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Algebra

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by BTGmoderatorRO » Sat Sep 16, 2017 11:20 am
What is the value of x^2 - y^2 ?
(1) x + y = 2y - 1
(2) 5x - 5y = 1/(2x + 2y)

a. statement 1 and 2 are sufficient
b. statement 1 is not sufficient while statement 2 is sufficient
c. Both are not sufficient
d. statement 1 is sufficient while statement 2 is not sufficient
e. All of the above

OA is b.
what is the best approach to use to determine that the two statement are sufficient and thus, agree with option A
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Algebra

by Brent@GMATPrepNow » Sun Sep 17, 2017 7:28 am
Roland2rule wrote:What is the value of x² - y² ?
(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: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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