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# Is x=y?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8027
GMAT 1: 760 Q51 V42
GPA: 3.82

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11 Aug 2017, 01:02
2
4
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:24) correct 43% (01:34) wrong based on 117 sessions

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Is $$x=y?$$

1) $$x^4+y^4=2x^2y^2$$
2) $$x^4+y^4=0$$

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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" Retired Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1331 Location: Viet Nam Re: Is x=y? [#permalink] ### Show Tags 11 Aug 2017, 01:36 2 MathRevolution wrote: Is $$x=y?$$ 1) $$x^4+y^4=2x^2y^2$$ 2) $$x^4+y^4=0$$ (1) $$x^4+y^4 -2x^2y^2 = 0 \implies (x^2-y^2)^2=0 \implies x^2-y^2=0 \implies (x+y)(x-y)=0$$ insufficient. (2) $$x^4+y^4=0 \implies x=y=0$$. Sufficient. The answer is B _________________ Intern Joined: 06 Feb 2016 Posts: 47 Location: Poland Concentration: Finance, Accounting GMAT 1: 730 Q49 V41 GPA: 3.5 Re: Is x=y? [#permalink] ### Show Tags 11 Aug 2017, 13:35 Shouldn't we add a condition that x and y are integers. For statement B, for example, x=1/2 and y=4th root of 15/2 can also be solutions. Director Status: I don't stop when I'm Tired,I stop when I'm done Joined: 11 May 2014 Posts: 524 Location: Bangladesh Concentration: Finance, Leadership GPA: 2.81 WE: Business Development (Real Estate) Re: Is x=y? [#permalink] ### Show Tags 12 Aug 2017, 03:24 Top Contributor Devbek wrote: Shouldn't we add a condition that x and y are integers. For statement B, for example, x=1/2 and y=4th root of 15/2 can also be solutions. Confused on your point.May I know more details about it? Statement (2) IMO, If each number has even exponent and the sum of all numbers equals to Zero, each number must be equal to Zero.Hence X=Y=0 So Statement (2) is Sufficient and Correct Answer is B _________________ Md. Abdur Rakib Please Press +1 Kudos,If it helps Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges Intern Joined: 06 Feb 2016 Posts: 47 Location: Poland Concentration: Finance, Accounting GMAT 1: 730 Q49 V41 GPA: 3.5 Re: Is x=y? [#permalink] ### Show Tags 12 Aug 2017, 13:46 AbdurRakib wrote: Devbek wrote: Shouldn't we add a condition that x and y are integers. For statement B, for example, x=1/2 and y=4th root of 15/2 can also be solutions. Confused on your point.May I know more details about it? Statement (2) IMO, If each number has even exponent and the sum of all numbers equals to Zero, each number must be equal to Zero.Hence X=Y=0 So Statement (2) is Sufficient and Correct Answer is B OMG. My bad. It is one of those days... I don't know why but I was sure that x^4+y^4=1 not 0. Thanks for the answer. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8027 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x=y? [#permalink] ### Show Tags 13 Aug 2017, 18:18 ==> In the original condition, 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), for con 1), from $$x^4+y^4-2x^2y^2=0, (x^2-y^2)^2=0$$, you get $$x^2=y^2$$, and from x=±y, yes and no coexists, hence it is not sufficient. For con 2), you only get x=y=0, hence yes, it is sufficient. The answer is B. Answer: B _________________ 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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Joined: 07 Jun 2017
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13 Aug 2017, 20:54
I didn't think B is correct because x could be negative, and y could be positive.
can someone correct my logic please?
Thank you
Intern
Joined: 18 Aug 2017
Posts: 30
GMAT 1: 670 Q49 V33

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25 Aug 2017, 05:52
1
pclawong wrote:
I didn't think B is correct because x could be negative, and y could be positive.
can someone correct my logic please?
Thank you

It can't be.

$$x^4$$>=0
$$y^4$$ >=0

Therefore in order for $$x^4$$ + $$y^4$$ =0, x = y= 0
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16 Feb 2019, 18:54
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Re: Is x=y?   [#permalink] 16 Feb 2019, 18:54
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