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Intern  Joined: 02 Jul 2013
Posts: 18
Schools: LBS MIF '15
What is the value of x^2 - y^2?  [#permalink]

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54 00:00

Difficulty:   45% (medium)

Question Stats: 54% (00:50) correct 46% (00:41) wrong based on 848 sessions

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

(1) x + y = 2x
(2) x - y = 0
Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Re: What is the value of x^2 - y^2?  [#permalink]

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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.

##### General Discussion
Intern  B
Joined: 28 Jun 2011
Posts: 11
Re: What is the value of x^2 - y^2?  [#permalink]

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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)?
Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Re: What is the value of x^2 - y^2?  [#permalink]

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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 re-arrange and simplify $$x + y = 2x$$ to get $$x - y = 0$$ or $$x=y$$. If you substitute it leads nowhere.
Manhattan Prep Instructor G
Joined: 22 Mar 2011
Posts: 1605
Re: What is the value of x^2 - y^2?  [#permalink]

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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!
_________________ Dmitry Farber | Manhattan Prep GMAT Instructor | San Diego

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Intern  B
Joined: 28 Jun 2011
Posts: 11
Re: What is the value of x^2 - y^2?  [#permalink]

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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...
Intern  Joined: 29 Oct 2013
Posts: 18
Re: What is the value of x^2 - y^2?  [#permalink]

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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

Posted from my mobile device
Manager  G
Joined: 31 May 2015
Posts: 129
Re: What is the value of x^2 - y^2?  [#permalink]

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Re: What is the value of x^2 - y^2?  [#permalink]

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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.
Manager  Joined: 03 Dec 2013
Posts: 67
Location: United States (HI)
GMAT 1: 660 Q49 V30 GPA: 3.56
Re: What is the value of x^2 - y^2?  [#permalink]

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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)?

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.
Manager  B
Joined: 26 Mar 2017
Posts: 105
Re: What is the value of x^2 - y^2?  [#permalink]

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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)?

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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Manager  B
Joined: 23 Dec 2013
Posts: 137
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44 GPA: 3.76
Re: What is the value of x^2 - y^2?  [#permalink]

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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.
Intern  B
Joined: 31 Jan 2018
Posts: 5
Re: What is the value of x^2 - y^2?  [#permalink]

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Ix x < 0?

1. |x-5| = 7x+2
2. |x+5| = |4x+5|
Director  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 991
WE: Supply Chain Management (Energy and Utilities)
Re: What is the value of x^2 - y^2?  [#permalink]

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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
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: What is the value of x^2 - y^2?  [#permalink]

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 59561
What is the value of x^2 - y^2?  [#permalink]

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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.
Intern  Joined: 04 May 2019
Posts: 1
Re: What is the value of x^2 - y^2?  [#permalink]

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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?
Director  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 991
WE: Supply Chain Management (Energy and Utilities)
Re: What is the value of x^2 - y^2?  [#permalink]

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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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Regards,

PKN

Rise above the storm, you will find the sunshine Re: What is the value of x^2 - y^2?   [#permalink] 04 May 2019, 17:49
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