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

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What is the value of x^2 - y^2? [#permalink] New post   20 Oct 2013, 06:32
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What is the value of x^2 - y^2?

(1) x + y = 2x
(2) x - y = 0
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D
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Bunuel
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Re: What is the value of x^2 - y^2? [#permalink] New post   20 Oct 2013, 06:36
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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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Re: What is the value of x^2 - y^2? [#permalink] New post   29 May 2014, 03:26
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(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

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Re: What is the value of x^2 - y^2? [#permalink] New post   27 May 2014, 09:11
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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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What is the value of x^2 - y^2? [#permalink] New post   28 May 2014, 04:59
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steilbergauf wrote:
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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Re: What is the value of x^2 - y^2? [#permalink] New post   28 May 2014, 12:37
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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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Re: What is the value of x^2 - y^2? [#permalink] New post   19 Jul 2016, 09:13
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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Re: What is the value of x^2 - y^2? [#permalink] New post   19 Jul 2016, 09:16
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sony1000 wrote:
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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Re: What is the value of x^2 - y^2? [#permalink] New post   16 Jul 2017, 11:37
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bulletpoint wrote:
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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Re: What is the value of x^2 - y^2? [#permalink] New post   25 May 2020, 15:04
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bulletpoint wrote:
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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Re: What is the value of x^2 - y^2? [#permalink] New post   29 Jun 2021, 10:12
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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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Re: What is the value of x^2 - y^2? [#permalink] New post   16 Dec 2022, 17:38
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CrackverbalGMAT wrote:
\(x^2 – y^2\) = (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


CrackverbalGMAT

When I was first thinking of solving this problem, I tried squaring both sides of statement 2 --> so (x + y)^2=36 to see if I could manipulate the equations together when combined. This turned out to be a waste of time. So, is there any way up front to know that you cannot do this? I realize that testing numbers was a good strategy, but I was curious if you can tell up front that squaring statement 2/then trying to use it with statement 1 will not work? Thank you :)
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Re: What is the value of x^2 - y^2? [#permalink] New post   21 Dec 2023, 10:21
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