q: If 100!/30^n is an integer, which of the following is the greatest possible value of n?
Options:
(A) 28
(B) 24
(C) 20
(D) 15
(E) 10
a: 30^n = 2^n * 3^n * 5^n
100! has 97 2's, 48 3's and 24 5's
Since each of 2, 3 and 5 is required to form 30 and there are only 24 5's there can only be 24 30's in 100! The answer is (B).
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q: If 2^4, 3^3, and 13^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
Options:
(A) 198
(B) 288
(C) 363
(D) 396
(E) 468
a: I will go with E (pending elements to match is 2^2*3^2*13^1 = 468 The answer is (E).
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q: What is the are of an equilateral triangle of side 20 cm?
Options:
(A) 645
(B) 649
(C) 644
(D) 643
(E) 1003
a: Area of an equilateral triangle = 3/4 S2
If S = 20, Area of triangle = 3/4 * 20 * 20 = 1003 cm2; The answer is (E).
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q: A 160 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
Options:
(A) 96 kmph
(B) 94 kmph
(C) 92 kmph
(D) 86 kmph
(E) 76 kmph
a:
S = 160/6 * 18/5 = 96 kmph The answer is (A).
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