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What is the value of y?

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Math Expert
Joined: 02 Sep 2009
Posts: 46305
What is the value of y? [#permalink]

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18 Sep 2017, 11:35
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Difficulty:

55% (hard)

Question Stats:

63% (01:29) correct 37% (01:29) wrong based on 52 sessions

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What is the value of y?

(1) (x^2 – xy + y^2)(x + y) = x^3
(2) x^2 – x – y – y^2 = 0

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Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: What is the value of y? [#permalink]

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18 Sep 2017, 11:46
What is the value of y?

(1) $$(x^2 – xy + y^2)(x + y) = x^3$$

=> Formula : $$a^3 +b^3 = (a + b)(a^2 – ab + b^2)$$

$$(x^2 – xy + y^2)(x + y) = x^3$$ =>$$x^3+y^3=x^3$$ =>$$y^3 = 0$$ => $$y=0$$
sufficient

(2) $$x^2 – x – y – y^2 = 0$$

=> $$x^2 – x – y – y^2 = 0$$ => $$x^2 – y^2 = x+y$$ => $$(x + y)(x-y) = x+y$$ => $$x-y =1$$
=> $$y = x-1$$
Insufficient

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Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 664
Location: India
GPA: 3.64
What is the value of y? [#permalink]

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19 Sep 2017, 11:11
Bunuel wrote:
What is the value of y?

(1) (x^2 – xy + y^2)(x + y) = x^3
(2) x^2 – x – y – y^2 = 0

S1 - Using the formula $$x^3+y^3$$=$$(x^2 – xy + y^2)(x + y)$$
We see that $$y^3$$=0 i.e. y=0

S2 - $$x^2 – x – y – y^2 = 0$$
$$x^2 – y^2 = x+y$$
$$(x+y)(x-y) = x+y$$
therefore x-y=1
y cannot be determined.

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What is the value of y?   [#permalink] 19 Sep 2017, 11:11
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