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# What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2

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Intern
Joined: 02 Jan 2011
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What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2 [#permalink]

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02 Jan 2011, 13:08
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What is the value of x^2 - y^2?

(1) x + y = 0
(2) x - y = 2
[Reveal] Spoiler: OA

Kudos [?]: 31 [1], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135874 [1], given: 12715

Re: What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2 [#permalink]

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02 Jan 2011, 13:22
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SergeNew wrote:
Hello Folks,

This question is from the review published in 2010. Could anyone please explain to me why the correct answer is A instead of D?

What is the value of x^2-y^2?

1) x+y=0
2) x-y=2

A) Statement (1) Alone is Sufficient but Statement (2) Alone is not sufficient.
D) Each statement Alone is sufficient.

Thank you so much and Happy new decade to everyone.

Serge.

Welcome to Gmat Club Serge!

What is the value of x^2-y^2?

Question: $$x^2-y^2=(x-y)*(x+y)=?$$

(1) x+y=0 --> as one of the multiples is zero then $$(x-y)*(x+y)$$ must equal to zero. Sufficient.

(2) x-y=2 --> we can not get a single numerical value of x^2-y^2 from this statement. For example: if $$x=2$$ and $$y=0$$ then the answer will be 4 but if $$x=1$$ and $$y=-1$$ then the answer will be 0. Not sufficient.

Hope it's clear.
_________________

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Target Test Prep Representative
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Re: What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2 [#permalink]

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12 Nov 2017, 07:40
SergeNew wrote:
What is the value of x^2-y^2?

(1) x+y=0
(2) x-y=2 .

We need to determine the value of x^2 - y^2. Notice that x^2 - y^2 = (x + y)(x - y).

Statement One Alone:

x + y = 0

Since x + y = 0, regardless of the value of x - y, we have x^2 - y^2 = (x + y)(x - y) = (0)(x - y) = 0. Statement one alone is sufficient to answer the question.

Statement Two Alone:

x - y = 2

We do not have enough information to determine a definitive value for x^2 - y^2. For example, if x = 4 and y = 2, then x^2 - y^2 = 16 - 4 = 12; however, if x = 3 and y = 1, then x^2 - y^2 = 9 - 1 = 8. Statement two alone is not sufficient to answer the question.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

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Intern
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Re: What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2 [#permalink]

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02 Dec 2017, 00:27
x^2 - y^2 = (x-y)*(x+y)
(1) x+y = 0 => x^2 - y^2 = 0 regardless of the value of (x-y)
(2) x-y = 2. We don't know anything about x+y => insufficient.

Kudos [?]: 21 [0], given: 13

Re: What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2   [#permalink] 02 Dec 2017, 00:27
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