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# Is y!/x! an integer?

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Manager
Joined: 27 Jul 2011
Posts: 181
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Kudos [?]: 176 [0], given: 103

Is y!/x! an integer? [#permalink]

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13 Jul 2012, 02:01
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Difficulty:

75% (hard)

Question Stats:

39% (01:27) correct 61% (01:46) wrong based on 18 sessions

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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, 04:17, edited 1 time in total.
Edited the question.
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Re: Is y!/x! an integer? [#permalink]

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13 Jul 2012, 04:47
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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, 04:47
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# Is y!/x! an integer?

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