q: 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
a: 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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q: A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:
Options:
(A) 553681
(B) 555181
(C) 555681
(D) 556581
(E) 556881
a: 987 = 3 x 7 x 47
So, the required number must be divisible by each one of 3, 7, 47
553681->(Sum of digits = 28, not divisible by 3)
555181->(Sum of digits = 25, not divisible by 3)
555681 is divisible by 3, 7, 47 The answer is (C).
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q: Some persons can do a piece of work in 12 days. Two times the number of these people will do half of that work in?
Options:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
a: 12/ (2 * 2) = 3 days The answer is (A).
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q: How much is 80% of 40 is greater than 4/5 of 25?
Options:
(A) 22
(B) 67
(C) 88
(D) 12
(E) 66
a:

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
(80/100) * 40 – (4/5) * 25
32 - 20 = 12 The answer is (D).
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