Data Sufficiency

[GMAT math practice question]

If n is positive integer, is 35 a factor of n?

1) 35 is a factor of n^2
2) 35 is a factor of 5n

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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)
Since 35=5*7 is a factor of n^2, 5 and 7 are factors of n^2.
Since 5 and 7 are prime integers and n2 is divisible by 5 and 7, n is divisible by both 5 and 7.
Thus, 35 is a factor of n.
Condition 1) is sufficient.

Condition 2)
If n = 35, then 35 is a factor of n.
If n = 7, then 35 is not a factor of n.
Since we don't have a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.

Answer: A

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.