8. A certain zoo charges exactly twice as much for an adult admission ticket as for a child’s admission ticket. If the total admission price for the family of two adults and two children is $12.60, what is the price of a child’s ticket? (A) $1.60 (B) $2.10 (C) $3.20 (D) $3.30 (E) $4.20 9. If n is the first of two consecutive odd integers, and if the difference of their squares is 120, which of the following equations can be used to find their values? (A) (n 1 1) 2 2 n 2 5 120 (B) n 2 2 (n12) 2 5 120 (C) [(n 1 2) 2 n] 2 5 120 (D) n 2 2 (n 1 1) 2 5 120 (E) (n 1 2) 2 2 n 2 5 120 10. M is P% of what number? (A) MP 100 (B) 100P M (C) M 100P (D) P 100M (E) 100M P 11. Three carpet pieces—in the shapes of a square, a triangle, and a semi- circle—are attached to one another, as shown in the figure above, to cover the floor of a room. If the area of the square is 144 feet and the perimeter of the triangle is 28 feet, what is the perimeter of the room’s floor, in feet? (A) 32 1 12p (B) 40 1 6p (C) 34 1 12p (D) 52 1 6p (E) 52 1 12p 12. If (bN aN c) 5 ab 2 c, then (4N 3N 5) 1 (6N 5N 7) 5 (A) 6 (B) 11 (C) 15 (D) 30 (E) 40 13. Two competitors battle each other in each match of a tournament with nine participants. What is the minimum number of matches that must occur for every competitor to battle every other competitor? (A) 27 (B) 36 (C) 45 (D) 64 (E) 81 14. What is the value of x? (1) 4x 2 2 4x 521 (2) 2x 2 1 9x 5 5 diagnostic test Chapter 3: Practice Test 1: Diagnostic 63 www.petersons.com 15. If, 2y 9 5 y 2 1 3 then y 5 (A) 1 3 (B) 3 5 (C) 4 9 (D) 2 1 4 (E) 3 16. A 30-ounce pitcher is currently filled to exactly half its capacity with a lemonade mixture consisting of equal amounts of two lemonade brands—A and B. If the pitcher is then filled to capacity to conform to a certain recipe, how many ounces of each lemonade brand must be added to fill the pitcher? (1) The recipe calls for a mixture that includes 60 percent brand A. (2) When filled to capacity, the pitcher contains 12 ounces of brand B. 17. Lisa has 45 coins, which are worth a total of $3.50. If the coins are all nickels and dimes, what is the difference between the number of dimes and the number of nickels? (A) 5 (B) 10 (C) 15 (D) 20 (E) 25 18. In an election between two candi- dates—Lange and Sobel—70% of the voters voted for Sobel. Of the elec- tion’s voters, 60% were male. If 35% of the female voters voted for Lange, what percentage of the voters are males who voted for Sobel? (A) 14 (B) 16 (C) 26 (D) 44 (E) 65 19. Barbara invests $2400 in the Na- tional Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment? (A) $1200 (B) $3000 (C) $1000 (D) $3600 (E) $2400 20. ABC Company pays an average of $140 per vehicle each month in outdoor parking fees for three of its eight vehicles. The company pays garage parking fees for the remain- ing five vehicles. If ABC pays an average of $240 per vehicle overall each month for parking, how much does ABC pay per month in garage parking fees for its vehicles? (A) $300 (B) $420 (C) $912 (D) $1420 (E) $1500 21. If m 5 n and p , q, which of the following must be true? (A) m 2 p . n 2 q (B) p 2 m . q 2 n (C) m 2 p , n 2 q (D) mp . nq (E) m 1 q , n1 p 64 PART II: Diagnosing Strengths and Weaknesses www.petersons.com 22. If ab Þ 0, is c a . c b ? (1) c Þ 0 (2) a . b 23. If the price of a candy bar is doubled, by what percent will sales of the candy bar decrease? (1) For every ten cent increase in price, the sales will decrease by 5 percent. (2) Each candy bar now costs 60 cents. 24. What is the numerical value of the second term in the following se- quence: x, x 1 1, x 1 3, x 1 6, x 1 10, x 1 15, ? (1) The sum of the first and second terms is one-half the sum of the third and fourth terms. (2) The sum of the sixth and seventh terms is 43. 25. On the xy-plane, what is the area of a right triangle, one side of which is defined by the two points having the (x,y) coordinates (2,3) and (24,0)? (1) The triangle crosses the y-axis at exactly two points. (2) The y-coordinate of two of the tri- angle’s three vertices is 0 (zero). 26. In the figure above, what is the value of x? (1) y 5 130 (2) z 5 100 27. If xy , 0, and if x and y are both integers, what is the difference in value between x and y? (1) x 1 y 5 2 (2) 23 , x , y 28. A photographic negative measures 1 7 8 inches by 2 1 2 inches. If the longer side of the printed picture is to be 4 inches, what will be the length of the shorter side of the printed picture? (A) 2 3 8 inches (B) 2 1 2 inches (C) 2 3 4 inches (D) 3 inches (E) 3 1 8 inches 29. If the circumference of the circle pictured above is 16p, what is the length of AC? (A) 4 = 2 (B) 16 (C) 16 = 2 (D) 32 (E) 16p diagnostic test Chapter 3: Practice Test 1: Diagnostic 65 www.petersons.com QUESTIONS 30 AND 31 REFER TO THE FOLLOWING FIGURE: 30. With respect to the two-month period over which the average daily tem- perature in City X increased by the greatest percentage, City Y’s average daily temperature was approximately (A) 38° (B) 42° (C) 52° (D) 64° (E) 68° 31. During the time periods in which City Y’s average daily temperature was increasing while City X’s was decreasing, the average daily tem- perature in City Y exceeded that in City X by approximately (A) 0° (B) 4° (C) 10° (D) 15° (E) 19° 32. In the figure above, ABCD is a square. If AC is 8 units long, what is the perimeter of the square? (A) 16 (B) 12 = 2 (C) 24 (D) 16 = 2 (E) 30 33. Dan drove home from college at an average rate of 60 miles per hour. On his trip back to college, his rate was 10 miles per hour slower and the trip took him one hour longer than the drive home. How far is Dan’s home from the college? (A) 65 miles (B) 100 miles (C) 200 miles (D) 280 miles (E) 300 miles 34. Î y 2 2 2 y 2 18 5 (A) 0 (B) 2|y| 3 (C) 19y 3 (D) y = 3 6 (E) y = 5 3 66 PART II: Diagnosing Strengths and Weaknesses www.petersons.com 35. A certain cylindrical tank set on its circular base is 7.5 feet in height. If the tank is filled with water, and if the water is then poured out of the tank into smaller cube-shaped tanks, how many cube-shaped tanks are required to hold all the water? (1) The length of a cube-shaped tank’s side is equal to the radius of the cylindrical tank’s circular base. (2) If three cube-shaped tanks are stacked on top of one another, the top of the third cube stacked is the same distance above the ground as the top of the cylindri- cal tank. 36. The average of seven numbers is 84. Six of the numbers are: 86, 82, 90, 92, 80, and 81. What is the seventh number? (A) 76 (B) 77 (C) 79 (D) 81 (E) 85 37. A solution of 60 ounces of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar? (A) 20 ounces (B) 80 ounces (C) 100 ounces (D) 120 ounces (E) 180 ounces diagnostic test Chapter 3: Practice Test 1: Diagnostic 67 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. Health professionals widely concur that, beyond a certain amount of exercise each day, the benefits that an individual can expect to derive by further exercise is negligible. (A) by further exercise is (B) from further exercise are (C) in furthering exercise are (D) by exercising further would be (E) by exercising even more would be 2. After bounty hunters turn over their captives to the authorities, they often are denied due process of law. (A) After bounty hunters turn over their captives to the authorities, they often are denied due process of law. (B) After turning over bounty hunters’ captives to the authori- ties, the authorities often deny them due process of law. (C) The authorities often deny captives due process of law after bounty hunters turn the captives over to the authorities. (D) Bounty hunters turn over their captives to the authorities, often being denied due process of law. (E) A captive, when turned over by bounty hunters to the authorities, is often denied due process of law. 68 PART II: Diagnosing Strengths and Weaknesses www.petersons.com 3. The media often hasten to chastise celebrities who have come into sudden and unexpected prominence, whether they be actors, musicians, or some other high-profile vocation. (A) they be actors, musicians, or some other high-profile vocation (B) their vocation be acting, music performance, or some other high-profile vocation (C) they be actors, music, or some other high profile vocation (D) their vocation is that of actor, musician, or otherwise a high-profile one (E) they are actors, are musicians, or in some other high-profile vocation 4. In a recent survey, 9 out of 10 people using Slim-Ease for two weeks as directed reported that they lost weight during this period. This fact surely proves that Slim-Ease is effective for anyone wanting to shed some unwanted pounds. The claim made above depends on which of the following assumptions? (A) The survey participants were not using Slim-Ease immedi- ately prior to the two-week period. (B) The survey participants did not exercise during the two-week period. (C) The survey participants were overweight prior to the two- week period. (D) The survey participants’ dietary habits were otherwise similar during the two-week period and prior to that period. (E) No other product is more effective than Slim-Ease to help lose weight. 5. Compared to older houses, new houses are sure to have newer, more efficient heating and cooling units, more modern kitchen appliances, and more contemporary-style bathroom fixtures. They also generally conform to current building-code regulations, whereas many older houses do not. Accordingly, it is always advanta- geous to purchase a new home rather than an old home. Which of the following, if true, is the best criticism of the advice given in the argument above? (A) Some people prefer more traditional styles of bathroom fixtures over contemporary styles. (B) Whether a house has new equipment and fixtures and conforms to current code requirements are not the only factors home buyers consider important when choosing a house. (C) New houses are generally more expensive than older houses of comparable size. (D) When an older house is sold, correcting any code violations is the responsibility of the seller. (E) In general, older houses have more of the kinds of details that lend charm to a home than do new houses. diagnostic test Chapter 3: Practice Test 1: Diagnostic 69 www.petersons.com QUESTIONS 6–8 ARE BASED ON THE FOLLOWING PASSAGE: Line In the 1970s, the idea of building so-called “New Towns” to absorb growth was considered a potential cure-all for urban problems in the United States. It was erroneously assumed that by diverting residents from existing centers, current urban problems would at least get no worse. It was also wrongly assumed that, since European New Towns had been financially and socially successful, the same could be expected in the United States. However, the ill-considered projects not only failed to relieve pressures on existing cities, but also weakened those cities further by drawing away high- income citizens. This increased the concentration of low-income groups— who were unable to provide the necessary tax base to support the cities. Taxpayers who remained were left to carry a greater burden, while industry and commerce sought to escape. As it turned out, the promoters of New Towns were the developers, builders, and financial institutions, all whose main interest was financial gain. Not surprisingly, development occurred in areas where land was cheap and construction profitable rather than where New Towns were genuinely needed. Moreover, poor planning and legislation produced not the sort of successful New Towns seen in Britain but rather nothing more than sprawling suburbs. Federal regulations designed to promote the New Town concept failed to consider social needs as the European plans did. In fact, the regulations specified virtually all of the ingredients of the typical suburban community. 6. The author’s primary concern in the passage is to (A) describe the characteristics of American New Towns that made them unsuccessful. (B) trace the development of the New Town concept in the United States. (C) list the differences between New Towns in the United States and those in Europe. (D) explain why New Towns in the United States failed to meet general expectations. (E) analyze the impact of New Towns on urban centers in the United States. 7. Based only on the information in the passage, with which of the following statements about New Towns in the United States would the author most likely agree? (A) They helped dissuade busi- nesses in urban centers from relocating to other areas. (B) They provided a thriving social center away from the problems of the older city. (C) They helped reduce air pollution by relocating workplaces to sub- urbs, where most workers lived. (D) They thwarted economic redevelopment plans for decaying urban centers. (E) They provided affluent urban resi- dents an escape from the city. 70 PART II: Diagnosing Strengths and Weaknesses 5 10 15 20 25 30 35 40 www.petersons.com 8. Which of the following phenomena is most closely analogous to the New Towns established in the United States? (A) A business that fails as a result of insufficient demand for its products or services (B) A new game that fails to attain widespread popularity because its rules are unfair (C) New utility software that solves one computer problem but creates another (D) A new drug whose side effects are severe enough to discourage people from using it (E) A scientific theory that lacks supporting empirical evidence 9. The rules of etiquette for formal dinner parties with foreign diplomats require citizens from both the host and from the diplomat’s countries to be seated across from each other. (A) citizens from both the host and from the diplomat’s countries to be seated across from each other (B) citizens of the host country and of the diplomat’s party to sit opposite each other (C) that the host country and diplomat’s country seat their citizens opposite one another (D) that citizens of the host country be seated opposite those of the diplomat’s country (E) the host country’s citizens to be seated opposite to the diplo- mat’s country’s citizens 10. Company X spokesperson: Although several of our key managerial employees have left our company since we merged with our leading competitor two months ago, we have no reason to believe that a significant number of our other employees will follow suit. Virtually all of Company X’s current employees are the same people who we employed prior to the merger, and our employee-relations department is making every effort to ensure that these employees are content here. Which of the following, if true, would tend to support most effectively the spokesperson’s prediction in the argument above? (A) The employees who left Com- pany X since the merger did so because they received more attractive employment offers from other firms. (B) Worsening economic conditions may force Company X to reduce the size of its workforce in the near future. (C) Company X has just hired a highly respected consultant who specializes in employee relations. (D) None of the employees who worked for the company that has merged with Company X have left voluntarily. (E) Most companies lose some workers to other firms as a result of a merger, but the number of workers lost is usually insignificant. diagnostic test Chapter 3: Practice Test 1: Diagnostic 71 www.petersons.com 11. Gwen: As we both know, the most popular restaurants among college students here in Collegetown are the ones that provide delivery service. So, local economic conditions, which rely on the student population, would improve if expensive Collegetown restaurants were replaced by less expensive ones that also provide delivery service. Jose: I disagree. After all, many expensive Collegetown restaurants also provide delivery service. Which of the following best expresses the point of disagreement between Gwen and Jose? (A) Whether inexpensive restau- rants are more popular among Collegetown students than expensive restaurants (B) Whether Collegetown should reduce the number of restau- rants providing delivery service (C) Whether inexpensive restau- rants in Collegetown should provide delivery service (D) Whether Collegetown students prefer delivery meal service over sit-down meal service (E) Whether inexpensive restau- rants are popular among Collegetown students 12. Whether the universe is bound is frequently asked but impossible to answer. (A) Whether the universe is bound is frequently asked but impos- sible to answer. (B) A question asked frequently is whether the universe is bound, and it is impossible to answer. (C) As to whether the universe is bound is frequently asked but impossibly answered question. (D) Whether the universe is bound is frequently asked but impos- sible answered. (E) Whether or not the universe is bound is a question asked frequently but a question impossible to answer. 13. Of the 1,000 chemicals in coffee, less than thirty have been tested, most of which produce cancer in laboratory rats. (A) less than thirty have been tested, most of which produce cancer in laboratory rats (B) most of which produce cancer in laboratory rats, fewer than thirty have been tested (C) most of the less than thirty tested produced cancer in laboratory rats (D) less than thirty of which have been tested, most of them pro- duce cancer in laboratory rats (E) fewer than thirty have been tested, and most of these pro- duce cancer in laboratory rats 14. If the corporate bureaucracy persists in its discriminatory hiring and job advancement practices, its chief executives will expose themselves to class-action litigation by the groups prejudiced thereby. (A) its chief executives will expose themselves (B) its chief executives would expose themselves (C) their chief executives will expose themselves (D) its chief executives themselves would become exposed (E) the chief executives will, by themselves, be exposed QUESTIONS 15–17 ARE BASED ON THE FOLLOWING PASSAGE: Line When Ralph Waldo Emerson pro- nounced America’s declaration of cultural independence from Europe in his “American Scholar” address, he was actually articulating the transcenden- tal assumptions of Jefferson’s political independence. In the ideal new world envisioned by Emerson, America’s becoming a perfect democracy of free and self-reliant individuals was within reach. Bringing Emerson’s metaphysics down to earth, Henry David Thoreau’s Walden (1854) asserted that one can 72 PART II: Diagnosing Strengths and Weaknesses 5 10 www.petersons.com . 4x 2 2 4x 521 (2) 2x 2 1 9x 5 5 diagnostic test Chapter 3: Practice Test 1: Diagnostic 63 www.petersons.com 15. If, 2y 9 5 y 2 1 3 then y 5 (A) 1 3 (B) 3 5 (C) 4 9 (D) 2 1 4 (E) 3 16. A 30-ounce. average of seven numbers is 84. Six of the numbers are: 86, 82, 90 , 92 , 80, and 81. What is the seventh number? (A) 76 (B) 77 (C) 79 (D) 81 (E) 85 37. A solution of 60 ounces of sugar and water. The survey participants were not using Slim-Ease immedi- ately prior to the two-week period. (B) The survey participants did not exercise during the two-week period. (C) The survey participants