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555-605 Level|   Algebra|            
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Bunuel
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steilbergauf
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Bunnuel, I have a hard time getting my approach clear on problems like that.

What made you rearrange statement (1) and not insert it in the q stem such as (2x)(x+y)?
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Bunnuel, I have a hard time getting my approach clear on problems like that.

What made you rearrange statement (1) and not insert it in the q stem such as (2x)(x+y)?

Seems natural to combine like terms by re-arranging and simplify \(x + y = 2x\) to get \(x - y = 0\) or \(x=y\). If you substitute it leads nowhere.
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GMAT Focus 1: 745 Q86 V90 DI85
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It's a good habit to combine like terms when possible to make sure you are getting what the equation is really telling you. If x appears on both sides of the equation, there is room to simplify!
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Hi, I am quite lost on this one...to get (1) x + y = 2x, why it breaks up to (x−y)(x+y)=0 and not (x−y)(x+y)=2x.
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Hi, I am quite lost on this one...to get (1) x + y = 2x, why it breaks up to (x−y)(x+y)=0 and not (x−y)(x+y)=2x.

x + y = 2x

Re-arrange: x - y = 0.
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What is the value of x^2 - y^2?

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

The goal is to find the unique value equal to x^2-y^2.

Statement 1) x+y = 2x

x+y=2x
x=y
x-y=0

x^2-y^2 = (x+y)(x-y)
(x+y)*0 =0

Sufficient.

Statement 2) x-y = 0

x^2-y^-2 =(x+y)*(x-y)

(x+y)*0 = 0

Sufficient.
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What is the value of x^2 - y^2?

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

Although the question is really simple, it is a little tricky if we do not see the implication of the statements

To find:
x^2 - y^2 = (x+y) (x-y)

Statement 1
x+y = 2x
(It is possible that the brain will want us to substitute the value of (x+y) in the equation and come up with a value in the pressure of time, however, had we solved the equation it becomes very obvious)
x = y

If both are equal then x^2 - Y^2 has to be zero... Statement 1 is sufficient

Statement 2 almost directly gives the relation x= y.. Sufficient

Answer is D
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\(x^2 – y^2\) = (x+y) (x-y).

From statement I alone, x+y = 2x.

Therefore, x – y = 0.
Since \(x^2 – y^2\) = (x+y) (x-y) and (x-y) = 0, \(x^2 – y^2\) = 0.
Statement I alone is sufficient. Answer options B, C and E can be eliminated.

From statement II alone, x – y= 0.

Therefore, \(x^2 – y^2\) = 0.
Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

Hope that helps!
Aravind BT
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