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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # Is x^2 > y^2?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Is x^2 > y^2? [#permalink] ### Show Tags Updated on: 25 Sep 2016, 02:20 00:00 Difficulty: 55% (hard) Question Stats: 63% (01:49) correct 38% (01:32) wrong based on 283 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$99 for 3 month Online Course"
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Originally posted by MathRevolution on 24 Sep 2016, 21:48.
Last edited by Bunuel on 25 Sep 2016, 02:20, edited 2 times in total.
Renamed the topic and edited the question.
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25 Sep 2016, 02:31
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.
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Re: Is x^2 > y^2?  [#permalink]

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25 Sep 2016, 03:34
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 , $$X^2 > Y^2$$
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Re: Is x^2 > y^2?  [#permalink]

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27 Sep 2016, 08:09
==> 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.

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"Only $99 for 3 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: 515 Location: India Re: Is x^2 > y^2? [#permalink] ### Show Tags 23 Feb 2017, 03:55 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 Moderator Joined: 21 Jun 2014 Posts: 1096 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, 18:41 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. _________________ --------------------------------------------------------------- Target - 720-740 Project PS Butler - https://gmatclub.com/forum/project-ps-butler-practice-everyday-280904.html http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Is x^2>y^2? [#permalink] ### Show Tags 18 Apr 2017, 00:58 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$99 for 3 month Online Course"
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18 Apr 2017, 01:44
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

It is showing D. How?
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19 Apr 2017, 10:58
MathRevolution wrote:
Is $$x^2>y^2$$?

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

why is it D. I think it should be C.
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19 Apr 2017, 11:00
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.
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20 Apr 2017, 00:37
==> 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.

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26 Apr 2017, 21:54
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
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Re: Is x^2 > y^2?  [#permalink]

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06 Aug 2018, 12:23
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Re: Is x^2 > y^2? &nbs [#permalink] 06 Aug 2018, 12:23
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