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DS question involving prime properties

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by saadishah » Mon Dec 21, 2015 11:39 am
Can somebody explain how this is a DS question involving prime properties and how to go about it?

Does there exist an integer d such that x > d > 1 and x/d is an integer?

(1) 11! + 2 =< x =< 11! + 12
(2) x >= 2^5
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Source: — Data Sufficiency |
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by Matt@VeritasPrep » Sun Dec 27, 2015 5:29 pm
Let's assume (as the question seems to want us to) that x is an integer.

If x is an integer, and x / d is an integer, then d is a factor of x. So the question is asking (in so many words) whether x is prime.

S1::

No, x is not prime. 11! + 2 is the sum of two multiples of 2, so it is not prime; 11! + 3 is the sum of two multiples of 3, so it is not prime; etc. Everything from 11! + 2 to 11! + 12 has this property, so none of these numbers are prime; SUFFICIENT.

S2::

x could be prime (e.g. x = 37) or not (e.g. x = 33); NOT SUFFICIENT.
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