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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
What is the value of x^2 - y^2 ?  [#permalink]

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21 Jan 2014, 03:05
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5
00:00

Difficulty:

5% (low)

Question Stats:

86% (00:57) correct 14% (01:24) wrong based on 540 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

(1) x - y = y + 2
(2) x - y = 1/(x+y)

Data Sufficiency
Question: 46
Category: Algebra First- and second-degree equations
Page: 156
Difficulty: 600

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Re: What is the value of x^2 - y^2 ?  [#permalink]

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21 Jan 2014, 03:06
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SOLUTION

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

(1) x - y = y + 2 --> x=2y+2, so x^2-y^2=(y+2)^2-y^2 --> to get the value of this expression we need to know the value of y. Not sufficient.

(2) x - y = 1/(x+y) --> cross-multiply: (x-y)(x+y)=1 --> x^2-y^2=1. Sufficient.

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Re: What is the value of x^2 - y^2 ?  [#permalink]

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21 Jan 2014, 07:45
1
x^2-y^2 = (x-y)(x+y)

(1) x - y = y + 2
x^2-y^2 = (y + 2)(x+y) not sufficient

(2) x - y = 1/(x+y)
x^2-y^2 = [1/(x+y)](x+y) = 1 sufficient

Correct answer is (B)
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Re: What is the value of x^2 - y^2 ?  [#permalink]

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24 Jan 2014, 00:56
Bunuel wrote:
What is the value of x^2 - y^2 ?

(1) x - y = y + 2
(2) x - y = 1/(x+y)

x^2 - y^2 can we written as (x+y)(x-y), so question becomes what is the value of (x+y)(x-y)?

(1) x - y = y + 2 we have (x-y) no info about (x+y) insufficient.

(2) x - y = 1/(x+y) can we written as (x-y)(x+y)= 1 , just what we were looking for , Sufficient.

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Re: What is the value of x^2 - y^2 ?  [#permalink]

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11 Sep 2015, 01:54
st (1) x - y = y + 2, X-2y=2, insufficient

st (2) x - y = 1/(x+y), on rearranging it x^2-Y^2==1, sufficient

hence B
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Re: What is the value of x^2 - y^2 ?  [#permalink]

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10 Oct 2018, 21:34
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Re: What is the value of x^2 - y^2 ?   [#permalink] 10 Oct 2018, 21:34
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# What is the value of x^2 - y^2 ?

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