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# What is the value of x^2 – y^2 ?

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Re: What is the value of x^2 – y^2 ? [#permalink]
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Bunuel wrote:
What is the value of x^2 – y^2 ?

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

Target question: What is the value of x² – y² ?

Statement 1: x + y = 2y – 1
Subtract 2y from both sides to get: x - y = -1
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 1, in which case x² – y² = 0² – 1² = 0 - 1 = -1
Case b: x = 1 and y = 2, in which case x² – y² = 1² – 2² = 1 - 4 = -3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 5x - 5y = 1/(2x + 2y)
Multiply both sides of the equation by (2x + 2y) to get: (2x + 2y)(5x - 5y) = 1

ASIDE: If you recognize that x² – y² = (x+y)(x-y), then you'll see that we're well on our way to answering the target question

Rewrite as: (2)(x + y)(5)(x - y) = 1
Or we can write: (2)(5)(x + y)(x - y) = 1
Simplify: (10)(x² – y²) = 1
Divide both sides by 10 to get: x² – y² = 1/10
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

Cheers,
Brent
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Re: What is the value of x^2 – y^2 ? [#permalink]
By using statement 1 we can deduce (x+y)(x-y)= (2y-1) ;"Y" is still unknown.

By using statement 2 we can find (x+y)(x-y)= 1/10

so Answer is "B"
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Re: What is the value of x^2 y^2 ? [#permalink]
chipsy wrote:
We need to find x^2 - y^2 = (x-y) (x+y)

(A) x - y = -1 , Not suff.

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

5 (x-y) * 2(x+y) = 1
10 (x-y) (x+y) =1
(x-y) (x+y) = 1/10
Sufficient.

answer is Option B.

hey chipsy in option B the 3 step, i think mathematical it is not correct
Re: What is the value of x^2 y^2 ? [#permalink]
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