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# Is x=y?

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Math Revolution GMAT Instructor
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11 Aug 2017, 01:02
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Is $$x=y?$$

1) $$x^4+y^4=2x^2y^2$$
2) $$x^4+y^4=0$$
[Reveal] Spoiler: OA

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11 Aug 2017, 01:36
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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.

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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.

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12 Aug 2017, 03:24
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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.

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
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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.

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.

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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.

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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

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25 Aug 2017, 05:52
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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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Re: Is x=y?   [#permalink] 25 Aug 2017, 05:52
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