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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? [#permalink] New post 09 Jul 2012, 03:56
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Re: If m and n are positive integers, is root(m)^n an integer? [#permalink] New post 09 Jul 2012, 03:56
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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] New post 09 Jul 2012, 04:27
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] New post 13 Jul 2012, 03:09
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If m and n are positive integers, is root(m)^n an integer? [#permalink] New post 17 Jul 2014, 19:49
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Re: If m and n are positive integers, is root(m)^n an integer?   [#permalink] 17 Jul 2014, 19:49
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