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# number theory good question

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Manager
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 247
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
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27 Mar 2011, 00:04
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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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Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
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Re: number theory good question [#permalink]

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27 Mar 2011, 00:19
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] 27 Mar 2011, 00:19
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