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What is the value of x^2 – y^2?

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What is the value of x^2 – y^2?

by VJesus12 » Mon May 14, 2018 1:21 am

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What is the value of x^2 - y^2?

(1) x + y = 2y - 1
(2) 5x - 5y = 1/(2x + 2y)

The OA is the option B.

Why is sufficient the second statement? I couldn't get a value. Could someone explain this DS question to me? Thanks.
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Source: — Data Sufficiency |
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by Vincen » Mon May 14, 2018 2:20 am

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Hello vjesus12.

Here, we want to know the value of x^2-y^2.
(1) x + y = 2y - 1
Here we cannot say anything about x^2-y^2. Therefore, this statement is NOT SUFFICIENT.
(2) 5x - 5y = 1/(2x + 2y)
Now, we can get: $$5x-5y=\frac{1}{2x+2y}$$ $$\Rightarrow\ \ 5\left(x-y\right)=\frac{1}{2\left(x+y\right)}$$ $$\Rightarrow\ \ \left(x-y\right)\left(x+y\right)=\frac{1}{2\cdot5}$$ $$\Rightarrow\ \ x^2-y^2=\frac{1}{10}.$$ Hence, this statement is SUFFICIENT.

Therefore, the correct answer is the option B.
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