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
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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! So the answer is: (B).
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Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
(A) Rs.345
(B) Rs.270
(C) Rs.275
(D) Rs.324
(E) Rs.325
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I = (500*9*6)/100 = 270 So the answer is: (B).
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A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
(A) 40
(B) 48
(C) 45
(D) 50
(E) 25
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Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec So the answer is: (B).
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