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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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SergeNew
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What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2 [#permalink] New post   02 Jan 2011, 14:08
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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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A
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Re: What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2 [#permalink] New post   02 Jan 2011, 14:22
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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.

Answer: A.

Hope it's clear.
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Re: What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2 [#permalink] New post   12 Nov 2017, 08:40
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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.

Answer: A
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Re: What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2 [#permalink] New post   02 Dec 2017, 01:27
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.

Hence the answer is A
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Re: What is the value of x^2 - y^2? (1) x + y = 0 (2) x - y = 2 [#permalink] New post   14 Jul 2022, 07:06
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The theory involved is the difference of a square.
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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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