GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Sep 2019, 18:32

### 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 > y^2?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7892
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

Updated on: 25 Sep 2016, 03:20
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:47) correct 39% (01:27) wrong based on 254 sessions

### HideShow timer Statistics

Is x^2 > y^2?

(1) x + y = 2
(2) x > y

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 24 Sep 2016, 22:48. Last edited by Bunuel on 25 Sep 2016, 03:20, edited 2 times in total. Renamed the topic and edited the question. Retired Moderator Joined: 26 Nov 2012 Posts: 585 Is x^2 > y^2? [#permalink] ### Show Tags 25 Sep 2016, 03:31 2 1 MathRevolution wrote: Is x^2 > y^2? (1) x + y = 2 (2) x > y Given x^2 > y^2 and we can write (x+y)(x-y) > 0 and need to find this. Stat 1: Given x+y = 2.. then we get (2)(x-y) > 0 and here we are not sure whether (x-y) > 0 or (x-y) < 0 ..Insufficient. Stat 2: we have only (x-y) > 0 information and we are not sure about (x+y) > 0 or (x+y) < 0...Insufficient.. Both : x + y = 2 which is positive and (x-y) > 0 then we can say (2)(x-y) > 0...Sufficient... Option C. Manager Joined: 24 Aug 2016 Posts: 62 Location: India WE: Information Technology (Computer Software) Re: Is x^2 > y^2? [#permalink] ### Show Tags 25 Sep 2016, 04:34 1 1 (1) x + y = 2 we don't have information about x or y. x=1 , y =1 or x =3 , y =1 -- Not sufficient (2) x > y x = -3 and y = -4 or x = 2 and y =1 -- Not sufficient. But if combine (1) and (2). If x>y and x+y=2. X need to be positive and greater than Y. so , $$X^2 > Y^2$$ _________________ "If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate." Intern Joined: 04 Jun 2016 Posts: 1 Re: Is x^2>y^2? [#permalink] ### Show Tags 18 Apr 2017, 02:44 1 x^2-y^2>0 (x+y)(x-y)>0 We have to prove the above: a). x+y=2; satisfies (x+y) > 0; Insufficient b). x>y; satisfies (x-y)>0; Insufficient Together both (x+y) & (x-y) > 0; Sufficient Answer should be C. It is showing D. How? Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7892 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x^2 > y^2? [#permalink] ### Show Tags 27 Sep 2016, 09:09 ==> In the original condition, C is highly likely to be an answer since the variable becomes two (x,y). 1) & 2), x^2-y^2>0?, in (x-y)(x+y)>0? you get x-y>0, and thus x+y=2>0. The answer is always yes, therefore suffi. Hence, the answer is C. answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 537
Location: India
Re: Is x^2 > y^2?  [#permalink]

### Show Tags

23 Feb 2017, 04:55
PROMPT ANALYSIS
x and y are real numbers.
SUPERSET
The answer will be either yes or no.

Translation
In order to find the answer we need:
1# exact value of x and y
2# any equation to conclude the condition

STATEMENT ANALYSIS
ST 1: x+y = 2. Take the value of (x, y) = (1,1), (1.5,0.5) and (0.5, 1.5). For these set of values, the condition the different in each case.INSUFFICIENT. HEnce option a and d eliminated

St 2: x>y. Take (x,y) = (2,-1) and (1,-2). Both the cases have different answer.INSUFFICIENT. Option b eliminated.

St 1 & St 2: Combining both, we get x>1. Therefore, for all values that suffice the 1st equation, y<1, hence x^2>y^2.

Option C
_________________
GMAT Mentors
Retired Moderator
Joined: 22 Jun 2014
Posts: 1094
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Re: Is x^2 > y^2?  [#permalink]

### Show Tags

28 Feb 2017, 19:41
is x^2 > y^2 ?
is x^2 - y^2 > 0 ?
is (x+y)(x-y) > 0?

stmt-1:
x+y = 2 but we also need to know whether x-y is +ve or negative. in fact x=y is a possiblity in which case (x+y)(x-y) = 0.
insuff.

stmt-2:
x > y
x-y > 0 but we also want to know whether x+y is +ve or -ve. because if y is -ve then also x-y>0 but x+y might not.

stmt-1 + stmt-2:
x+y=2
x-y>0

it means (x+y)(x-y) > 0 because 2*(anything greater than zero) > 0 only.
sufficient.
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7892
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

18 Apr 2017, 01:58
Is $$x^2>y^2$$?

1) x+y=2
2) x>y
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Current Student Joined: 28 Oct 2014 Posts: 31 Location: India Concentration: General Management, Operations Schools: ISB '19 (A) GMAT 1: 680 Q50 V30 GPA: 3.89 WE: Engineering (Aerospace and Defense) Re: Is x^2>y^2? [#permalink] ### Show Tags 19 Apr 2017, 11:58 MathRevolution wrote: Is $$x^2>y^2$$? 1) x+y=2 2) x>y why is it D. I think it should be C. Math Expert Joined: 02 Sep 2009 Posts: 58117 Re: Is x^2>y^2? [#permalink] ### Show Tags 19 Apr 2017, 12:00 maheshaero20 wrote: MathRevolution wrote: Is $$x^2>y^2$$? 1) x+y=2 2) x>y why is it D. I think it should be C. ____________ Edited the OA. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7892 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x^2>y^2? [#permalink] ### Show Tags 20 Apr 2017, 01:37 ==> If you modify the original condition and the question, you get$$x^2>y^2$$??, or$$x^2-y^2$$?0?, or (x-y)(x+y)>0?. There are 2 variables (x,y) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get x+y>2 and x-y>0, hence yes, it is always sufficient. Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Joined: 17 Aug 2012
Posts: 122
Location: India
Concentration: General Management, Strategy
Schools: Copenhagen, ESMT"19
GPA: 3.75
WE: Consulting (Energy and Utilities)

### Show Tags

26 Apr 2017, 22:54
Is x2>y 2?

1) x+y=2
2) x>y

is (x+y)(x-y) >0
statement 1 -> we dont know (x-y) hence insufficient
statement 2- > x>y -> (x-y) > 0 but we dont know (x+y) hence insufficient

combining statemetn 1 and 2 answer is C
Non-Human User
Joined: 09 Sep 2013
Posts: 12399
Re: Is x^2 > y^2?  [#permalink]

### Show Tags

27 Aug 2019, 12:52
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.
_________________
Re: Is x^2 > y^2?   [#permalink] 27 Aug 2019, 12:52
Display posts from previous: Sort by