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

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Intern
Joined: 02 Jul 2013
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What is the value of x^2 - y^2?  [#permalink]

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20 Oct 2013, 06:32
4
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54
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Difficulty:

45% (medium)

Question Stats:

54% (00:50) correct 46% (00:41) wrong based on 854 sessions

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

(1) x + y = 2x
(2) x - y = 0
Math Expert
Joined: 02 Sep 2009
Posts: 59721
Re: What is the value of x^2 - y^2?  [#permalink]

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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.

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Re: What is the value of x^2 - y^2?  [#permalink]

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28 May 2014, 12:37
4
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]

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16 Jul 2017, 11:37
2
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]

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19 Jul 2016, 09:16
1
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]

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27 Aug 2018, 00:04
1
anushilaghosh wrote:
Ix x < 0?

1. |x-5| = 7x+2
2. |x+5| = |4x+5|

Hi anushilaghosh,
I would request to post the question in DS forum.

You may go through the below links that will guide you:
https://gmatclub.com/forum/how-to-make- ... 47089.html
https://gmatclub.com/forum/rules-for-po ... l#p1092822
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Re: What is the value of x^2 - y^2?  [#permalink]

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04 May 2019, 17:49
1
nuvz wrote:
For Statement I, I understand why x=y, but when you just subtract 2x from each side you get -x+y=0 or y-x=0, which is a different equation from the prompt's difference of squares equation, leading me to believe it is insufficient. Can someone help explain?

Hi nuvz,
You can always write y-x=0 as -(x-y)=0 or, x-y=0.
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Re: What is the value of x^2 - y^2?  [#permalink]

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27 May 2014, 09:11
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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Re: What is the value of x^2 - y^2?  [#permalink]

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28 May 2014, 04:59
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 re-arrange 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]

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28 May 2014, 12:48
DmitryFarber wrote:
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!

Thank you. That makes sense!

Cheers...
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Re: What is the value of x^2 - y^2?  [#permalink]

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29 May 2014, 03:26
1
(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

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Re: What is the value of x^2 - y^2?  [#permalink]

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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]

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20 Aug 2016, 17:27
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)?

That's exactly what I did and got this wrong.
I incorrectly solved this within 20 seconds: 10 seconds on each stem. I should've spent more time since it was way too easy.
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Re: What is the value of x^2 - y^2?  [#permalink]

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15 Jun 2017, 09:33
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)?

well you just have to recognise that we are dealing with a differences of squares, thats it.

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

Even if you get statement one wrong, statement 2 will safe your ass

For instance:

(1) x+y=2x
lets say insufficient

(2) x-y=0

now you should recognise where this is going,

so lets go back to

(1) x+y=2x

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

--> sufficient
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Re: What is the value of x^2 - y^2?  [#permalink]

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26 Aug 2018, 23:43
Ix x < 0?

1. |x-5| = 7x+2
2. |x+5| = |4x+5|
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Re: What is the value of x^2 - y^2?  [#permalink]

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07 Feb 2019, 08:06
bulletpoint wrote:
What is the value of x^2 - y^2?

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

Overthinking marks such questions incorrect

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

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

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

D
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What is the value of x^2 - y^2?  [#permalink]

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07 Feb 2019, 08:13
anushilaghosh wrote:
Ix x < 0?

1. |x-5| = 7x+2
2. |x+5| = |4x+5|

This question is discussed here: https://gmatclub.com/forum/is-x-0-1-x-5 ... 16394.html It's flawed.
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Re: What is the value of x^2 - y^2?  [#permalink]

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04 May 2019, 14:10
For Statement I, I understand why x=y, but when you just subtract 2x from each side you get -x+y=0 or y-x=0, which is a different equation from the prompt's difference of squares equation, leading me to believe it is insufficient. Can someone help explain?
Re: What is the value of x^2 - y^2?   [#permalink] 04 May 2019, 14:10
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