[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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If x ≠y, what is the value of ( x^2y – xy^2 ) / ( x^3 â
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Max@Math Revolution
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Max@Math Revolution
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- Joined: Fri Jul 24, 2015 2:28 am
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Your Answer
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E
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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
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
Math Revolution
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[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
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