If the positive integer n has 4 different factors, n=?

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[GMAT math practice question]

If the positive integer n has 4 different factors, n=?

1) n has 1 prime factor
2) n<10

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by Max@Math Revolution » Wed Jul 04, 2018 12:36 am

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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 of the conditions on their own first.

Condition 1)
2^3 and 3^3 are positive integers with 4 different factors.
Since the solution is not unique, condition 1) is not sufficient.

Condition 2)
6 = 2*3 and 8 = 2^3 are positive integers with 4 different factors.
Since the solution is not unique, condition 2) is not sufficient.

Condition 1) & 2)
8 = 2^3 is the unique positive integer less than 10 with 4 different factors and one prime factor.
Since the solution is unique, both conditions 1) & 2) are sufficient, when considered together.

Therefore, the answer is C.
Answer: C

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.