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Intern Joined: 30 Oct 2017
Posts: 30
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Question Stats: 50% (00:47) correct 50% (01:21) wrong based on 2 sessions
If n is a positive integer and (n + 1)(n + 3) is odd, then (n + 2)(n + 4) must be a multiple of which one of the following?

(A) 3 (B) 5 (C) 6 (D) 8 (E) 16
GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Kudos [?]: 1782 , given: 397

Re: number theory [#permalink]
Expert's post
shahul wrote:
If n is a positive integer and (n + 1)(n + 3) is odd, then (n + 2)(n + 4) must be a multiple of which one of the following?

(A) 3 (B) 5 (C) 6 (D) 8 (E) 16

For $$(n + 1)(n + 3)$$ to be odd $$(n+1)$$ is odd and $$(n+3)$$ is also odd.

Since only $$odd \times odd=odd$$. So $$n$$ must be even since only $$even + odd = odd$$.

$$(n + 2)(n + 4)= 2 \times (\frac{n}{2}+1) \times 2 \times (\frac{n}{2}+2)$$.

Either $$(\frac{n}{2}+1)$$ is even or $$(\frac{n}{2}+2)$$ is even.

So this means there must be a factor of 8 ($$2 \times 2 \times 2$$).
_________________

Sandy
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Try our free Online GRE Test Re: number theory   [#permalink] 01 Jun 2018, 15:31
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