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What is the value of (x+y)(2x-y)-(x-y)(2x+y)?

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by Max@Math Revolution » Tue Sep 17, 2019 11:04 pm

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Answers

A

B

C

D

E

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Difficulty—

[GMAT math practice question]

What is the value of (x+y)(2x-y)-(x-y)(2x+y)?

1) x=3/2
2) xy=2
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Sep 19, 2019 11:18 pm
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

The expression of the question (x+y)(2x-y)-(x-y)(2x+y) is equivalent to 2xy as below.
(x+y)(2x-y)-(x-y)(2x+y)
= 2x^2 + xy - y^2 - (2x^2 -xy -y^2)
= 2xy
Thus, condition 2) is sufficient since 2xy = 2*2 = 4.

Condition 1)
Since we don't have any information about the variable y, condition 2) is not sufficient, obviously.

Therefore, B is the answer.
Answer: B
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