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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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02 Oct 2017, 04:42
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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 $$\sqrt{3x - y} = \sqrt{2x - 2y}$$ ?

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

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

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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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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

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

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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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