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2) x+y=6--Insuff as we don't know the value of x-y.
Hence A
I don't think we can eliminate that answer choice just 'cause the value of (x-y) is unknown. Rather it should be because the simplied xy is unknown. Just my way of thinking
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Target question:What is the value of (x+y)² - (x-y)² ?
This is a good candidate for rephrasing the target question. (x+y)² - (x-y)² = [x² + 2xy + y²] - [x² - 2xy + y²] = 4xy
REPHRASED target question:What is the value of 4xy?
Statement 1: xy = 5 If xy = 5, then 4xy = 4(5) = 20 Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: x + y = 6 There are several values of x and y that satisfy statement 2. Here are two: Case a: x = 0 and y = 6 in which case, 4xy = 4(0)(6) = 0 Case b: x = 1 and y = 5 in which case, 4xy = 4(1)(5) = 20 Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
2) x+y=6--Insuff as we don't know the value of x-y.
Hence A
I don't think we can eliminate that answer choice just 'cause the value of (x-y) is unknown. Rather it should be because the simplied xy is unknown. Just my way of thinking
You are right, however here we know x+y don't know about x-y. x-y can be anything...4xy comes only after simplification....if we know x-y as well then ans would be B also.
==> If you modify the original condition and the question, \((x+y)^2-(x-y)^2=?\) becomes (x+y-x+y)(x+y+x-y)=?, and if you simplify this, you get (2y)(2x)=?, 4xy=?. Thus, for con 1), you get xy=5, hence it is unique and sufficient.
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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