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# If n is a positive integer, then n(n+1)(n+2) is

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Senior Manager
Joined: 02 Jul 2017
Posts: 269

Kudos [?]: 79 [0], given: 65

Location: India
Re: If n is a positive integer, then n(n+1)(n+2) is [#permalink]

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17 Sep 2017, 00:29
n is a positive integer
n(n+1)(n+2) = ?

(A) even only when n is even
(B) even only when n is odd
(C) odd whenever n is odd

=> Here we have multiple of 3 consecutive integers so we can have => odd*even*odd or even*odd*even. Both cases product will be even.
So Above 3 options does not give any additional information: n even or odd will not matter. Final product is always even

(D) divisible by 3 only when n is odd
As we have product of 3 consecutive integers, it will always be multiple of 3, whether n is even or odd :
n =odd => 1*2*3 <- divisible by 3
n= even => 2*3*4 <-divisible by 3

(E) divisible by 4 whenever n is even
as we have product of 3 numbers, value of n will decide by product is divisible by 4 or not
n =odd => 1*2*3 <- not divisible by 4
n= even => 2*3*4 <-divisible by 4

Kudos [?]: 79 [0], given: 65

Re: If n is a positive integer, then n(n+1)(n+2) is   [#permalink] 17 Sep 2017, 00:29
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