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If m and n are nonzero integers, is m^n an integer? (1) n^m is positve (2) n^m is an integer.

If m and n are nonzero integers, is m^n an integer?

If n is a positive integer then m^n will be an integer for any value of m (taking into account that both are nonzero integers). If n is negative then m^n will be an integer if and only m=1 or m=-1, for example: (-1)^(-2)=1/(-1)^2=1

So basically we are asked: is n positive or m=|1|?

(1) n^m is positive --> either m=even (and in this case n can take any value) or n=positive (and in this case m can take any value). Not sufficient.

(2) n^m is an integer --> either m=positive (and in this case n can take any value) or m=negative and in this case n=1 or -1. Not sufficient.

(1)+(2) If n^m=(-1)^2=positive integer, then the answer will be NO as m^n=2^(-1)=1/2 but if n^m=1^2=positive integer, then the answer will be YES as m^n=2^1=2. Not Sufficient.

Re: If m and n are nonzero integers, is m^n an integer? [#permalink]

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26 Mar 2015, 03:29

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This DS question is built around a few Number Property rules. You can take advantage of these rules by TESTing VALUES and keeping your TESTs simple....

We're told that M and N are NON-ZERO INTEGERS. We're asked if M^N is an integer. This is a YES/NO question.

Fact 1: N^M is POSITIVE

IF.... N = 1 M = 1 1^1 is positive 1^1 is an integer and the answer to the question is YES

IF.... N = -2 M = 2 (-2)^2 is positive 2^(-2) is NOT an integer and the answer to the question is NO Fact 1 is INSUFFICIENT

Fact 2: N^M is an integer

The same two TESTs that we used in Fact 1 also 'fit' Fact 2....

IF.... N = 1 M = 1 1^1 is an integer 1^1 is an integer and the answer to the question is YES

IF.... N = -2 M = 2 (-2)^2 is an integer 2^(-2) is NOT an integer and the answer to the question is NO Fact 2 is INSUFFICIENT

Combined, we have the SAME TESTs for both Facts which give us a YES and a NO answer. Combined, INSUFFICIENT

Re: If m and n are nonzero integers, is m^n an integer? [#permalink]

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03 Apr 2016, 09:55

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Re: If m and n are nonzero integers, is m^n an integer? [#permalink]

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26 Apr 2017, 11:02

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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