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DS- Multiplication by zero

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by redpearl » Wed May 09, 2012 11:10 pm
OG Quant Review - 2nd Edition - DS-Question 46

What is the value of x^2 - y^2 ? (x square minus y square)

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

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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Source: — Data Sufficiency |
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by aneesh.kg » Wed May 09, 2012 11:23 pm
Great doubt, because that would've escaped most people's notice.

Firstly, When a certain DS statement states something, it is considered as something that holds true.
Statement (1) tells us that LHS = RHS. (x - y) = 1/(x + y) is true, undoubtedly.
When that happens, you can multiply with anything on both sides (even a zero) and it will do no harm to the equation.
Had the question been on finding if LHS was indeed equal to RHS, we could not have multiplied with anything on both sides without knowing for sure that it is not equal to zero.

So, you do not have to worry about multiplying with a zero on both sides of this equation.

Secondly, yes, if the denominator is zero then the fraction is undefined. So, if such a fraction is stated in a GMAT problem, the fraction cannot be an undefined value and thus the denominator cannot be zero.

I would like to see if other experts concur with me on this.
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by GmatKiss » Thu May 10, 2012 1:08 am
IMO: C what is OA?
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