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# (x+y)^2-(x-y)^2=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42
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23 Feb 2017, 20:25
1
3
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:00) correct 24% (01:45) wrong based on 191 sessions

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$$(x+y)^2-(x-y)^2=?$$

1) xy=5
2) x+y=6

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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" Senior Manager Joined: 19 Apr 2016 Posts: 268 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) Re: (x+y)^2-(x-y)^2=? [#permalink] ### Show Tags 23 Feb 2017, 20:42 2 MathRevolution wrote: $$(x+y)^2-(x-y)^2=?$$ 1) xy=5 2) x+y=6 $$(x+y)^2-(x-y)^2$$ $$=x^2+y^2+2xy-x^2-y^2+2xy$$ $$=4xy$$ St I xy=5 ==> 4*xy = 4*5 = 20 ----------Sufficient St II x+y=6, we have no information about x-y ----------Insufficient Hence Option A is correct Hit Kudos if you liked it GMAT Club Legend Joined: 12 Sep 2015 Posts: 4015 Location: Canada Re: (x+y)^2-(x-y)^2=? [#permalink] ### Show Tags 24 Feb 2017, 08:16 Top Contributor MathRevolution wrote: $$(x+y)^2-(x-y)^2 =?$$ 1) xy = 5 2) x + y = 6 Target question: What is the value of (x+y)² - (x-y)² ? This is a good candidate for rephrasing the target question. (x+y)² - (x-y)² = [x² + 2xy + y²] - [x² - 2xy + y²] = 4xy REPHRASED target question: What is the value of 4xy? Statement 1: xy = 5 If xy = 5, then 4xy = 4(5) = 20 Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT Statement 2: x + y = 6 There are several values of x and y that satisfy statement 2. Here are two: Case a: x = 0 and y = 6 in which case, 4xy = 4(0)(6) = 0 Case b: x = 1 and y = 5 in which case, 4xy = 4(1)(5) = 20 Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT Answer: A RELATED VIDEOS FROM OUR COURSE _________________ Test confidently with gmatprepnow.com Director Joined: 06 Jan 2015 Posts: 689 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: (x+y)^2-(x-y)^2=? [#permalink] ### Show Tags 24 Feb 2017, 10:48 MathRevolution wrote: $$(x+y)^2-(x-y)^2=?$$ 1) xy=5 2) x+y=6 $$(x+y)^2-(x-y)^2==>4xy=?$$ 1)x+y=5 hence 4xy==>20 -- Suff 2) x+y=6--Insuff as we don't know the value of x-y. Hence A _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution Manager Joined: 15 Mar 2014 Posts: 141 Location: Singapore Concentration: Technology, General Management GPA: 3.5 WE: Operations (Telecommunications) Re: (x+y)^2-(x-y)^2=? [#permalink] ### Show Tags 25 Feb 2017, 02:02 1 NandishSS wrote: 2) x+y=6--Insuff as we don't know the value of x-y. Hence A I don't think we can eliminate that answer choice just 'cause the value of (x-y) is unknown. Rather it should be because the simplied xy is unknown. Just my way of thinking _________________ Hit +1 Kudos If you like my post! Director Joined: 06 Jan 2015 Posts: 689 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: (x+y)^2-(x-y)^2=? [#permalink] ### Show Tags 25 Feb 2017, 03:31 ashwink wrote: NandishSS wrote: 2) x+y=6--Insuff as we don't know the value of x-y. Hence A I don't think we can eliminate that answer choice just 'cause the value of (x-y) is unknown. Rather it should be because the simplied xy is unknown. Just my way of thinking Hi ashwink, You are right, however here we know x+y don't know about x-y. x-y can be anything...4xy comes only after simplification....if we know x-y as well then ans would be B also. Happy Prepping!!! _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8025 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: (x+y)^2-(x-y)^2=? [#permalink] ### Show Tags 26 Feb 2017, 21:25 ==> If you modify the original condition and the question, $$(x+y)^2-(x-y)^2=?$$ becomes (x+y-x+y)(x+y+x-y)=?, and if you simplify this, you get (2y)(2x)=?, 4xy=?. Thus, for con 1), you get xy=5, hence it is unique and sufficient. The answer is A. Answer: A _________________ 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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02 Feb 2019, 19:47
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Re: (x+y)^2-(x-y)^2=?   [#permalink] 02 Feb 2019, 19:47
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