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08 Nov 2022, 02:30
Kudos
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B
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Difficulty:
35%
(medium)
Question Stats:
66% (00:53) correct
34%
(01:17)
wrong
based on 58
sessions
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Not Attempted Yet
If \(xy ≠ 0\), is \(\frac{x^3y^2}{x^2y^3}=1\)?
(1) \(\frac{x^2}{y^2} =1\)
(2) \(\frac{x^3}{y^3} =1\)
(1) \(\frac{x^2}{y^2} =1\)
(2) \(\frac{x^3}{y^3} =1\)
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
08 Nov 2022, 03:34
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Bunuel
\(\frac{x^3y^2}{x^2y^3}=1\)
\(\frac{x^2y^2*x}{x^2y^2*y}=1\)
\(\frac{x}{y}=1\)
So, we are looking for: Is x=y?
(1) \(\frac{x^2}{y^2} =1\)
Taking square root, we get either x=y or x=-y
Insufficient
(2) \(\frac{x^3}{y^3} =1\)
Taking cube root, we get x=y
Sufficient
B
08 Nov 2022, 05:10
Kudos
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Bunuel
Question
\(\frac{x^3y^2}{x^2y^3}=1\)
\(\frac{x^2y^2(x)}{x^2y^2(y)}=1\)
\(\frac{ x }{ y }=1\)
x = y
Basically the question is asking us if x = y ?
Statement 1
\(\frac{x^2}{y^2} =1\)
If we take square root on both sides
\(\frac{|x| }{ |y|} =1\)
So the magnitude of x and y is same, however the signs could be different.
Hence this statement is not sufficient and we can eliminate A and D.
Statement 2
\(\frac{x^3}{y^3} =1\)
If \(x^3 = y^3\), then x and y should have the same magnitude and should have the same same sign.
Hence we can say, x = y.
This statement is sufficient.
Option B
