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If n is a positive integer, is n a prime number?

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If n is a positive integer, is n a prime number?

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[GMAT math practice question]

If n is a positive integer, is n a prime number?

1) n is the least factor of 77 greater than 1
2) n has exactly two factors

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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 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
The factors of 77 are 1, 7, 11 and 77. We have n = 7 since the least factor of 77 other than 1 is 7.
Condition 1) is sufficient.

Condition 2)
n is a prime number, by definition, since it has exactly two factors.
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

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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