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If x and y are positive integers and

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Intern
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Joined: 17 Jan 2012
Posts: 41
GMAT 1: 610 Q43 V31
If x and y are positive integers and  [#permalink]

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New post 21 Feb 2012, 14:45
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10
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A
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  85% (hard)

Question Stats:

46% (01:52) correct 54% (02:15) wrong based on 240 sessions

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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!
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Joined: 02 Sep 2009
Posts: 58449
Re: If x and y are positive integers and  [#permalink]

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New post 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.

Answer: A.

Hope it's clear.
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Joined: 30 Mar 2013
Posts: 101
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Re: If x and y are positive integers and  [#permalink]

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New post 08 Oct 2014, 04:19
ok well square both the sides to get x^y = y^2.

Now to get option A as an answer, we can plug in x=2, and y=4.

we get 2^4= 4^2 (where the LHS = RHS) and therefore option A is correct.
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Re: If x and y are positive integers and  [#permalink]

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New post 03 Mar 2018, 05:25
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Re: If x and y are positive integers and   [#permalink] 03 Mar 2018, 05:25
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