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M11-37

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M11-37 [#permalink]

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New post 16 Sep 2014, 00:45
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A
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D
E

Difficulty:

  5% (low)

Question Stats:

88% (00:43) correct 13% (00:48) wrong based on 80 sessions

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Kudos [?]: 128980 [0], given: 12185

Expert Post
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Re M11-37 [#permalink]

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New post 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: \({(3+1)}^3=4^3=64\)


Answer: D
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Re: M11-37 [#permalink]

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New post 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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Re: M11-37 [#permalink]

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New post 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

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Re: M11-37   [#permalink] 24 Aug 2017, 19:18
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M11-37

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