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# M19 Q3

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Manager
Joined: 06 Jul 2010
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11 Jul 2011, 07:57
Is integer $$x$$ even?

1.) $$(x + 1)(x - 2)$$ is even
2.) $$(x - 3)(x + 5)$$ is even
[Reveal] Spoiler:
OA is C
I disagree. X could be 3 such that statement 2 is 0. As 0 is an even integer x could be even or odd. So OA should be E
Math Forum Moderator
Joined: 20 Dec 2010
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Re: M19 Q3 [#permalink]

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11 Jul 2011, 14:44
heyholetsgo wrote:
Is integer $$x$$ even?

1.) $$(x + 1)(x - 2)$$ is even
2.) $$(x - 3)(x + 5)$$ is even
[Reveal] Spoiler:
OA is C
I disagree. X could be 3 such that statement 2 is 0. As 0 is an even integer x could be even or odd. So OA should be E

OA is B and I think it's correct.

Do you still think B is NOT sufficient alone? If yes, please explain why?
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GMAT Date: 08-08-2011
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Re: M19 Q3 [#permalink]

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12 Jul 2011, 05:45
I too say it's B.

Knowing that X is an integer:

Stmt 1) if (X-2) is odd then (X+1) is even and (X-2)(X+1) is even and X is odd.
If (X-2) is even then (X+1) is odd and (X-2)(X+1) is even and X is even.
This tells us X is even or odd. Not sufficient.

Stmt 2 - For (X+3)(X+5) to be even, X has to be odd.

NB: If X is an integer and X is odd, X+1 has to be even and X-1 has to be even.

Last edited by Yalephd on 16 Jul 2011, 05:24, edited 2 times in total.
Senior Manager
Joined: 28 Jun 2009
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Location: United States (MA)
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Re: M19 Q3 [#permalink]

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12 Jul 2011, 10:45
Good explanation Yalephd!

I tested the statements in similar manner. Additionally, I substituted actual numbers in place of X and confirmed my answer.
Re: M19 Q3   [#permalink] 12 Jul 2011, 10:45
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# M19 Q3

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