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# M11-37

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Math Expert
Joined: 02 Sep 2009
Posts: 46300

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16 Sep 2014, 00:45
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Difficulty:

5% (low)

Question Stats:

89% (00:44) correct 11% (00:48) wrong based on 88 sessions

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If $$N$$ is a positive integer, is $$N$$ even?

(1) $$N^{N + 1}$$ is even

(2) $$(N + 1)^N$$ is odd

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Math Expert
Joined: 02 Sep 2009
Posts: 46300

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16 Sep 2014, 00:46
Official Solution:

Statement (1) by itself is sufficient. From S1 it follows that $$N$$ must be even. If $$N$$ were odd then $$N^{(N + 1)}$$ would be odd. For example: $$3^4=81$$, which is odd.

Statement (2) by itself is sufficient. From S2 it also follows that $$N$$ must be even. If $$N$$ were odd then $$(N + 1)^N$$ would be even. For example: $${(3+1)}^3=4^3=64$$

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28 Jul 2016, 04:41
Top Contributor
Bunuel wrote:
If $$N$$ is a positive integer, is $$N$$ even?

(1) $$N^{N + 1}$$ is even

(2) $$(N + 1)^N$$ is odd

I kept plugging in the numbers and tried 1, 2, 3, 4, and 5 for both statements, which took about a minute to get to the right answer D.
If I hadn't looked at Bunuel's solution, I may not have remembered the simple concept about odd & even numbers because if which both statements themselves are sufficient.

Looks like, gotta thoroughly revise all the concepts and math foundations.
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24 Aug 2017, 19:18
To asnwer this question I found useful the property that the power of a number doesn’t impact the even-odd nature of the number
Re: M11-37   [#permalink] 24 Aug 2017, 19:18
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# M11-37

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