q: How long does a train 110 m long traveling at 36 kmph takes to cross a bridge of 170 m in length?
Options:
(A) 28
(B) 16.0
(C) 16.4
(D) 16.8
(E) 16.1
a: Stream of consciousness: D = 110 + 170 = 280 m
S = 36 * 5/18 = 10
T = 280 * 1/10 = 28 sec The answer is (A).
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q: If n is the smallest integer such that 432 times n is the square of an integer, what is the value of n?
Options:
(A) 2
(B) 3
(C) 6
(D) 12
(E) 24
a: Stream of consciousness: The prime factorization of a square has to have even powers of all its prime factors. If the original number has a factor, say of 7, then when it's squared, the square will have a factor of 7^2. Another way to say that is: any positive integer all of whose prime factors have even powers must be a perfect square of some other integer. Look at the prime factorization of 432
432 = (2^4)*(3^3)
The factor of 2 already has an even power - that's all set. The factor of 3 currently has an odd power. If n = 3, then 432*n would have an even power of 2 and an even power of 3; therefore, it would be a perfect square. Thus, n = 3 is a choice that makes 432*n a perfect square. The answer is (B).
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q: a piece of ribbon 4 yard long is used to make bows requiring 15 inches of ribbon for each.What is the maximum number of bows that can be made.
Options:
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
a:
Stream of consciousness: 1 yard = 36 Inch
4 yard = 36*4 = 144 inch
15 inch req. for 1 bow
Max. no. of bows possible = 144/15 = 9 bows and 9 inch ribbon left. The answer is (A).
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