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# M27-20

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:27
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45% (medium)

Question Stats:

61% (00:50) correct 39% (00:51) wrong based on 23 sessions

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If $$x$$ and $$y$$ are integers, is $$x$$ a positive integer?

(1) $$x*|y|$$ is a prime number.

(2) $$x*|y|$$ is a non-negative integer.
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:27
Official Solution:

(1) $$x*|y|$$ is a prime number. Since only positive numbers can be primes, then: $$x*|y|=positive$$ hence $$x=positive$$. Sufficient.

(2) $$x*|y|$$ is a non-negative integer. Notice that we are told that $$x*|y|$$ is non-negative, not that it's positive, so $$x$$ can be positive as well as zero. Not sufficient.

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28 Feb 2017, 13:53
|y| means y can be -y or +y. so x can be -x when y is negative and x is positive when y is positive. How is A the answer? I think it is E
Math Expert
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28 Feb 2017, 20:19
Shiridip wrote:
|y| means y can be -y or +y. so x can be -x when y is negative and x is positive when y is positive. How is A the answer? I think it is E

Absolute value of a number is always non-negative. So, |y| (absolute value of y), regardless whether y itself is negative or positive, will be non-negative.

(1) $$x*|y|$$ is a prime number. Since only positive numbers can be primes, then: $$x*|y|=positive$$ hence $$x=positive$$. Sufficient.
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Re: M27-20   [#permalink] 28 Feb 2017, 20:19
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# M27-20

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