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(x-y)^2-(x+y)^2=?

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(x-y)^2-(x+y)^2=?

by Max@Math Revolution » Sun Jul 24, 2016 2:07 am
(x-y)^2-(x+y)^2=?
1) xy=5
2) x+y=6

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sun Jul 24, 2016 6:02 am
Max@Math Revolution wrote:(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 an ideal candidate for REPHRASING the target question.
(x-y)² - (x+y)² = [x² - 2xy + y²] - [x² + 2xy + y²]
= -4xy
Great, this is a much easier expression.
REPHRASED target question: What is the value of -4xy ?

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 = 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

Answer = A

RELATED VIDEOS:
- Rephrasing the target question: https://www.gmatprepnow.com/module/gmat ... video/1100

- The FOIL method: https://www.gmatprepnow.com/module/gmat ... /video/952

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Mon Jul 25, 2016 6:32 pm
If we modify the original condition and the question, from (x-y)^2-(x+y)^2=? --> -4xy=? Hence, we only have to know the value of xy and the correct answer is A.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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