question: What is the greatest positive integer x such that 4^x is a factor of 64^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
answer: Stream of consciousness: 64^10 = (4^3)^10 = 4^30 The answer is (E).
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question: A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was?
Options:
(A) 3887
(B) 2768
(C) 15000
(D) 76887
(E) 16711
answer: Stream of consciousness: Principal = (100 * 5400) / (12 * 3) = Rs. 15000 The answer is (C).
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question: Which of the following is equal to the average (arithmetic mean) of (x+3)^2 and (x-3)^2?
Options:
(A) x^2
(B) x^2+2
(C) x^2 +4
(D) x^2+9
(E) x^2+4x
answer: Stream of consciousness: Avg = [(x+3)^2 + (x-3)^2] / 2
Expanding and simplifying, (x^2 + 6x + 9 + x^2 - 6x + 9 ) / 2 = x^2 + 9 The answer is (D).
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question: If f(x) = x^3/(x^4 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x)
(B) f(x)
(C) 2*f(x)
(D) 1/f(x)
(E) 2/f(x)
answer:
Stream of consciousness: If x = 2 then f(x) = 8/15 and f(1/x) = -8/15 which is equal to -f(x) The answer is (A).
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