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# What is the value of of integer x? 1) x has exactly 2

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What is the value of of integer x? 1) x has exactly 2 [#permalink]  21 Oct 2009, 19:47
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What is the value of of integer x?
1) x has exactly 2 factors
2) When x is divided by 2, the remainder is 0

I have problem understanding this basic data sufficiency test. I know the answer is C "2", but would you be able to tell me
why answer can not be -2.
-2 has two factors as well, 1, 2
and when it is divided by 2, the remainder is 0

Thank you
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Re: Basic question [#permalink]  21 Oct 2009, 20:15
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-2 can also be divided by -1 and -2. So I guess you could say it has 4 factors.
Statement 1 says that the number is prime, as that is the definition of a prime number. Examples of X are 2,3,5,7,11.
Statement 2 says that the number is even. As only even numbers can be divisible by 2.
Examples of X are 2,4,6,8,10

If you combine it you are looking for a prime even integer. The only one that exists is 2. You need to know that as a basic number property rule but if you don’t know it writing down a few primes and a few evens as above you can determine that.
Hope that helps.
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Re: Basic question [#permalink]  21 Oct 2009, 22:44
Thanks,
My concern was that I have read in MGMAT that factor is only positive integer. I guess it can be negative as well.
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Re: Basic question [#permalink]  21 Oct 2009, 23:02
I’ve not read MGMAT Number props but generally prime numbers are non negative. http://en.wikipedia.org/wiki/Prime_number
As the first statement basically defines a prime number, negative numbers aren’t allowable for this specific question for that statement.
For statement 2 I do not see why a negative shouldn’t be included. So that reinforces the point that it is insufficient.
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Re: Basic question [#permalink]  22 Oct 2009, 07:08
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If this were a real GMAT question, it would ask "What is the value of positive integer x?", and Statement 1 would say that "x has exactly two positive factors". Factors can certainly be negative; technically 2 has four factors (-2, -1, 1, and 2). The GMAT *never* tests this, however; every real GMAT question about divisibility is always restricted to positive integers only.

(note that as the question in the original post is written, there is no number which satisfies both statements. From Statement 1, x could only be 1 or -1, and neither of these leaves a remainder of zero when divided by 2 - the word 'positive' needs to be included in the question to make it mathematically correct).
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Re: Basic question [#permalink]  22 Oct 2009, 08:40
Thanks for prompt explanation. I guess the question needed to have the word "positive," since it is omitted the answer even could be E, although MGMAT Number Properties book says it is C (2)
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Re: Basic question   [#permalink] 22 Oct 2009, 08:40
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