Data Sufficiency

[Math Revolution GMAT math practice question]

If m and n are positive integers and $$\sqrt{m}\sqrt{n}=6$$ then n=?

1) Both m and n are the squares of integers.
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.

Since we have 2 variables (m and n) and 1 equation, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Condition 1)
There are at least two possible pairs of solutions. Two of these pairs are: m = 4, n = 9 and m = 9, n = 4.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
There are more than two pairs of solutions. Two of these are m = 9, n = 4 and m = 12, n = 3.
Since we don't have a unique solution, condition 2) is not sufficient.

Conditions 1) and 2)
There are two possible pairs of solutions: m = 36, n = 1 and m = 9, n = 4.
Since we don't have a unique solution, both conditions together are not sufficient.
Note: This question includes an example of a "hidden 1".

Therefore, E is the answer.

Answer: E

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.