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not make sense, and in E it is unclear from could have done so whether this refers to profiting or refusing to profit

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41 Product marketing jobs at MegaCorp are difficult to fill because they require specialized skills, demand great responsibility, but also barely any vacation time A B C D E demand great responsibility, but also great responsibility, and also great responsibility, and with carry great responsibility, and carry great responsibility, and offer

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ANSWER: E A is incorrect because vacation time requires a verb before it in this construction Either each item in the list of three must take the verb require or each must have its own verb D is incorrect on the same grounds B and C could be correct if all three items take require, but in the context it does not make sense for barely any vacation time to be the object of require Only E makes sense and is grammatically correct

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1 Sam is training for the marathon He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 3 miles to Rock Creek If he is then n miles from home, what is the range of possible values for n A B C D E 1 n 23 3 n 21 5 n 19 6 n 18 9 n 15

3 There are 450 birds at a small zoo The number of birds is 5 times the number of all the other animals combined How many more birds are there than nonbird animals at the zoo A B C D E 400 360 270 180 90

ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home The range then is between 12 + 6 - 2 + 3 = 19 for the maximum, and 12 - 6 + 2 - 3 = 5 for the minimum, so C is the answer

ANSWER: B If the 450 birds are 5 times the number of nonbird animals, then nonbirds = 450/5 = 90 450 - 90 = 360 more birds than nonbirds at the zoo

4 If x, y, and z are positive integers, and 4x = 5y = 6z, then the least possible value of x + y + z is A B C D E 15 28 37 42 60

2 Amber works 20 days a month at d dollars per day for m months out of the year Which of the following represents her monthly pay m A 20d B 20d C 10md 6 20d D m E 20md

ANSWER: B The passage states that she works 20 days a month at d dollars per day, so 20d is her monthly pay

ANSWER: C The least common multiple of 4, 5, and 6 is 60, so the numbers are x = 15; y = 12; z = 10; 15 + 12 + 10 = 37

PRACTICE TEST 5

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5 Three hundred multiples of three are picked at random, and three hundred multiples of four are picked at random Approximately what percentage of the six hundred selected numbers are even A B C D E 100% 75% 66% 50% 33%

ANSWER: C 722 is the same thing as (8 9)2, which is the same as (23 32)2, which is the same as (26)(34); consequently, everything factors out of the fraction except 52, which equals 25

8 What is the value of y (1) y 2 + 8y + 16 = 0 (2) y < 0

ANSWER: A (1) alone is sufficient because the equation can be restated as (y + 4)(y + 4) = 0, so y = -4 (2) alone is insufficient because there are infinite negative numbers that meet the condition

ANSWER: B All multiples of four are even, and half of the multiples of three are even; since they each make up 50% of the 600, the combined percentage is approximately 75%