question: In an office, 60 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
Options:
(A) 96
(B) 64
(C) 50
(D) 144
(E) 160
answer: Stream of consciousness: (10/100)Workers = 16 = > number of workers = 160
(60/100)*Workers = x+16 = > x = 96 The answer is (A).
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question: What is the greatest positive integer x such that 7^x is a factor of 343^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
answer: Stream of consciousness: 343^10 = (7^3)^10 = 7^30 The answer is (E).
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question: Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the number's sum will be 13?
Options:
(A) 3/14
(B) 2/7
(C) 1/3
(D) 1/42
(E) 12/21
answer: Stream of consciousness: Both Dice addition result is 13 = (6+7)
Probability that the number on first die is 6 = 1/6
Probability that the number on Second die is 7 = 1/7
Probability that Both Dice addition result is 13 = 1/6 * 1/7 = 1/42 The answer is (D).
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question: Solve below question 3x - 5 = -20
Options:
(A) -8
(B) -9
(C) -5
(D) -4
(E) 1
answer:
Stream of consciousness: 1. Subtract 1 from both sides: 3x - 5 + 5 = -20 + 5 2. Simplify both sides: 3x = -15 3. Divide both sides by 3: 4. Simplify both sides: x = -5 The answer is (C).
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