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