Data Sufficiency

[GMAT math practice question]

If m and n are non-negative integers, what is the value of mn?

1) 3^m = 5^n
2) |m| = - √n

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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.

Condition 1) implies that m = n = 0, since 3^m and 5^n are powers of prime numbers that are equal. Thus, condition 1) is sufficient.
Condition 2) also implies that m = n = 0, since |m|=- √n is only possible when m = n = 0 (- √n <=0 and |m| >=0). Thus, condition 2) is also sufficient.

Therefore, D is the answer.
Answer: D

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).