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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) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # Is x^2 equal to xy?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 51218 Is x^2 equal to xy? [#permalink] ### Show Tags 06 Oct 2015, 04:50 00:00 Difficulty: 45% (medium) Question Stats: 68% (01:22) correct 32% (01:30) wrong based on 129 sessions ### HideShow timer Statistics Is x^2 equal to xy? (1) x^2 + y^2 = -(x^2 – y^2) (2) x = y Kudos for a correct solution. _________________ CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2711 Location: India GMAT: INSIGHT WE: Education (Education) Re: Is x^2 equal to xy? [#permalink] ### Show Tags 06 Oct 2015, 06:43 Bunuel wrote: Is x^2 equal to xy? (1) x^2 + y^2 = -(x^2 – y^2) (2) x = y Kudos for a correct solution. Question : Is x^2 = xy? i.e. Is x^2 - xy = 0 i.e. Is x(x-y)=0? i.e. Is x = 0 OR x = y? i.e. Question : Is x = 0 OR x = y? Statement 1: x^2 + y^2 = -(x^2 – y^2) x^2 + y^2 = y^2 – x^2 i.e. 2x^2 = 0 i.e. x = 0 SUFFICIENT Statement 2: x = y SUFFICIENT Answer: option D _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Current Student Joined: 07 Jan 2015 Posts: 82 Location: Thailand GMAT 1: 540 Q41 V23 GMAT 2: 570 Q44 V24 GMAT 3: 550 Q44 V21 GMAT 4: 660 Q48 V33 GPA: 3.31 WE: Science (Other) Re: Is x^2 equal to xy? [#permalink] ### Show Tags 06 Oct 2015, 23:36 1 1 Statement 1 $$x^2 + y^2 = -(x^2 - y^2)$$ $$x^2 + y^2 = (y^2 - x^2)$$ $$x^2 + x^2 = y^2 - y^2$$ $$2x^2 = 0$$ therefore, $$x = 0$$ Sufficient Statement 2 $$x = y$$ therefore $$xy = x^2$$ Sufficient Answer D Manager Joined: 21 Jun 2014 Posts: 131 Location: United States Concentration: General Management, Strategy GMAT 1: 630 Q45 V31 GPA: 3.4 WE: Engineering (Computer Software) Is x^2 equal to xy? [#permalink] ### Show Tags 07 Oct 2015, 09:50 the question can be rephrased as $$x^2-xy$$ or$$x(x-y)$$ So for the inequality to be equal to 0 either $$x=0$$ or $$x=y$$ From A: $$x^2 + y^2 = -(x^2 – y^2)$$ $$2x^2=0$$ so $$x=0$$ A is sufficient From b: x=y Y is sufficient Correct answer is D _________________ Regards, Manish Khare "Every thing is fine at the end. If it is not fine ,then it is not the end " Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x^2 equal to xy? [#permalink] ### Show Tags 07 Oct 2015, 22:18 Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. Is x^2 equal to xy? (1) x^2 + y^2 = -(x^2 – y^2) (2) x = y If we modify the original condition and the question, we want to know whether x^2-xy=0, which can further be simplified into x(x-y)=0 and whether x=0 or x=y. There are 2 variables (x,y), meaning we need 2 equations to match the number of variables. The conditions give us 2 equations in total, making it likely that (C) is going to be our answer, but if we look closely into the conditions, For condition 1, x^2+y^2=-x^2+y^2, x^2=-x^2, 2x^2=0, so x=0, answering the question ‘yes’ For condition 2, x=y, also answering the question ‘yes’. Therefore the 2 conditions are each sufficient alone to answer the question, and the answer becomes (D) For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E. _________________ 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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Math Expert
Joined: 02 Sep 2009
Posts: 51218
Is x^2 equal to xy?  [#permalink]

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11 Oct 2015, 06:20
Bunuel wrote:
Is x^2 equal to xy?

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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No The question asks: “Is x2 = xy?”

For this question it is easier to begin with Statement 2.

Statement 2: x = y. If x = y then x^2 will automatically equal xy. So this statement is sufficient. The answer is either B or D.

Statement 1: x^2 + y^2 = - (x^2 – y^2). Generally with algebra you want to eliminate parentheses, so in this case you’ll want to multiply each term in (x^2 – y^2) by -1 to distribute that negative sign; the statement becomes x^2 + y^2 = -x^2 + y^2. If you then manipulate this statement algebraically by adding x^2 to both sides and by subtracting y^2 from both sides you get 2x^2 = 0. For this to be true x must 0. And if x = 0, then 0^2 = 0(y) by definition—both sides of the equation would equal 0. This statement is also sufficient and the correct answer is D.
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Joined: 08 Dec 2015
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Is x^2 equal to xy?  [#permalink]

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24 Jun 2016, 08:25

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

$$x^2+y^2+(x^2-y^2)=0$$

$$x^2+y^2+((x+y)(x-y))=0$$

$$x^2+x^2+y^2-y^2-2xy=0$$

$$2x^2-2xy=0$$

$$2x^2=2xy$$

$$x^2=xy$$ same as stem. Suf.
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Re: Is x^2 equal to xy?  [#permalink]

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05 Jul 2018, 10:53
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).

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Re: Is x^2 equal to xy? &nbs [#permalink] 05 Jul 2018, 10:53
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