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# If x and y are positive integers and

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

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21 Feb 2012, 14:45
2
10
00:00

Difficulty:

85% (hard)

Question Stats:

46% (01:51) correct 54% (02:16) wrong based on 247 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!
Math Expert
Joined: 02 Sep 2009
Posts: 60569
Re: If x and y are positive integers and  [#permalink]

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21 Feb 2012, 15:09
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2
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.

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

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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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Joined: 09 Sep 2013
Posts: 13994
Re: If x and y are positive integers and  [#permalink]

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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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