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Is x^2 > y^2?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Updated on: 25 Sep 2016, 02:20
11
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:47) correct 40% (01:27) wrong based on 284 sessions

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Is x^2 > y^2?

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

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"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, 21:48. Last edited by Bunuel on 25 Sep 2016, 02:20, edited 2 times in total. Renamed the topic and edited the question. Retired Moderator Joined: 26 Nov 2012 Posts: 547 Is x^2 > y^2? [#permalink] Show Tags 25 Sep 2016, 02:31 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: 57 Location: India WE: Information Technology (Computer Software) Re: Is x^2 > y^2? [#permalink] Show Tags 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 , $$X^2 > Y^2$$ _________________ "If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate." Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9014 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x^2 > y^2? [#permalink] Show Tags 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. 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"
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Re: Is x^2 > y^2?  [#permalink]

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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
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Re: Is x^2 > y^2?  [#permalink]

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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.
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18 Apr 2017, 00:58
Is $$x^2>y^2$$?

1) x+y=2
2) x>y
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"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" Intern Joined: 04 Jun 2016 Posts: 1 Re: Is x^2>y^2? [#permalink] Show Tags 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 Answer should be C. It is showing D. How? Intern 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, 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. Math Expert Joined: 02 Sep 2009 Posts: 64152 Re: Is x^2>y^2? [#permalink] Show Tags 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. _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9014 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x^2>y^2? [#permalink] Show Tags 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. 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"
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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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27 Aug 2019, 11:52
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Re: Is x^2 > y^2?   [#permalink] 27 Aug 2019, 11:52