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Is y!/x! an integer?

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Is y!/x! an integer? [#permalink] New post 13 Jul 2012, 01:01
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36% (00:00) correct 64% (01:54) wrong based on 14 sessions
Is y!/x! an integer?

(1) (x + y)(x-y) = 5! + 1
(2) x + y = 112
[Reveal] Spoiler: OA

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Last edited by Bunuel on 13 Jul 2012, 03:17, edited 1 time in total.
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Re: Is y!/x! an integer? [#permalink] New post 13 Jul 2012, 03:47
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This is a flawed question.

Is y!/x! an integer?

First of all, factorial is defined only for non-negative integers, so realistic GMAT question would mention that x and y are non-negative integers.

Next, \frac{y!}{x!}=integer will hold true if y\geq{x}. So, the question basically asks whether y\geq{x}.

(1) (x + y)(x-y) = 5! + 1 --> x^2-y^2=121. As discussed, since x and y must be non-negative integers, then x>y and the asnwer to the question is NO. Sufficient.

(2) x + y = 112. Not sufficient to answer whether y\geq{x}.

Answer: A.

Now, even though formal answer to the question is A, this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. But from (1) the only non-negative integer solutions for x and y are: (11, 0) and (61, 60), so x+y cannot equal to 112 as the second statement says, which means that the statements clearly contradict each other.

The question is flawed. You won't see such a question on the GMAT.

Hope it's clear.
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Re: Is y!/x! an integer?   [#permalink] 13 Jul 2012, 03:47
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