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What is the value of y?

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What is the value of y? [#permalink]

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New post 18 Sep 2017, 10:35
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

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

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Re: What is the value of y? [#permalink]

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New post 18 Sep 2017, 10:46
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

Answer: A
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What is the value of y? [#permalink]

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New post 19 Sep 2017, 10:11
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.

Answer A.

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What is the value of y?   [#permalink] 19 Sep 2017, 10:11
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