question: If x, y, and z are positive integers such that x is divisible by y, and y is divisible by z, which of the following is NOT necessarily an integer?
Options:
(A) xy/z
(B) (x + y) /z
(C) xz/y
(D) (x - y) /z
(E) (x + z) /y
answer: Stream of consciousness: As per the question, let x = 12, y = 6, and z = 2. Plugging these into the answer choices, only E does not yield an integer. The reason is that (x + z)/y = x/y + z/y, and while x/y must be an integer, z/y is only an integer if y = z. The answer is (E).
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question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
Options:
(A) 6 2/3%
(B) 6 2/9%
(C) 6 3/3%
(D) 9 2/3%
(E) 7 2/3%
answer: Stream of consciousness: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3% The answer is (A).
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question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40
(B) 99
(C) 77
(D) 66
(E) 12
answer: Stream of consciousness: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec The answer is (A).
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question: In wardrobe Marry has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens hiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?
Options:
(A) 1/2
(B) 2/3
(C) 3/5
(D) 3/7
(E) 4/9
answer:
Stream of consciousness: Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
Required probability = 2/3 x 3/4 = 1/2 The answer is (A).
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