Bunuel wrote:
What is the value of \((x+y)^2-(x-y)^2\) ?
(1) xy = 5
(2) x + y = 6
Target question: What is the value of \((x+y)^2-(x-y)^2\) ?This is a good candidate for rephrasing the target question.
Take: \((x+y)^2-(x-y)^2\)
Expand and simplify each power: \((x^2 + 2xy + y^2)-(x^2 - 2xy + y^2)\)
Simplify to get: \(4xy\)
REPHRASED target question:
What is the value of \(4xy\)?Aside: the video below has tips on rephrasing the target question Statement 1: \(xy = 5\) Perfect!
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 = 6There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 5. In this case, the answer to the REPHRASED target question is
4xy = 4(1)(5) = 20Case b: x = 2 and y = 4. In this case, the answer to the REPHRASED target question is
4xy = 4(2)(4) = 32Since we can’t answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: AVIDEO ON REPHRASING THE TARGET QUESTION: