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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?

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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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New post 02 Oct 2017, 04:42
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

39% (00:47) correct 61% (01:13) wrong based on 29 sessions

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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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New post Updated on: 05 Oct 2017, 06:29
Bunuel wrote:
If x is an integer, is \(\sqrt{3x - y} = \sqrt{2x - 2y}\) ?

(1) x^2 = y
(2) x^3 = y


\(\sqrt{3x - y} = \sqrt{2x - 2y}\), square both sides to get

\(3x-y=2x-2y\) or the question becomes Is \(x=-y\) ?

Statement 1: implies that \(x=\sqrt{y}\) or \(-\sqrt{y}\). \(x\) can be equal to \(-y\) in one situation; if \(y=1\) and \(x=-\sqrt{y}\) but if \(y\) has any other value then \(x\) will not be equal to \(-y\). hence no unique value. Insufficient

Statement 2: \(x=y^\frac{1}{3}\).
If \(x=1, y=1\), then \(x\) is not equal to \(-y\)
but if \(x=0, y=0\), then \(x=-y\) Hence. Sufficient

Combining 1 & 2, there is no unique answer. Hence Insufficient

IMO E

Originally posted by niks18 on 03 Oct 2017, 09:25.
Last edited by niks18 on 05 Oct 2017, 06:29, edited 1 time in total.
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Re: If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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New post 05 Oct 2017, 05:22
Bunuel wrote:
If x is an integer, is \(\sqrt{3x - y} = \sqrt{2x - 2y}\) ?

(1) x^2 = y
(2) x^3 = y


Question : is \(\sqrt{3x - y} = \sqrt{2x - 2y}\) ?
Squaring both sides
Question : is 3x - y = 2x - 2y?
Question : x = -y ?


Statement 1: x^2 = y
@x = 1, y = 1 Answer to the question is NO
@x = -1, y = 1 Answer to the question is YES
NOT SUFFICIENT

Statement 2: x^3 = y
@x = 1, y = 1 Answer to the question is NO
@x = 0, y = 0 Answer to the question is YES i.e. x = -y
NOT SUFFICIENT

Combining the two statements
@x = 1, y = 1 Answer to the question is NO
@x = 0, y = 0 Answer to the question is YES i.e. x = -y
NOT SUFFICIENT

Answer: Option E
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Re: If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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New post 07 Oct 2017, 10:14
After squaring the question becomes
Is X = -Y
St 1
X^2 = Y
For x = 0 Yes
For x = 1 No
Hence insufficient.
St 2
X^3 = Y
For X = 0 Yes and for any other value No
Insufficient
Combining 1 and 2
Same problem if we consider values as 0 And 1
Hence E

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Re: If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ? &nbs [#permalink] 07 Oct 2017, 10:14
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