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If x and y are positive integers and

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If x and y are positive integers and [#permalink] New post 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] New post 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.

Answer: A.

Hope it's clear.
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If x and y are positive integers [#permalink] New post 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] New post 20 Oct 2013, 05:12
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Re: If x and y are positive integers and [#permalink] New post 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] New post 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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What do arrows mean in equations? [#permalink] New post 20 Jan 2015, 16:06
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?
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Re: If x and y are positive integers and [#permalink] New post 20 Jan 2015, 16:19
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If x and y are positive integers and   [#permalink] 20 Jan 2015, 16:19
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