GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 22 Jan 2020, 18:47

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Is x^2 equal to xy?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 22 Nov 2008
Posts: 13
Is x^2 equal to xy?  [#permalink]

### Show Tags

Updated on: 14 Dec 2018, 10:56
17
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:44) correct 30% (01:46) wrong based on 548 sessions

### HideShow timer Statistics

Project DS Butler: Day 39: Data Sufficiency (DS78)

Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

Originally posted by dobinnoli on 15 Dec 2009, 23:28.
Last edited by gmatbusters on 14 Dec 2018, 10:56, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 60605
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

16 Dec 2009, 06:39
4
4
Is x^2 equal to xy?

Question: is $$x^2=xy$$? --> $$x(x-y)=0$$ --> Equation holds true if $$x=0$$ or/and $$x=y$$.

So, basically question asks: Is $$x=0$$ or/and $$x=y$$ true?

Obviously statement (2) is sufficient, as it gives directly that $$x=y$$.

(1) x^2 – y^2 = (x + 5)(y - 5) --> $$(x+y)(x-y)=(x + 5)(y-5)$$

If $$y=5$$ --> $$(x+5)(x-5)=(x+5)(5-5)$$ --> $$(x+5)(x-5)=0$$ --> Either $$x=5=y$$ and in this case answer to the question is YES OR $$x=-5$$, hence $$x$$ is not equal to $$y$$ (nor to zero) and in this case answer to the question is NO. So two different answers.

Not sufficient.

_________________
##### General Discussion
Intern
Joined: 03 Mar 2010
Posts: 34
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

02 Aug 2010, 08:08
Statement 1:
(x,y)=(5,5) --> x²=xy
(x,y)=(-5,5) --> x²<>xy
not sufficient

Statement 2:
x=y --> xx=xy or x²=xy
sufficient

B
Intern
Joined: 10 Apr 2008
Posts: 18
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

02 Aug 2010, 20:23
1
I agree with bogos.

Stmt1:
x^2 - y^2 = (x+5)(x-5)
x^2 - y^2 = x^2 - 25
0 = y^2 - 25
y = +5, -5

plugin a possible value of y into the equation x^2 - y^2 = x^2 - 25
you can see when that y can be -5 and x can 5. But plugging in the same value into x^2 = xy would yield 25 = -25.
Intern
Joined: 12 Oct 2009
Posts: 8
Concentration: Operations, Finance
GPA: 3.09
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

04 Oct 2010, 00:21
X=5 =>> y=+/-5
But if you substitute back in eqn only y=5 is valid

SVP
Joined: 06 Sep 2013
Posts: 1525
Concentration: Finance
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

02 Feb 2014, 17:06
dobinnoli wrote:
Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

Is x(x-y)=0

So is x=0 or x=y?

Statement 1

Obviously x is not equal to y otherwise LHS and RHS should be zero

Is x = 0

Is -y^2 = -25, could be but we don't know

Statement 2

x=y, yes. This is correct and sufficient

B
Senior Manager
Joined: 08 Dec 2015
Posts: 282
GMAT 1: 600 Q44 V27
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

26 Jun 2016, 06:41
Omg, can someone please post detailed explanation for this one? I don't understand why are we using Y=5 to evaluate the (x+y)(x-y)=(x+5)(y-5) why not use 10 or 40 or something else? why 5? Does it have something to do with question stem?

Im totally confused here
Intern
Joined: 11 Apr 2015
Posts: 31
Location: Germany
Concentration: General Management, Entrepreneurship
GPA: 3.1
WE: Project Management (Energy and Utilities)
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

08 Jul 2016, 03:42
iliavko wrote:
Omg, can someone please post detailed explanation for this one? I don't understand why are we using Y=5 to evaluate the (x+y)(x-y)=(x+5)(y-5) why not use 10 or 40 or something else? why 5? Does it have something to do with question stem?

Im totally confused here

I guess we are using 5 in order to make (x+y)(x-y) = 0, which is the easiest way to figure out the possible values of x
_________________
"I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times." Bruce Lee

"I hated every minute of training, but I said, "Don’t quit. Suffer now and live the rest of your life as a champion."" Muhammad Ali
Retired Moderator
Joined: 27 Oct 2017
Posts: 1397
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

14 Dec 2018, 10:57

Project DS Butler: Day 39: Data Sufficiency (DS78)

Bumping for DS Butler Project
_________________
Intern
Joined: 16 Jul 2019
Posts: 19
Is x^2 equal to xy?  [#permalink]

### Show Tags

14 Dec 2019, 11:32
ScottTargetTestPrep @EMPOWERgmat can you please explain this question?
Retired Moderator
Joined: 27 Oct 2017
Posts: 1397
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

14 Dec 2019, 20:03
What is ur doubt in this question, because explanation has already been provided in the thread.

Rocknrolla21 wrote:
ScottTargetTestPrep @EMPOWERgmat can you please explain this question?

_________________
Intern
Joined: 16 Jul 2019
Posts: 19
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

14 Dec 2019, 22:35
gmatbusters I don't understand how we proved that statement 1 is insufficient.

Posted from my mobile device
Retired Moderator
Joined: 27 Oct 2017
Posts: 1397
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

15 Dec 2019, 05:44
To prove that St 1 is insufficient, see the beautiful explanation provided by Bunuel here

Rocknrolla21 wrote:
gmatbusters I don't understand how we proved that statement 1 is insufficient.

Posted from my mobile device

_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9095
Location: United States (CA)
Re: Is x^2 equal to xy?  [#permalink]

### Show Tags

17 Dec 2019, 20:53
dobinnoli wrote:

Project DS Butler: Day 39: Data Sufficiency (DS78)

Is x^2 equal to xy?

(1) x^2 – y^2 = (x + 5)(y - 5)
(2) x = y

Statement One Only:

x^2 – y^2 = (x + 5)(y - 5)

If y = 5, we have:

x^2 - 25 = (x + 5)(0)

x^2 - 25 = 0

(x + 5)(x - 5) = 0

x = 5 or x = -5

If x = 5, then x^2 and xy will be equal since both are 25. However, if x = -5, then x^2 and xy will not be equal since the former is 25 and the latter is -25. Statement one alone is not sufficient.

Statement Two Only:

x = y

Since x = y, if we multiply both sides by x, we have:

x * x = y * x

x^2 = xy

Statement two alone is sufficient.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Is x^2 equal to xy?   [#permalink] 17 Dec 2019, 20:53
Display posts from previous: Sort by