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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]

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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.
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Re: If x is a positive integer, is (x)(x + 2)(x + 4) div by 12? [#permalink]

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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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If x is a positive integer, is (x)(x + 2)(x + 4) divisible by 12? [#permalink]

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New post 14 Nov 2016, 11:17
If x is a positive integer, is (x)(x + 2)(x + 4) divisible by 12?

(1) x2 + 2x is a multiple of 3.

(2) 3x is a multiple of 2.
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Re: If x is a positive integer, is (x)(x + 2)(x + 4) div by 12? [#permalink]

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New post 14 Nov 2016, 11:22
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Ilomelin wrote:
If x is a positive integer, is (x)(x + 2)(x + 4) divisible by 12?

(1) x2 + 2x is a multiple of 3.

(2) 3x is a multiple of 2.


Merging topics. Please refer to the solution above.
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If x is a positive integer, is (x)(x + 2)(x + 4) div by 12? [#permalink]

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New post 14 Nov 2016, 11:37
Bunuel wrote:
Ilomelin wrote:
If x is a positive integer, is (x)(x + 2)(x + 4) divisible by 12?

(1) x2 + 2x is a multiple of 3.

(2) 3x is a multiple of 2.


Merging topics. Please refer to the solution above.



Thank you Bunuel.

Could you please explain me how do we know (other than plugging in numbers) that out of 3 consecutive odd or even integers, one must be divisible by 3? I understand why it works with consecutive integers, but why does it also apply to evenly spaced odds or evens?

Thanks.
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If x is a positive integer, is (x)(x + 2)(x + 4) div by 12?   [#permalink] 14 Nov 2016, 11:37
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