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m and n are positive integers such that m(n+10) = 75. What i

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m and n are positive integers such that m(n+10) = 75. What i

by Max@Math Revolution » Mon Aug 19, 2019 11:31 pm

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[GMAT math practice question]

m and n are positive integers such that m(n+10) = 75. What is the value of m?

1) n is not less than m
2) m is not a prime number
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Aug 21, 2019 11:40 pm

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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 condition on its own first.

Condition 1)
We can find two pairs of solutions: m = 1 and n = 65, and m = 3 and n = 15.
Since condition 1) doesn't yield a unique solution, it is not sufficient.

Condition 2)
We can find only one pair of solutions: m = 1 and n = 65.
Since condition 2) yields a unique solution, it is sufficient.

Therefore, B is the answer.
Answer: B

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.
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