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# If x<=y and y = (x^2 - y^2)(x-y), then what is the value of

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If x<=y and y = (x^2 - y^2)(x-y), then what is the value of [#permalink]

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12 Oct 2008, 13:38
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If $$x\neq{y}$$ and $$y = \frac{x^2 - y^2}{x-y}$$, then what is the value of $$y$$ ?

(1) $$x+y-3=0$$
(2) $$x(y-3)=0$$

Source: GMAT Club Tests - hardest GMAT questions

Last edited by Bunuel on 07 Nov 2013, 02:13, edited 2 times in total.
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Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: If y = \frac {x^2 - y^2}{x-y} ( x \ne y ), then what is the [#permalink]

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09 Nov 2012, 06:41
icandy wrote:
If $$y = \frac {x^2 - y^2}{x-y}$$ ( $$x \ne y$$ ), then what is the value of $$y$$ ?

1. $$x + y = 3$$
2. $$x - y = 2$$

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Given is y=x+y meaning x=0

(1) says y=3 and (2) says y=-2

Given answer is D.

Isn't it one of the cardinal rules of GMAT that (1) and (2) do not contradict each other? Am I misinterpreting some thing here? The way I understood is if D were to be the answer for any DS Q, we should get the same value. If we are not getting such same answer, either we are doing some thing wrong or the Q itself is wrong.

Thoughts Fellas.

BELOW IS REVISED QUESTION OF THIS QUESTION:

If $$x\neq{y}$$ and $$y = \frac{x^2 - y^2}{x-y}$$, then what is the value of $$y$$ ?

$$y = \frac {x^2 - y^2}{x-y}$$ --> $$y = \frac {(x - y)(x+y)}{x-y}$$ --> $$y=x+y$$ --> $$x=0$$.

(1) $$x+y-3=0$$ --> $$y=3$$. Sufficient.
(2) $$x(y-3)=0$$ --> since $$x=0$$ then $$y$$ can take ANY value. Not sufficient.

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Re: If y = \frac {x^2 - y^2}{x-y} ( x \ne y ), then what is the [#permalink]

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09 Nov 2012, 10:43
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Since both the options are independently sufficient to answer the question. (Value of y)

Although the value of y is not unique, if we get a solution for y it makes the option valid.
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Joined: 12 Dec 2012
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Concentration: Leadership, Social Entrepreneurship
GMAT 2: 660 Q48 V33
GMAT 3: 740 Q49 V41
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Re: If x<=y and y = (x^2 - y^2)(x-y), then what is the value of [#permalink]

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06 Nov 2013, 08:44
The OA to this question should be edited. I also got A but it said my answer was incorrect. Only realized once I read Bunuel's explanation.

OA still shows D.
Manager
Joined: 11 Jan 2011
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Re: If x<=y and y = (x^2 - y^2)(x-y), then what is the value of [#permalink]

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06 Nov 2013, 10:15

Given: $y = \frac {x^2 - y^2}{x-y}$ = $$\frac{(x+y)(x-y)}{(x-y)}$$, which simplifies to y = x + y

Asked: What does y equal but is actually asking for x + y

1) Given: x + y = 3 --> insta-sufficient
2) Given: x - y = 2 --> insufficient since it tells us nothing about x + y

Therefore, A.

I'm really not sure why the OA says D....
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Joined: 18 May 2013
Posts: 41
Concentration: Real Estate, Finance
GPA: 3.73
WE: Analyst (Real Estate)
Re: If x<=y and y = (x^2 - y^2)(x-y), then what is the value of [#permalink]

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06 Nov 2013, 17:41
Answer should be A.
Intern
Joined: 04 Aug 2013
Posts: 4
Re: If x<=y and y = (x^2 - y^2)(x-y), then what is the value of [#permalink]

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06 Nov 2013, 22:10
I think the answer is D

From question y = x+y
1) x+y-3=0 ==> Since y = x+y ==> y-3=0 and y=3
2) x-y = 2 ==> x-(x+y) = 2 ==> x-x-y = 2 ==> -y=2 and y = 2

How X(y-3)=0 is obtained ?

Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: If x<=y and y = (x^2 - y^2)(x-y), then what is the value of [#permalink]

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07 Nov 2013, 02:15
mhknair wrote:
I think the answer is D

From question y = x+y
1) x+y-3=0 ==> Since y = x+y ==> y-3=0 and y=3
2) x-y = 2 ==> x-(x+y) = 2 ==> x-x-y = 2 ==> -y=2 and y = 2

How X(y-3)=0 is obtained ?

The revised version of this question is here: if-x-y-and-y-x-2-y-2-x-y-then-what-is-the-value-of-71567.html#p1141701 and the OA is A.
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Re: If x<=y and y = (x^2 - y^2)(x-y), then what is the value of   [#permalink] 07 Nov 2013, 02:15
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# If x<=y and y = (x^2 - y^2)(x-y), then what is the value of

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