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## OG If m and n are positive integers

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AbeNeedsAnswers Master | Next Rank: 500 Posts
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#### OG If m and n are positive integers

Wed Aug 23, 2017 9:29 pm

00:00

A

B

C

D

E

# Global Stats

Difficult

If m and n are positive integers, is (âˆšm)^n an integer?

(1) (âˆšm) is an integer
(2) (âˆšn) is an integer

A

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Feb 19, 2018 9:03 pm
Hi All,

We're told that M and N are POSITIVE INTEGERS. We're asked if (âˆšM)^N is an integer. This is a YES/NO question. We can solve it with a mix of Number Property rules and TESTing VALUES.

1) (âˆšM) is an integer

Fact 1 tells us that M is a 'perfect square' (re: 1, 4, 9, 16, 25, etc.). Since (âˆšM) is a positive integer - and N is a positive integer - then we're raising a positive integer to a positive integer power. That will ALWAYS lead to a positive integer, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) (âˆšN) is an integer

Fact 2 tells us that N is a 'perfect square' (re: 1, 4, 9, 16, 25, etc.), but we do NOT know whether (âˆšM) is an integer or not.
IF....
M=1 and N=1, then 1^1 = 1 and the answer to the question is YES.
M=2 and N=1, then âˆš2^1 = âˆš2 and the answer to the question is NO.
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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