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number theory good question

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number theory good question [#permalink] New post 26 Mar 2011, 23:04
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If x and y are positive integers and (\sqrt{x})^y=y , then x-y could equal which of the following?

A -2
B -1
C 1
D 2
E 4

OA
[Reveal] Spoiler:
A


can anyone provide a way to get the answer through theory
:) :)
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Re: number theory good question [#permalink] New post 26 Mar 2011, 23:19
Yeah it is. 4^2= 2^4 Hence x- y = 2-4 =-2. This is intuitive.

Now lets look at algebra.

The stem can be written in this form

x^(y/2) = y
Squaring both sides

x^y =y^2

There are two possibilities. 2^2 = 2^2. Hence x-y = 0 or 2^4= 4^2 Hence x -y = 2-4 = -2.

Warlock007 wrote:
If x and y are positive integers and (\sqrt{x})^y=y , then x-y could equal which of the following?

A -2
B -1
C 1
D 2
E 4

OA
[Reveal] Spoiler:
A


can anyone provide a way to get the answer through theory
:) :)
Re: number theory good question   [#permalink] 26 Mar 2011, 23:19
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