Quantitative Section 1. D 2. C 3. D 4. A 5. C 6. D 7. B 8. A 9. E 10. C 11. D 12. C 13. A 14. C 15. B 16. B 17. E 18. C 19. E 20. A 21. E 22. D 23. A 24. A 25. D 26. D 27. E 28. E 29. E 30. D 31. B 32. A 33. B 34. A 35. E 36. D 37. B 1. The correct answer is (D). The two statements provide essentially the same information: the rate at which a typist types. Since this rate would be sufficient information to answer the question, the correct answer must be choice (D). If you don’t recognize this shortcut, you can determine the speed (or rate) at which a typist types, in terms of pages per unit of time, by setting up a general equation to express the time required by a typist to type one page: ~# of typists!~time! # of pages 5 time per page Based on the values provided in either statement (1) or (2), the typing rate of a single typist is 7 1 2 minutes per page: ~1 typist!~30 minutes! 4 pages 5 7 1 2 Once you know the typing rate, you can apply that rate to the numbers given in the question; so the correct answer is choice (D). You don’t need to actually answer the question. Just for the record, however, 5 typists could type thirty pages in 45 minutes. 2. The correct answer is (C). This problem involves a system of three equations with three variables. One way to solve it is with both the substitution and addition- subtraction methods. Express x in terms of y: x 5 8–y. Substitute this expression for x in the second equation: (8 2 y) 1 z 5 7or2y 1 z 521. Add this equation to the third equation in the system. 2y 1 z 521 y 1 z 5 6 2z 5 5 z 5 2.5 To find the value of x, substitute z’s value for z in the second equation: x 1 2.5 5 7; x 5 4.5 3. The correct answer is (D). Any multiple-digit prime number must end in an odd digit other than 5 (1, 3, 7, or 9). Since the sum of the three digits is 7, Z must be either 1 or 3, and four possibilities emerge: 601, 421, 241, and 223. answers practice test 6 Practice Test 6 633 www.petersons.com 4. The correct answer is (A). Divide the fraction by 100, dropping the percent sign: 1 4 % 5 1 4 100 5 S 1 4 DS 1 100 D 5 1 400 5. The correct answer is (C). Extend BE to F (as shown in the diagram below). m∠EFD 5 m∠ABE 5 40°. m∠FED must equal 110° because the three interior angles of DDEF must total 180° in measure. Since ∠BED and ∠FED are supplementary (the sum of their measures is 180°), m∠BED 5 70° (x 5 70). x 6. The correct answer is (D). Notice that the b-term’s coefficient is 21. This means that the sum of the two numbers whose product is 220 (the c-term) must be 21. The number pair (25,4) meets this condition. The factored form of the trinomial is (x 2 5)(x 1 4). 7. The correct answer is (B). Statement (1) tells you that you can disregard the exponent p; all you need to determine is the value of the fraction given. But since m and n could each be any number at all, so could the value of the fraction. Statement (2) establishes that the numerator and the denominator of the fraction are equal in value, and therefore that the fraction’s value is 1. Since 1 raised to any power is still 1, statement (2) is sufficient to establish that the expression equals 1. 8. The correct answer is (A). Statement (1) tells you that there are 4 distinguishable people to be arranged. That’s all you need to know to determine the number of possible sequences or permutations. From that number, you’d determine the probability that the 4 students are lined up in any one specific order simply by dividing 1 by the number of possibilities. Statement (1) alone suffices to answer the question. (For the record, to find the number of permutations, you can either list them systematically or apply the factorial 4! 5 4 3 3 3 2 3 1 5 24. Of 24 possibilities, in only one would the 4 students line up in the order given in the question, and the answer to the question is 1 24 .) Statement (2) alone provides no useful information—except that there are at least 3 students in the group. 9. The correct answer is (E). Statement (1) alone provides no information about R. Statement (2) provides a value for R, but provides no information about either P or Q. Together, the two statements are still insufficient to answer the question. The values of P and Q relative to R are still unknown. 634 PART VI: Five Practice Tests www.petersons.com 10. The correct answer is (C). You can determine the area of the semicircle in any event—without either statement (1) or (2). So you need more information only to determine the triangle’s area. Given statement (1) alone, the triangle could be any shape, so its area could vary. Given statement (2) alone, AB and BC each could be any length, and so the area of the triangle could vary. Thus, neither statement alone suffices to answer the question. Given both statements together, the triangle must be equilateral, and you can determine its area. (Although you don’t need to do the math, the semicircle’s area is p 2 , the triangle’s area is = 3, and so the total area is p 2 1 = 3.) 11. The correct answer is (D). The question describes an arithmetic sequence—an evenly spaced, finite sequence of numbers. In any arithmetic sequence, the average of all terms is the same as the median. The average is also equal to half the sum of the first and last number in the sequence. Thus, either statement (1) or (2) alone suffices to answer the question. For example, the sequence might include four integers {33, 35, 37, 39} or it might include 6 integers {31, 33, 35, 37, 39, 41}. As you can see, regardless of the number of terms, the average and median are each the same as half the sum of the least and greatest terms. 12. The correct answer is (C). Any term raised to a negative power is the same as “one over” the term, but raised to the positive power. Also, a negative number raised to a power is negative if the exponent is odd, yet positive if the exponent is even: 21 (23) 1 [21] (22) 1 [21] 2 1 [21] 3 52 1 1 1 1 1 1 1 2 1 5 0 13. The correct answer is (A). Given that a total of 500 products were sold, statement (1) alone is sufficient to answer the question. If A sold 166 products, A sold just less than 1 3 of the total number. Either B or C must sell more than 1 3 , and the answer to the question is no. Statement (2) alone is insufficient to answer the question. If C sold 249 products, A could have sold anywhere from 0 to 251 products; if A sold either 250 or 251 products, A would have sold more products than either B or C. However, if A sold 0–249 products, A would not have sold more products than C. 14. The correct answer is (C). Since the distance from the two given points to (4,t)isthe same, apply the distance formula twice, then equate the results and solve for t: = ~4 2 1! 2 1~t 2 1! 2 5 = ~5 2 4! 2 1~3 2 t! 2 = 9 1~t 2 2 2t 1 1! 5 = 1 1~9 2 6t 1 t 2 ! = 10 1 t 2 2 2t 5 = 10 2 6t 1 t 2 10 1 t 2 2 2t 5 10 2 6t 1 t 2 22t 526t 4t 5 0 t 5 0 answers practice test 6 Practice Test 6 635 www.petersons.com 15. The correct answer is (B). Each trip consists of 5 jumps, after which the glip starts over at point X. In jumps 1–5, the first jump is to A , as the question stem tells us. In jumps 6–10, the first jump is to B, and so on clockwise around the circuit. After 25 jumps (5 trips of 5 jumps each), the glip begins exactly the same sequence of 25 jumps again: Jumps 1–5: X to A to B to X to D to X Jumps 6–10: X to B to C to X to E to X Jumps 11–15: X to C to D to X to A to X Jumps 16–20: X to D to E to X to B to X Jumps 21–25: X to E to A to X to C to X Since the pattern indicated above begins again after each multiple of 25 jumps, jump 472 is the same as jump 22: from E to A. 16. The correct answer is (B). Although trying each answer choice in turn is one way to solve this problem, doing the math, especially calculating and then working with the square root of a large number, might be more trouble than it’s worth. A better idea is to solve for x algebraically: = 4x 2 4 5 8 1 4 = 4~x 2 1! 5 12 2 = x 2 1 5 12 = x 2 1 5 6 ~ = x 2 1! 2 5 6 2 x 2 1 5 36 x 5 37 17. The correct answer is (E). Statement (1) alone provides no number values and therefore is obviously insufficient to answer the question. Statement (2) alone provides the value of one number, but the value of all three numbers is needed to compute their average. Considered together, statements (1) and (2) still allow for many possibilities. Statement (2) tells us that one (and only one) of the three numbers equals 0. Combining this fact with statement (1), the other two numbers might either have the same positive value or they might be additive reciprocals. If the three numbers are 0, 2, and 2, for example, then the average of the three numbers 5 (0 1 2 1 2) 4 3 5 4 3 . However, if the three numbers are 0, 22, and 2, then the average of the three numbers 5 (0 1 2 2 2) 4 3 5 0. Since both statements considered together allow for more than one answer to the question, the correct answer is choice (E). 636 PART VI: Five Practice Tests www.petersons.com 18. The correct answer is (C). You can solve for x in statement (1): 24x 2 7 .214 24x .27 2x . 2 7 4 x , 7 4 You can solve for x in statement (2): 5x 1 3 .22~x 1 1! 5x 1 3 .22x 2 2 7x.25 x . 2 5 7 Neither statement (1) nor (2) alone suffices to determine the value of x. However, con- sidering both statements together, 2 5 7 , x , 7 4 . Only two integral x-values—0 and 1—fall within this range. Given that x is a non-zero integer, x 5 1. Both statements (1) and (2) together suffice to determine the value of x, which is 1. 19. The correct answer is (E). Neither statement provides any information about the dimensions of the larger box. (It might be a cube, or it might be only one-inch in height, or it might have any other shape.) Without this information, it’s impossible to answer the question. 20. The correct answer is (A). You can easily answer this question by plugging in simple values for m and k. Assume that it takes Paul 10 minutes to mow the lawn (m 5 10) and that you want to know what portion of the job remains after 5 minutes (k 5 5). Obviously, exactly half S 1 2 D the job remains after 5 minutes. Now, in each answer choice, substitute 10 and 5 for m and k, respectively, to see which one gives you a value of 1 2 . You don’t need to go any farther than choice (A): m 2 k m 5 10 2 5 10 5 5 10 ,or 1 2 You can also solve this problem abstractly. Here’s how. The longer Paul mows, the more lawn is mowed, so the variation is direct. Let x equal the portion of the lawn Paul has mowed after k minutes, set up the proportion, and solve for x: m 1 5 k x mx 5 k x 5 k m Paul has mowed k m of the lawn in k minutes. Still not mowed, then, is 1 2 k m ,or m 2 k m . answers practice test 6 Practice Test 6 637 www.petersons.com 21. The correct answer is (E). When removing the first pair, the probability the pair removed will be black is 2 5 . Four pairs remain, two of which are white. The probability of removing a white pair from among those four is 2 4 . Combine the two probabilities by multiplying: 2 5 3 2 4 5 4 20 ,or 1 5 . This is the probability of choosing a black pair and then a white pair. So, the probability of choosing a white pair and then a black pair is also 1 5 . The probability, then, that the two pairs of socks are white and black is 1 5 1 1 5 5 2 5 . 22. The correct answer is (D). From statement (1) alone, you know that washers are bought at 45 cents per dozen and sold at 54 (3 3 18) cents per dozen. Calculating the profit on seven dozen washers is simply a matter of multiplying the difference (9 cents) by 7. Hence, statement (1) alone suffices to answer the question. (The answer is 63 cents.) From statement (2) alone, you know that a single washer costs $0.0375 ($3.75 4 100); therefore, a dozen washers cost 0.0375 3 12 5 45 cents, and seven dozen washers cost 45 3 7 cents. The profit would simply be 20% of this total cost. As you can see, you can answer the question based on statement (2) alone. (Again, the answer is 63 cents.) 23. The correct answer is (A). You can express the equation in statement (1) as x 1 y 5 190; thus, x and y are not supplementary angles. (Their measures don’t add up to 180°.) This information suffices to establish that the angles created by the intersection of l 1 and l 3 are different from those created by the intersection of l 2 and l 3 . Accordingly, l 1 cannot be parallel to l 2 , and statement (1) alone suffices to answer the question. Statement (2) adds nothing to the question. It merely reiterates what is already assumed in any GMAT figure: that all lines are straight. 24. The correct answer is (A). Suppose digits M and N are both 1. To find the product of 0.01 and 0.01, you multiply 1 by 1 (M 3 N), then add together the decimal places in the two numbers. There are four places altogether, so the product would be 0.0001, which is equivalent to 1 10,000 . Thus, whatever the values of M and N, 0.0M 3 0.0N 5 1 10,000 3 (M 3 N). 638 PART VI: Five Practice Tests www.petersons.com 25. The correct answer is (D). You can solve this problem by setting up and solving a system of two equations in two variables (let c and d equal the number of cats and dogs, respectively): c d 5 5 6 d 5 c 1 8 Substitute c 1 8ford in the first equation, then solve for c: c c 1 8 5 5 6 6c 5 5c 1 40 c 5 40 Hence, d 5 48, and the total number of boarded cats and dogs is 88. 26. The correct answer is (D). By definition, the longest possible chord of a circle is equal in length to the circle’s diameter. Since the x-coordinates of the two endpoints of chord RS are the same (7), the chord is vertical. Accordingly, the length of RS is simply the vertical distance from 23 to 7, which is 10. The circle’s diameter is 10, and thus its radius is 5. The circle’s area is p(5) 2 5 25p. 27. The correct answer is (E). The money earned by b workers at D dollars per week is bD dollars. The number of workers remaining is (m 2 b), and because they earn 1 2 D dollars per week, the money they earn is: 1 2 D(m 2 b) 5 1 2 mD 2 1 2 bD Thus, the total amount earned is: bD 1 1 2 mD 2 1 2 bD 5 1 2 bD 1 1 2 mD 5 1 2 D(b 1 m) 28. The correct answer is (E). To determine standard deviation, you need to know the value of each number, not just their average and range. For example, considering statements (1) and (2) together, here are just two of many possible distributions: {6, 9, 12, 15, 18} and {6, 11, 12, 13, 18}. Notice that the second and fourth terms in the second set are closer to the mean than the corresponding terms in the first set. Accordingly, the standard deviation of the second distribution is less than that of the first set. 29. The correct answer is (E). On the map, the number of centimeters from City 1 to City 2 5 825 4 75 5 11. To convert this number to millimeters, multiply by 10: 11 3 10 5 110. 30. The correct answer is (D). The greatest ten-year change in nonminority scholarship funds awarded occurred from 1980 to 1990: $750,000 to $600,000 (approximately). During this period, the greatest percent change in funds awarded occurred from 1980 to 1985—an increase of approximately 33%—from about $450,000 to $600,000. (The increase from 1985 to 1990 is about the same in dollar amount but less in percent.) answers practice test 6 Practice Test 6 639 www.petersons.com 31. The correct answer is (B). A quick visual inspection reveals that the aggregate amount awarded in 1990 exceeded that of any of the other three years shown. During that year, minority awards totaled approximately $770,000 and nonminority awards totaled approximately $600,000. The difference between the two amounts is $170,000. 32. The correct answer is (A). Statement (1) alone suffices to answer the question. If x is an even integer, all three terms are even, and combining them by subtracting always yields an even integer. If x is an odd integer, x 3 , x 2 , and x are each odd, and combining them by subtraction always yields an odd integer. Based on statement (1) alone, the answer to the question must be yes. On the other hand, statement (2) alone does not suffice to answer the question. 3x 1 2x 1 x 5 6x, which is an even integer regardless of whether x is even or odd. 33. The correct answer is (B). First, solve for a in terms of b (or vice versa). Solving for a: 3a 5 5b a 5 5b 3 Substitute this value for a in the equation ab 5 135: S 5b 3 D ~b! 5 135 5b 2 5~135!~3! b 2 5 ~135!~3! 5 b 2 5 81 b 569 If b 5 9, a 5 15. If b 529, a 5215. Thus, there are two possible values for a 1 b : 224 and 24. 34. The correct answer is (A). The value of a pounds of nuts is ab cents. The value of c pounds of nuts is cd cents. The value of the mixture is ab 1 cd cents. Since there are a 1 c pounds, each pound is worth ab 1 cd a 1 c cents. Since the merchant wants to add 10 cents to each pound for profit, and the value of each pound is in cents, add 10 to the value of each pound. 35. The correct answer is (E). The answer to the question is the least value of x that is a multiple of all three denominators—in other words, the question asks for the least common denominator. Work your way up in multiples of the largest denominator, 9, and you’ll find that 63 is the lowest multiple that is also a multiple of both 7 and 3. Thus, x 5 63. 36. The correct answer is (D). Given m∠BAD 5 60°, m∠ABC 5 120° because the two angles are supplementary. (Their measures total 180°.) m∠ABC 5 m∠ADC. Thus, their sum is 240°. 640 PART VI: Five Practice Tests www.petersons.com 37. The correct answer is (B). Statement (1) alone does not suffice to answer the question. For example, assume that B 5 1.1. If A 5 2.2, then A B 5 2 (an integer), but if A 5 2.3, then A B is a non-integer. Statement (2) alone establishes that A B 5 3 (an integer) and therefore suffices alone to answer the question. Verbal Section 1. C 2. B 3. E 4. E 5. D 6. C 7. E 8. C 9. A 10. A 11. B 12. E 13. A 14. D 15. A 16. E 17. B 18. B 19. D 20. D 21. C 22. C 23. B 24. D 25. A 26. A 27. B 28. D 29. C 30. A 31. E 32. E 33. B 34. C 35. A 36. E 37. A 38. B 39. C 40. A 41. E 1. The correct answer is (C). The original sentence makes an illogical comparison between aircraft and accidents. The grammatical construction suggests that twin- engine aircraft are accidents. Choice (C) corrects the problem by reconstructing the sentence. Choice (B) also corrects the problem, but the result is not a complete sentence. 2. The correct answer is (B). The original sentence improperly mixes the past tense (won) with the past perfect tense (had become and had seen). Choice (B) corrects this problem by reconstructing the first clause. In choice (B), the noun clause Margaret Thatcher’s winning correctly uses the possessive verb form. 3. The correct answer is (E). Although the passage’s second premise (that farm subsidies discourage farm productivity) doesn’t suffice to prove that they will in fact result in lower farm productivity, it does suggest that this result is probable to some degree. Given that a decrease in productivity would run contrary to public policy, it is reasonable to infer that farm subsidies are, or will be, responsible for a public policy violation. Answer choice (E) expresses this conclusion. 4. The correct answer is (E). In the original version, the phrase an obscene one is wordy. Also, the correct idiom is either consider tobeor simply consider, not consider as. Although choices (C), (D), and (E) each corrects both of these problems, choices (C) and (D) are awkward and confusing. Of the three, choice (E) provides the clearest and most graceful sentence. answers practice test 6 Practice Test 6 641 www.petersons.com 5. The correct answer is (D). The passage strongly suggests that motor vehicle traffic is the primary cause of the congestion and noise that detract from enjoyment of the park, which is what the park authorities are concerned with. Hence, prohibiting motorized vehicles would clearly be the most effective way to abate the problem. Although the courses of action that choices (B) and (E) propose would each be likely to reduce noise and congestion caused by motorists, especially during peak tourism season, neither would be as effective as an outright ban on motor vehicle traffic. 6. The correct answer is (C). If choice (C) is true, then the Cougars are likely to score more goals than if choice (C) is not true. The more goals the Cougars score, the less likely the coach’s prediction will come true. 7. The correct answer is (E). Although according to the passage the Third Plenum adopted initiatives aimed in part at reforming state-owned enterprises (lines 21–26), the passage does not support the assertion that any such reforms occurred or that such reforms actually included a reduction in the number of such enterprises. 8. The correct answer is (C). In pointing out the prosperity of Guangdong province, the author seeks to highlight the disparity in economic development among various regions within China and asserts that such disparity may result in political unrest in the less prosperous areas (lines 40–42). Thus, the prosperity of Guangdong is evidence in support of the author’s prediction of political unrest. 9. The correct answer is (A). The second paragraph deals exclusively with the possible political consequences of economic reform without political reform, presenting three possible scenarios that might result in political instability. 10. The correct answer is (A). The original version is the best one. The singular pronoun its is proper here because it refers to the singular society; the word regarding (which means “with respect to” or “concerning”), is also used properly here. Choices (B), (C), and (E) are grammatically correct, but they all fail to convey the sentence’s intended recommendation to shift priorities between education and national defense. Choice (D) incorrectly uses the plural pronoun form their instead of its. 11. The correct answer is (B). The original version creates confusion by separating the two parallel clauses the greater and theless Also, will be is unnecessary and undermines the parallel structure of the two clauses. Choice (B) remedies both problems. (The words smaller and lesser may be used interchangeably here, because both refer to amount rather than quantity.) 12. The correct answer is (E). In the original version, the modifying phrase that follows the comma is separated from the noun that it modifies (court reporter), resulting in confusion as to who produces the inaccurate transcript—a court reporter or a witness. Choice (E) solves the problem without creating a new one. Choices (B), (C), and (D) each solve the problem by reconstructing the sentence, but each one creates a new modifier problem. In choices (B) and (C), the person speaking too quickly seems to refer to a court reporter, while in choice (D) it appears to be the transcript that speaks too quickly. 642 PART VI: Five Practice Tests www.petersons.com . insufficient to answer the question. The values of P and Q relative to R are still unknown. 634 PART VI: Five Practice Tests www.petersons.com 10. The correct answer is (C). You can determine. of 500 products were sold, statement (1) alone is sufficient to answer the question. If A sold 166 products, A sold just less than 1 3 of the total number. Either B or C must sell more than 1 3 ,. together allow for more than one answer to the question, the correct answer is choice (E). 636 PART VI: Five Practice Tests www.petersons.com 18. The correct answer is (C). You can solve