PRACTICE TEST 5

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26 Of 40 applicants for a job, 32 had at least 5 years of prior work experience, 24 had advanced degrees, and 16 had at least 5 years of prior work experience and advanced degrees How many of the applicants had neither 5 years of prior work experience nor advanced degrees A B C D E 0 2 4 8 16

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2 7 14 80, 698 28 If and represent single digits in the correctly worked computation above, what is the value of times A B C D E 6 10 12 15 18

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ANSWER: A To solve this problem, you need to divide the applicants into four exclusive groups that do not overlap The 16 with both experience and degrees are the first group; we can subtract the 16 from the 24 with advanced degrees to determine that 8 have advanced degrees but not 5 years of experience, and we can subtract the 16 from the 32 with experience to determine that there are 16 applicants with 5 years of experience but no advanced degrees We can then subtract these three groups from the total pool of 40 applicants to determine how many lack both experience and advanced degrees; 40 - 16 - 16 - 8 = 0, so there were no such applicants among the 40

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27 If a A B C D E

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3a 2 15 = b 0, and a , then b = a a (5 a)(3+a) (3 a)(5+a) 2a2 15 3a2 + a 15 15 2a2

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ANSWER: D It is probably easiest to determine the values of and by plugging in values, which is ugly, but there are ways to simplify your computations If you look at the answer choices, you will see that 8 and 7 are not factors of any of the choices, so you do not need to try them Also, if you examine possible values for , you might realize that has to be greater than 2 because 200 200 = 40,000, which is much less than 80,698, so is probably 3 or 4, since 200 300 = 60,000 and 200 400 = 80,000 Neither 3 nor 4 is a factor of answer B, 10, so you can eliminate that answer Plug in the corresponding values of the other answer choices for and : A: (3, 2); C: (3, 4) and (4, 3); and D: (3, 5); you will find that D, 15, is the only answer with factors that will make the computation work properly, so D is the answer

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ANSWER: E If you multiply a times both sides of the equation, you get b = a2-3a2 + 15 = 15 -2a2

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29 A retailer sells 5 shirts The first 2 he sells for $64 and $39 If the retailer wishes to sell the 5 shirts for an overall average price of over $50, what must be the minimum average price of the remaining 3 shirts A B C D E $4900 $4967 $5000 $5133 $5550

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ANSWER: A For the average price of 5 shirts to be over $50, the total price of the shirts must be at least $250 250 minus the sum of the two sold shirts (64 + 39 = 103) equals 147 $147 divided by 3 equals $49

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ANSWERS AND EXPLANATIONS

30 The MegaTek Corporation is displaying its distribution of employees by department in a circle graph The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department If the section of the circle graph representing the manufacturing department takes up 72 of the circle, what percentage of MegaTek employees are in manufacturing A B C D E 20% 25% 30% 35% 72%

be true because if you square both sides of x = y + z you get x2 = y2 + 2yz + z2, which does not agree with the original statement

33 If M is a set of five numbers p, q, r, s, and t, is the range of numbers in M greater than 5 (1) The average (arithmetic mean) of p, q, r, s, and t is 5 (2) p r > 5

ANSWER: B (1) alone is insufficient, because the spread of numbers could be 1, 1, 1, 1, 21 or 5, 5, 5, 5, 5 (2) alone is sufficient, because it states that the range between p and r is greater than 5, so the range of M, which includes p and r, must be greater than 5 as well