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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   35% (medium)

Question Stats: 66% (01:12) correct 34% (01:35) wrong based on 174 sessions

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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) $$x(y-3)=0$$

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Math Expert V
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Official Solution:

Given $$y = \frac{x^2 - y^2}{x-y}$$. Simplify: $$y = \frac {(x - y)(x+y)}{x-y}$$. Reduce by x-y: $$y=x+y$$. So, we have that $$x=0$$.

(1) $$x+y-3=0$$. Since $$x=0$$, then $$y=3$$. Sufficient.

(2) $$x(y-3)=0$$. Since $$x=0$$, then $$y$$ can take ANY value. Not sufficient.

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If x≠yx≠y and y=x2−y2x−yy=x2−y2x−y, then what is the value of yy?
(1) x+y−3=0x+y−3=0
(2) x(y−3)=0

I am not so sure for statement 2.
If x(y−3)=0
They x=0 or y=3
If x=0, they y=0. As per question If x≠y, so y cannot be 0.
Not sure whats wrong with my logic.
Any expert can explain.
ThankS
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Given y=x2−y2x−yy=x2−y2x−y. Simplify: y=(x−y)(x+y)x−yy=(x−y)(x+y)x−y. Reduce by x-y: y=x+yy=x+y. So, we have that x=0x=0.

(1) x+y−3=0x+y−3=0. Since x=0x=0, then y=3y=3. Sufficient.

(2) x(y−3)=0x(y−3)=0. Since x=0x=0, then y can take ANY value. Not sufficient.

regarding point two .
i did not understand why Y can take any value ? .
(y-3) has to be equal to zero ?
Math Expert V
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ashimd wrote:
Given y=x2−y2x−yy=x2−y2x−y. Simplify: y=(x−y)(x+y)x−yy=(x−y)(x+y)x−y. Reduce by x-y: y=x+yy=x+y. So, we have that x=0x=0.

(1) x+y−3=0x+y−3=0. Since x=0x=0, then y=3y=3. Sufficient.

(2) x(y−3)=0x(y−3)=0. Since x=0x=0, then y can take ANY value. Not sufficient.

regarding point two .
i did not understand why Y can take any value ? .
(y-3) has to be equal to zero ?

Hi statement 2 says x(y-3)=0..
If x=0, y-3 can be anything including 0 because 0*(y-3) will always be 0 irrespective of value of y-3..
But if x is Not EQUAL to 0, y-3 has to be 0...
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This is a great question!

I chose D, because my approach for the 2) was

=X(Y-3)=0
= Xy-3x = 0
= xy = 3x
y=3

But I found why I was wrong.
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I did exactly the same way... hanamana

=X(Y-3)=0
= Xy-3x = 0
= xy = 3x
y=3

Is it because we know from stem that X = 0 and 0/0 is undefined ?

But its not explicitly given in the question stem ?

can you me your opinion on this ? and Bunuel chetan2u Sirs ?
Math Expert V
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hero_with_1000_faces wrote:
I did exactly the same way... hanamana

=X(Y-3)=0
= Xy-3x = 0
= xy = 3x
y=3

Is it because we know from stem that X = 0 and 0/0 is undefined ?

But its not explicitly given in the question stem ?

can you me your opinion on this ? and Bunuel chetan2u Sirs ?

From the stem (after we simplified given equation $$y = \frac{x^2 - y^2}{x-y}$$) we got that x = 0. Since we cannot divide by 0, then you cannot divide xy = 3x by x to get y = 3. Basically for (2) we have that 0(y - 3) = 0. Now, 0(y - 3) is 0 regardless of the value of y.
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I think this is a poor-quality question and I don't agree with the explanation. For statement 2, if you know one of the values in an equation, you substitute and find the other value. (Basic of GMAT math). this explanation seems to violate that
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Bunuel wrote:
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) $$x(y-3)=0$$

y = x-y * x+y / x-y

y = x + y

from this we can say x =0 but y can be any value, integer ,fraction or a number

(1) $$x+y-3=0$$
From here we get a definite value as y = 3
Sufficient

(2) $$x(y-3)=0$$[/quote]
Now, i didn't realize this initially

0 * (y-3) = 0

y can be any value > 3

3.1, 6 , 9, these values will satisfy the statement

But will give multiple values for the question what is the value of y

A

NEVER assume things.
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Math Expert V
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itsrahulmohan wrote:
I think this is a poor-quality question and I don't agree with the explanation. For statement 2, if you know one of the values in an equation, you substitute and find the other value. (Basic of GMAT math). this explanation seems to violate that

Have you read this?
(2) $$x(y-3)=0$$. Since $$x=0$$, then $$y$$ can take ANY value. Not sufficient.

We want of find the value of y. Can you?
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Hi for statement 2,
We do know x = 0, but..
Divide both sides by x
x(y−3)=0
=> x/x * (y-3) = 0/x
=> y-3 = 0
y = 3

Please tell me why we can't use this. Because x is zero from the stem, does it mean this method is invalid?
Math Expert V
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Boltions wrote:
Hi for statement 2,
We do know x = 0, but..
Divide both sides by x
x(y−3)=0
=> x/x * (y-3) = 0/x
=> y-3 = 0
y = 3

Please tell me why we can't use this. Because x is zero from the stem, does it mean this method is invalid?

We cannot divide by 0.

(2) $$x(y-3)=0$$. Since $$x=0$$, then $$y$$ can take ANY value. Not sufficient.

Basically for (2) we have that 0(y - 3) = 0. Now, 0(y - 3) is 0 regardless of the value of y.
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Thank you very much Re: M28-03   [#permalink] 11 Jul 2019, 17:59
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