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Is 3(a-b)>0?

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by Max@Math Revolution » Mon Feb 11, 2019 11:37 pm

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A

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E

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[GMAT math practice question]

Is 3(a-b) > 0?

1) a^3 > b^3
2) a > b
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Feb 14, 2019 12:42 am
=>

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.

Asking if 3(a-b)>0 is equivalent to asking if a - b > 0, or, equivalently, if a > b.
Thus, condition 2) is sufficient.

Condition 1)
a^3 > b^3
=> a^3 - b^3 > 0
=> (a-b)(a^2+ab+b^2) > 0
=> a - b > 0 since a^2+ab+b^2 > 0
=> a > b
Thus, condition 1) is sufficient too.

Therefore, D is the answer.
Answer: D

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
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