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

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If m and n are positive integers, is root(m)^n an integer? [#permalink]

09 Jul 2012, 04:56

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If m and n are positive integers, is (\sqrt{m})^n an integer?

(1) \sqrt{m} is an integer.
(2) \sqrt{n} is an integer.

Diagnostic Test
Question: 44
Page: 26
Difficulty: 600

[Reveal] Spoiler: OA

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Re: If m and n are positive integers, is root(m)^n an integer? [#permalink]

09 Jul 2012, 04:56

SOLUTION

If m and n are positive integers, is (\sqrt{m})^n an integer?

(1) \sqrt{m} is an integer --> (\sqrt{m})^n=(integer)^{positive \ integer}=integer. Sufficient.

(2) \sqrt{n} is an integer. If m=n=1, then the answer is YES but if m=2 and n=1, then (\sqrt{m})^n=\sqrt{2}\neq{integer}, so in this case the answer is NO. Not sufficient.

Answer: A.
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Re: If m and n are positive integers, is root(m)^n an integer? [#permalink]

09 Jul 2012, 05:27

Bunuel wrote:

If m and n are positive integers, is (\sqrt{m})^n an integer?

(1) \sqrt{m} is an integer.
(2) \sqrt{n} is an integer.

Hi,

Difficulty level: 600

We have to find whether (\sqrt{m})^n is an integer,
or m^{\frac n2} is an integer.

Given, m & n are integers,

Using (1),
\sqrt{m} is an integer
then, (integer)^{(integer)} is Integer. Sufficient.

Using (2),
\sqrt{n} is an integer, or n is an integer.
lets say, m=3, n=9,
(\sqrt{m})^n=(\sqrt{3})^9 which is not an integer. Insufficient.

Thus, Answer is (A)

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Re: If m and n are positive integers, is root(m)^n an integer? [#permalink]

11 Jul 2012, 11:58

Bunuel wrote:

The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If m and n are positive integers, is (\sqrt{m})^n an integer?

(1) \sqrt{m} is an integer.
(2) \sqrt{n} is an integer.

Diagnostic Test
Question: 44
Page: 26
Difficulty: 650

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I thnk ..iTS A ... M and n both are integers

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Re: If m and n are positive integers, is root(m)^n an integer? [#permalink]

13 Jul 2012, 04:09

Re: If m and n are positive integers, is root(m)^n an integer? [#permalink] 13 Jul 2012, 04:09

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

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

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