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Schools: LBS MIF '15
Posts: 16
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What is the value of x^2 - y^2?
(1) x + y = 2x
(2) x - y = 0
(1) x + y = 2x
(2) x - y = 0
Solving this question helps.
Taking a timed set of similar questions in
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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What is the value of x^2 - y^2?
\(x^2 - y^2=(x-y)(x+y)\)
(1) x + y = 2x --> re-arrange: \(x-y=0\) --> \((x-y)(x+y)=0\). Sufficient.
(2) x - y = 0 --> \(x-y=0\) --> \((x-y)(x+y)=0\). Sufficient.
Answer: D.
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\(x^2 - y^2=(x-y)(x+y)\)
(1) x + y = 2x --> re-arrange: \(x-y=0\) --> \((x-y)(x+y)=0\). Sufficient.
(2) x - y = 0 --> \(x-y=0\) --> \((x-y)(x+y)=0\). Sufficient.
Answer: D.
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Posts: 7
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)?
What made you rearrange statement (1) and not insert it in the q stem such as (2x)(x+y)?
steilbergauf
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 
Posts: 3,003
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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Manhattan Prep Instructor from 2009-2025
(1) x+y=2x
We know that x+x=2x, so it is obvious that x=y and x^2-y^2=0
SUFFICIENT
(2) x-y=0
Rearranging this, we get x=y, so again x^2-y^2=0
SUFFICIENT
Answer is D
Posted from my mobile device
We know that x+x=2x, so it is obvious that x=y and x^2-y^2=0
SUFFICIENT
(2) x-y=0
Rearranging this, we get x=y, so again x^2-y^2=0
SUFFICIENT
Answer is D
Posted from my mobile device
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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GMAT loosers are born not made !!!
sony1000
x + y = 2x
Re-arrange: x - y = 0.
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mbaapp1234
Joined: 23 Dec 2013
Last visit: 05 Jul 2019
Posts: 81
Location: United States (CA)
GMAT 1: 710 Q45 V41
GMAT 2: 760 Q49 V44
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GMAT 2: 760 Q49 V44
Posts: 81
bulletpoint
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.
Posts: 18
bulletpoint
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
Posts: 4,849
\(x^2 – y^2\) = (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
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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