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If x is a positive integer, is (x)(x + 2)(x + 4) div by 12?

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If x is a positive integer, is (x)(x + 2)(x + 4) div by 12? [#permalink] New post 26 Nov 2012, 08:40
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If x is a positive integer, is (x)(x + 2)(x + 4) divisible by 12?

(1) x^2 + 2x is a multiple of 3.

(2) 3x is a multiple of 2.
[Reveal] Spoiler: OA

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Re: If x is a positive integer, is (x)(x + 2)(x + 4) div by 12? [#permalink] New post 26 Nov 2012, 08:58
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If x is a positive integer, is (x)(x + 2)(x + 4) divisible by 12?

Notice that no matter whether x is even or odd, out of x, x+2 and x+4 one must be a multiple of 3. So, we are basically asked to find whether (x)(x + 2)(x + 4) is divisible by 4. Now, if x=odd, then all three multiples are odd, thus (x)(x + 2)(x + 4) will be odd and not divisible by 4. If x=even, then (x)(x + 2)(x + 4)=even*even*even, thus it'll be divisible by 4.

Therefore, the question boils down to find whether x is even.

(1) x^2 + 2x is a multiple of 3 --> if x=1=odd, then the answer is NO but if x=4, then the answer is YES. Not sufficient.

(2) 3x is a multiple of 2. This statement implies that x=even. Sufficient.

Answer: B.

Hope it's clear.
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Re: If x is a positive integer, is (x)(x + 2)(x + 4) div by 12? [#permalink] New post 10 Sep 2013, 05:19
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Re: If x is a positive integer, is (x)(x + 2)(x + 4) div by 12?   [#permalink] 10 Sep 2013, 05:19
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