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# Does (x^2 - y^2)^(1/2) = x + y?

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
Does (x^2 - y^2)^(1/2) = x + y? [#permalink]

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02 Oct 2017, 23:50
1
2
00:00

Difficulty:

55% (hard)

Question Stats:

46% (01:24) correct 54% (01:05) wrong based on 28 sessions

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Does $$\sqrt{x^2 - y^2} = x + y$$?

(1) x = y
(2) x = 0

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Joined: 08 Jul 2010
Posts: 2119
Location: India
GMAT: INSIGHT
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Re: Does (x^2 - y^2)^(1/2) = x + y? [#permalink]

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03 Oct 2017, 00:06
Bunuel wrote:
Does $$\sqrt{x^2 - y^2} = x + y$$?

(1) x = y
(2) x = 0

Question : Does $$\sqrt{x^2 - y^2} = x + y$$?

Squaring both sides we get

Does $$x^2 - y^2= (x + y)^2$$?

Question : Does (x+y)(x-y) = (x+y)(x+y)?

Question : Does (x+y)*(x-y - x - y) = 0?

Question : Does (x+y)*(-2y) = 0?

Statement 1: x = y

x = 0 answer to the question is YES
@x = any value other than 0, the answer to the question is NO

NOT SUFFICIENT

Statement 2: x = 0
No information about Y which may or may NOT be 0 hence
NOT SUFFICIENT

Combining the two statements

x = y = 0
i.e. (x+y)*(-2y) = 0 hence

SUFFICIENT

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Joined: 19 Sep 2016
Posts: 35
Re: Does (x^2 - y^2)^(1/2) = x + y? [#permalink]

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07 Oct 2017, 09:30
(X^2-y^2)=(x+y)^2, simplifying, (x-y)=(x+y), statement 1 would mean 0=y, so insufficient as y is unknown and lhs is not equal to rhs, statement 2 states x=0, so -y=y, so still not sufficient to state if lhs=rhs.
But st1+st2, we know that x=0,y=0, so lhs=rhs and answer is C. Hope this makes sense

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Re: Does (x^2 - y^2)^(1/2) = x + y?   [#permalink] 07 Oct 2017, 09:30
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