NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 11:20 It is currently 24 Apr 2024, 11:20
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y

SORT BY:
Date
Kudos
Tags:
Difficulty: 555-605 Levelx   Algebrax               
Find Similar Topics 
Show Tags
Hide Tags
User avatar
dobinnoli
Intern
Intern
Joined: 22 Nov 2008
Posts: 9
Own Kudos [?]: 183 [100]
Given Kudos: 0
Send PM
Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   Updated on: 13 Sep 2022, 02:40
100
Bookmarks
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

72% (01:45) correct 28% (01:51) wrong based on 1827 sessions
Hide Show timer Statistics
Is x^2 equal to xy?

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


PS21275
ShowHide Answer
Official Answer
B

Originally posted by dobinnoli on 15 Dec 2009, 23:28.
Last edited by Bunuel on 13 Sep 2022, 02:40, edited 3 times in total.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618786 [22]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   16 Dec 2009, 06:39
10
Kudos
12
Bookmarks
Expert Reply
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.

Answer: B.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18754
Own Kudos [?]: 22046 [5]
Given Kudos: 283
Location: United States (CA)
Send PM
Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   17 Dec 2019, 20:53
2
Kudos
3
Bookmarks
Expert Reply
dobinnoli wrote:
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.

Answer: B­
General Discussion
User avatar
bogos
Intern
Intern
Joined: 03 Mar 2010
Posts: 23
Own Kudos [?]: 37 [0]
Given Kudos: 1
Send PM
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   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
avatar
swdatta
Intern
Intern
Joined: 10 Apr 2008
Posts: 17
Own Kudos [?]: 9 [2]
Given Kudos: 4
Send PM
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   02 Aug 2010, 20:23
2
Kudos
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.
User avatar
zajo
Intern
Intern
Joined: 12 Oct 2009
Posts: 8
Own Kudos [?]: [0]
Given Kudos: 0
Concentration: Operations, Finance
GPA: 3.09
Send PM
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   04 Oct 2010, 00:21
X=5 =>> y=+/-5
But if you substitute back in eqn only y=5 is valid

Please post OA
User avatar
jlgdr
VP
VP
Joined: 06 Sep 2013
Posts: 1345
Own Kudos [?]: 2391 [0]
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
Send PM
GMAT ToolKit User
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   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
User avatar
S
iliavko
Senior Manager
Senior Manager
Joined: 08 Dec 2015
Posts: 258
Own Kudos [?]: 117 [0]
Given Kudos: 36
GMAT 1: 600 Q44 V27
Send PM
Reviews Badge
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   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
User avatar
RussianDude
Intern
Intern
Joined: 11 Apr 2015
Posts: 28
Own Kudos [?]: 36 [0]
Given Kudos: 98
Location: Germany
Concentration: General Management, Entrepreneurship
Schools: INSEAD Jan '17 (S) HEC '18 IE '18 (I)
GPA: 3.1
WE:Project Management (Energy and Utilities)
Send PM
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   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
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 966
Own Kudos [?]: 223 [0]
Given Kudos: 434
Location: United States
Send PM
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   25 Nov 2020, 10:42
dobinnoli wrote:
Is x^2 equal to xy?

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


PS21275


\(x^2 = xy\)?
\(x^2 - xy = 0\)?
\(x(x-y) = 0\)?
\(x = 0\) or \(x = y\)?

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

if \(x = y = 5\), then \(x^2 = xy\)
if \(x = -5\), then \(x^2\) is not equal to xy

INSUFFICIENT.

(2) Directly gives us our answer; SUFFICIENT.

Answer is B.
User avatar
B
gmatpro15
Manager
Manager
Joined: 09 Aug 2022
Posts: 86
Own Kudos [?]: 22 [1]
Given Kudos: 48
Location: India
Concentration: General Management, Leadership
GPA: 4
WE:Design (Real Estate)
Send PM
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   31 Aug 2022, 09:19
1
Kudos
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.

s2

x=y sufficient
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32650
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink] New post   07 Oct 2023, 11:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Is x^2 equal to xy? (1) x^2 y^2 = (x + 5)(y - 5) (2) x = y [#permalink]
07 Oct 2023, 11:19
Moderator:
Bunuel
Math Expert
92902 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions