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Re: If x and y are positive integers and [#permalink]

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21 Feb 2012, 15:09

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docabuzar wrote:

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

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

MGMAT 1 (Q.9) The explanation given is unclear to me. Can someone help!

Square \(\sqrt{x}^y = y\) --> \(x^y=y^2\). Now, use plug-in method: since both \(x\) and \(y\) are positive integers start from the lowest value:

If \(y=1\) then \(x^1=1^2\) --> \(x=1\) --> \(x-y=0\), 0 is not among answer choices (it's better to plug for y as it'll give the value of x right away);

If \(y=2\) then \(x^2=2^2\) --> \(x=2\) --> \(x-y=0\), 0 is not among answer choices;

If \(y=3\) then \(x^3=3^2\) --> \(x\neq{integer}\);

If \(y=4\) then \(x^4=4^2\) --> \(x=2\) --> \(x-y=-2\), we have answer choice A and since we cannot have two correct answers we can stop at this point.

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