white customs and institutions, was a former member of the Great Council of Iroquois nations. Inspired by a near- death vision in 1799, Lake established a new religion among the Iroquois, which tied the more useful aspects of Christianity to traditional Indian beliefs and customs. 6. The passage mentions all the follow- ing events as contributing to the decline of the Iroquois culture EXCEPT: (A) new educational opportunities for the Iroquois people. (B) divisive power struggles among the leaders of the Iroquois nations. (C) introduction of new farming technologies. (D) territorial threats against the Iroquois nations. (E) discord among the nations regarding their role in the American Revolution. 7. Among the following reasons, it is most likely that the author considers Handsome Lake’s leading a revival of the Iroquois culture to be “ironic” because (A) he was a former member of the Great Council. (B) he was not a full-blooded relative of Seneca Cornplanter. (C) he was related by blood to an important proponent of assimi- lation. (D) Seneca Cornplanter was Lake’s alcoholic half-brother. (E) his religious beliefs conflicted with traditional Iroquois beliefs. 8. Assuming that the reasons asserted by the author for the decline of the Iroquois culture are historically representative of the decline of cultural minorities, which of the following developments would most likely contribute to the demise of a modern-day ethnic minority? (A) A bilingual education program in which children who are members of the minority group learn to read and write in both their traditional language and the language prevalent in the present culture. (B) A tax credit for residential- property owners who lease their property to members of the minority group. (C) Increased efforts by local government to eradicate the availability of illegal drugs. (D) The declaration of a national holiday commemorating a past war in which the minority group played an active role. (E) A government-sponsored program to assist minority- owned businesses in using computer technology to improve efficiency. 9. Over thirty million illegal immi- grants live in the United States, including greater than two million alone in California. (A) greater than two million alone in California. (B) in California greater than two million. (C) more in California than two million. (D) more than two million in California alone. (E) greater than two million such illegal immigrants in California. 482 PART VI: Five Practice Tests 25 30 35 www.petersons.com . of paperback books, each of which was sold for 75 cents, totaled $19 .50. (2) The proceeds from the book fair totaled $48 .50. QUESTIONS 28–29 REFER TO THE FOLLOWING FIGURE: 28. According to the. question.) This question presents a sentence, all or part of which is underlined. Beneath the sentence you will find five ways of phrasing the underlined part. The first of these repeats the original;. for himself. If newspapers sell for 40 cents each, how many papers did Kirk deliver? (A) 135 (B) 150 (C) 160 (D) 540 (E) 600 11. If x 1 y 5 a, and if x 2 y 5 b, then x 5 (A) 1 2 (a 1 b) (B) a 1