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E
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Difficulty:
45%
(medium)
Question Stats:
61% (01:46) correct
39%
(01:42)
wrong
based on 240
sessions
History
Date
Time
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Not Attempted Yet
If y does not equal 0. Does x = 0 ?
(1) x^2*y = x^3*y
(2) x^2/y = x^3*y
(1) x^2*y = x^3*y
(2) x^2/y = x^3*y
06 Jan 2011, 06:45
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Given: \(y\neq{0}\). Question does \(x=0\)?
(1) x^2*y=x^3*y --> as \(y\neq{0}\) we can reduce by \(y\) --> \(x^2=x^3\) --> \(x^2(x-1)=0\) --> either \(x=0\) or \(x=1\). Not sufficient.
(2) x^2/y=x^3*y --> \(x^2=x^3y^2\) --> \(x^2(xy^2-1)=0\) --> either \(x=0\) or \(xy^2=1\) (depending on \(y\) \(x\) can be any positive number). Not sufficient.
(1)+(2) Both \(x=0\) and \(x=1\) (in this case \(y=1\) or \(y=-1\)) satisfy the statements. Not sufficient.
Answer: E.
General Discussion
07 Sep 2011, 05:19
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Very clear explanation, Bunuel. Thanks!
Initially, I had answer A and realised my mistake after reading Bunuel's solution. My error came from the fact that I cross-multiplied and eliminated as below:
Given y does not equal to zero, does x=0?
Statement 1
x^2y = x^3y --> x^3=x^2 --> 0 = x^2(x-1)
So, x=0 or x=1
Insufficient.
Statement 2
x^2/y = x^3y --> 0 = x^2(xy^2-1)
So, x=0 or xy^2=1 (i.e. x is not zero)
Insufficient.
Statement 1 + 2
x^2(x-1) = x^2(xy^2-1)
x-1 = xy^2-1
x(1-y^2) = 0
So, x = 0 or x does not equals to zero (when y^2=1)
Insufficient.
Answer: E
Quote:
Very clear explanation, Bunuel. Thanks!
Initially, I had answer A and realised my mistake after reading Bunuel's solution. My error came from the fact that I cross-multiplied and eliminated as below:
Quote:
Given y does not equal to zero, does x=0?
Statement 1
x^2y = x^3y --> x^3=x^2 --> 0 = x^2(x-1)
So, x=0 or x=1
Insufficient.
Statement 2
x^2/y = x^3y --> 0 = x^2(xy^2-1)
So, x=0 or xy^2=1 (i.e. x is not zero)
Insufficient.
Statement 1 + 2
x^2(x-1) = x^2(xy^2-1)
x-1 = xy^2-1
x(1-y^2) = 0
So, x = 0 or x does not equals to zero (when y^2=1)
Insufficient.
Answer: E
