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# If n is an integer, is n even?

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Math Expert
Joined: 02 Sep 2009
Posts: 56257
If n is an integer, is n even?  [#permalink]

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26 Feb 2018, 03:01
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Difficulty:

35% (medium)

Question Stats:

64% (01:22) correct 36% (01:29) wrong based on 47 sessions

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If n is an integer, is n even?

(1) n(n + 2) is even
(2) n(n + 3) is even

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Joined: 31 Oct 2013
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Re: If n is an integer, is n even?  [#permalink]

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26 Feb 2018, 03:12
Bunuel wrote:
If n is an integer, is n even?

(1) n(n + 2) is even
(2) n(n + 3) is even

we have to find out weather n is even or not.

statement 1: n(n+2) is even. only even value of n makes it even. suppose, n=2 . 2(2+2)=8 but odd value . suppose n is 3. so, 3(3+2)=15. so any odd integer won't meet the condition stated in statement 1. sufficient.

statement 2: n+3 can be even , can be odd. it is dependent on the value of n. regardless of the situation statement 2 always gives us even. thus it's insufficient.

so, Answer is A. Statement 1 alone is sufficient to answer the question.
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If n is an integer, is n even?  [#permalink]

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26 Feb 2018, 04:36
Bunuel wrote:
If n is an integer, is n even?

(1) n(n + 2) is even
(2) n(n + 3) is even

Given : n is an Integer

Question: Is n an EVEN Integer?

Statement 1: n(n + 2) is even

but n and n+2 have to be two consecutive even integers for this to be true hence n must be an even integer

n = 2, 4, 6, 8, 10 ... etc.

SUFFICIENT

Statement 2: n(n + 3) is even

i.e. either n is even or n+3 is even
therefore n may be any number 1, 2, 3, 4, 5, ... etc.
NOT SUFFICIENT

Combining the two statements

Even after combining the two statements we find out that n may be any even integer and n+3 is odd for any even value of n hence
n = 2, 4, 6, 8 ... etc

NOT SUFFICIENT

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If n is an integer, is n even?   [#permalink] 26 Feb 2018, 04:36
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