What is the value of x^2 - y^2 ? : GMAT Data Sufficiency (DS)
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# What is the value of x^2 - y^2 ?

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

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09 May 2012, 23:07
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What is the value of x^2 - y^2 ?

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

OG Quant Review - 2nd Edition - DS-Question 46

This is an official question. OA and answer explanation is available.
My query is for second condition. How can we mutiply both sides by (x+y) unless it is specified that x+y is not equal to zero or x not equal to -y. Should we assume that denominator is not equal to zero in such GMAT questions ?
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Re: DS- Multiplication by zero [#permalink]

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09 May 2012, 23:53
Statement 2 itself gives you this answer:

Since (x-y) = 1/(x+y)
(x-y) (x+y) = 1
For this to be true, (x-y) cannot equal 0 and likewise, (x+y) cannot equal 0
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Re: What is the value of x^2 - y^2 ? [#permalink]

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10 May 2012, 00:29
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.

As for your doubt: since x+y is in denominator it cannot equal to zero (because if it does equal zero then 1/(x+y) won't be defined).

Hope it's clear.
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Re: What is the value of x^2 - y^2 ?   [#permalink] 10 May 2012, 00:29
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