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Difficulty:
75%
(hard)
Question Stats:
56% (02:01) correct
44%
(02:09)
wrong
based on 905
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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!
A. -2
B. -1
C. 1
D. 2
E. 4
MGMAT 1 (Q.9)
The explanation given is unclear to me. Can someone help!
docabuzar
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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General Discussion
usre123
Joined: 30 Mar 2013
Last visit: 25 Nov 2022
Posts: 73
Location: United States
Schools: Alberta '23 (WL)
GMAT 1: 760 Q50 V44
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.
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.
HarshavardhanR
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Kinshook
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Last visit: 09 Sep 2026
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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:
\(\sqrt{x}^y = y\)
\(x^y = y^2\)
If y=0; x=0; x-y=0; No answer choice
If y=1; x=1; x-y=0; No answer choice
If y=2; x=2 ; x-y=0; No answer choice
If y=3; No integer value of x
If y=4; x=2; x- y = - 2
IMO A
\(\sqrt{x}^y = y\)
\(x^y = y^2\)
If y=0; x=0; x-y=0; No answer choice
If y=1; x=1; x-y=0; No answer choice
If y=2; x=2 ; x-y=0; No answer choice
If y=3; No integer value of x
If y=4; x=2; x- y = - 2
IMO A
ablatt4
Joined: 18 Dec 2024
Last visit: 24 Sep 2025
Posts: 87
Location: United States (FL)
Concentration: Finance
Schools: Duke '26 Darden '26 Johnson '26 UNC '26
Schools: Duke '26 Darden '26 Johnson '26 UNC '26
Posts: 87
Sqaure both sides and get x^y=y^2
pick a set value for x (would recommend 2) and then plug answer for y to try each of the possible answers
2^4 = 4^2
A
pick a set value for x (would recommend 2) and then plug answer for y to try each of the possible answers
2^4 = 4^2
A
docabuzar
Take Y value as 1,2,3,4 and u will find out for y=4 , you will have x=2 and x-y=-2 which makes (a) correct answer
docabuzar
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