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If x ≠ y, what is the value of ( x^2y – xy^2 ) / ( x^3 â

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by Max@Math Revolution » Sun Jan 06, 2019 11:42 pm

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[Math Revolution GMAT math practice question]

If x ≠ y, what is the value of ( x^2y - xy^2 ) / ( x^3 - y^3 )?

1) xy / ( x^2 + xy + y^2) = 1/3
2) x^2y^2=9
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Jan 09, 2019 12:01 am
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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.

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

The expression from the question is equivalent to xy / ( x^2 + xy + y^2) as shown below, which is the same as condition 1):
( x^2y - xy^2 ) / ( x^3 - y^3 )
= xy(x-y) / (x-y)(x^2+xy+y^2)
= xy / ( x^2 + xy + y^2 )
Thus, condition 1) is sufficient.

Condition 2)
If x = 3, y = 1, then ( x^2y - xy^2 ) / ( x^3 - y^3 ) = ( 9 - 3 ) / ( 27 - 1) = 6/26 = 3/13.
If x = -3, y = 1, then ( x^2y - xy^2 ) / ( x^3 - y^3 ) = ( 9 + 3 ) / ( - 27 - 1) = -12/28 = -3/7.
Since it does not yield a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
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