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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
Followers: 1

Kudos [?]: 121 [1] , given: 16

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

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21 Feb 2012, 14:45
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85% (hard)

Question Stats:

41% (02:26) correct 59% (01:52) wrong based on 131 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!
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 34416
Followers: 6248

Kudos [?]: 79371 [0], given: 10016

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.

Hope it's clear.
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Joined: 24 Apr 2013
Posts: 71
Location: United States
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Kudos [?]: 10 [0], given: 23

If x and y are positive integers [#permalink]

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20 Oct 2013, 06:06
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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Struggling: make or break attempt

Math Expert
Joined: 02 Sep 2009
Posts: 34416
Followers: 6248

Kudos [?]: 79371 [0], given: 10016

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

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20 Oct 2013, 06:12
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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Joined: 10 Apr 2013
Posts: 15
Location: United States (TX)
Concentration: Finance, Entrepreneurship
GMAT 1: 740 Q50 V41
GPA: 3.3
WE: Analyst (Investment Banking)
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Kudos [?]: 9 [0], given: 14

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

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07 Oct 2014, 09:24
Is there any algebra that can be done here or is it strictly a brute force problem?
Manager
Joined: 30 Mar 2013
Posts: 137
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Kudos [?]: 38 [0], given: 196

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.
Intern
Joined: 05 Jan 2015
Posts: 13
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Kudos [?]: 2 [0], given: 3

What do arrows mean in equations? [#permalink]

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20 Jan 2015, 17:06
One question stem reads as follows:

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

I don't really know what those arrows mean in the stem. Do I need to know? Or is it sort of just a made up function?
Math Expert
Joined: 02 Sep 2009
Posts: 34416
Followers: 6248

Kudos [?]: 79371 [0], given: 10016

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

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20 Jan 2015, 17:19
CoolKevin wrote:
One question stem reads as follows:

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

I don't really know what those arrows mean in the stem. Do I need to know? Or is it sort of just a made up function?

Thar's just formatting error. Check proper version of this question in the original post.
_________________
Re: If x and y are positive integers and   [#permalink] 20 Jan 2015, 17:19
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