If x and y are positive integers and : GMAT Problem Solving (PS)
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# If x and y are positive integers and

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Intern
Joined: 17 Jan 2012
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If x and y are positive integers and [#permalink]

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21 Feb 2012, 13:45
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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!
[Reveal] Spoiler: OA
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Re: If x and y are positive integers and [#permalink]

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21 Feb 2012, 14:09
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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.

Hope it's clear.
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If x and y are positive integers [#permalink]

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20 Oct 2013, 05:06
If x and y are positive integers and ←( √x →)^ y =y , then x−y could equal which of the following?
A)-2
B)-1
C)1
D)2
E)4
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Re: If x and y are positive integers [#permalink]

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20 Oct 2013, 05:12
SaraLotfy wrote:
If x and y are positive integers and ←( √x →)^ y =y , then x−y could equal which of the following?
A)-2
B)-1
C)1
D)2
E)4

Merging similar topics. Please refer to the solution above.
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Re: If x and y are positive integers and [#permalink]

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07 Oct 2014, 08:24
Is there any algebra that can be done here or is it strictly a brute force problem?
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Re: If x and y are positive integers and [#permalink]

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08 Oct 2014, 03:19
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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26 Nov 2016, 03:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x and y are positive integers and   [#permalink] 26 Nov 2016, 03:14
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