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# What is the value of x^2 – y^2 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
What is the value of x^2 – y^2 ? [#permalink]

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11 Sep 2017, 00:28
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Difficulty:

35% (medium)

Question Stats:

77% (01:19) correct 23% (01:09) wrong based on 35 sessions

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What is the value of x^2 – y^2 ?

(1) $$2xy = x + y$$

(2) $$x^2y – xy^2 = 1$$

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Joined: 02 Nov 2015
Posts: 171
GMAT 1: 640 Q49 V29
Re: What is the value of x^2 – y^2 ? [#permalink]

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11 Sep 2017, 01:08
It's a C ...
Statement 1: not sufficient. We don't know the value of x-y.
Statement 2: not sufficient. We don't know the value of X+y.

Statement 1 and 2. We have the individual values of X+y and x-y.

It gives a value of 1.

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Intern
Joined: 21 Nov 2016
Posts: 45
Re: What is the value of x^2 – y^2 ? [#permalink]

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12 Sep 2017, 09:31
Stem : x^2 - y^2 = (x+y)(x-y)
S1 : 2xy = x+y Not Sufficient
S2 : x^2y-xy^2 = 1 ---> xy(x-y) = 1.
So both, xy = (x-y) = 1. Again Not sufficient.
S1 + S2 = as xy = 1, x+y = 2xy = 2(1) = 2 ---> x+y = 2
and x-y = 1. So (x+y)(x-y) = 2*1 = 2.
Intern
Joined: 04 Nov 2015
Posts: 33
Re: What is the value of x^2 – y^2 ? [#permalink]

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12 Sep 2017, 10:04
reachskishore wrote:
Stem : x^2 - y^2 = (x+y)(x-y)
S1 : 2xy = x+y Not Sufficient
S2 : x^2y-xy^2 = 1 ---> xy(x-y) = 1.
So both, xy = (x-y) = 1. Again Not sufficient.
S1 + S2 = as xy = 1, x+y = 2xy = 2(1) = 2 ---> x+y = 2
and x-y = 1. So (x+y)(x-y) = 2*1 = 2.

From statement 2: xy(x-y) = 1.Then why can't be xy = 2 and x-y be 1/2 or vice versa or any other combination (such as 1/3 and 3 etc. ) so that there product is 1.
I suppose the answer should be E.
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Joined: 21 Nov 2016
Posts: 45
Re: What is the value of x^2 – y^2 ? [#permalink]

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13 Sep 2017, 00:30
sandeep211986 wrote:
reachskishore wrote:
Stem : x^2 - y^2 = (x+y)(x-y)
S1 : 2xy = x+y Not Sufficient
S2 : x^2y-xy^2 = 1 ---> xy(x-y) = 1.
So both, xy = (x-y) = 1. Again Not sufficient.
S1 + S2 = as xy = 1, x+y = 2xy = 2(1) = 2 ---> x+y = 2
and x-y = 1. So (x+y)(x-y) = 2*1 = 2.

From statement 2: xy(x-y) = 1.Then why can't be xy = 2 and x-y be 1/2 or vice versa or any other combination (such as 1/3 and 3 etc. ) so that there product is 1.
I suppose the answer should be E.

Hi Sandeep,

Nice catch there. I never thought about that scenario. But, on a second note, the answer remains same as per your data.

We have xy(x-y) = 1. So, going by your data. Say xy = a and (x-y) = 1/a
so (x+y) = 2xy = 2a.
Now (x+y)(x-y_ = 2 * a * 1/a ---> a and 1/a cancels out and 2 remains.

Alternatively if you consider xy = 1/a and (x-y) = a , then too, 2 remains to be the answer.
Re: What is the value of x^2 – y^2 ?   [#permalink] 13 Sep 2017, 00:30
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