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Difficulty:
55%
(hard)
Question Stats:
56% (01:34) correct
44%
(01:57)
wrong
based on 41
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Is y!/x! an integer?
(1) (x + y)(x-y) = 5! + 1
(2) x + y = 112
(1) (x + y)(x-y) = 5! + 1
(2) x + y = 112
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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.
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.
14 Oct 2012, 12:47
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lrajiv74
y!/x! will be integer if y>=x
from 1. x^2-y^2 = positive value
Thus |x| > |y|
Since negative values cant have factorials. we have x>y . Hence it is NEVER an INTEGER. HENCE SUFFICIENT. Therefore A
Also, Please give answers ONLY in spoiler.
