Data Sufficiency

[GMAT math practice question]

What is the value of n?

1) n is the product of 2 different prime numbers less than 15
2) n and 210 are relatively prime

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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)
Both n = 6 and n = 10 are products of two different prime numbers less than 15. Thus, condition 1) is not sufficient since it does not yield a unique solution.

Condition 2)
Both n = 11 and n = 13 are relatively prime to 210. Thus, condition 2) is not sufficient since it doesn't yield a unique solution.

Conditions 1) & 2)
The prime numbers less than 15 are 2, 3, 5, 7, 11 and 13.
Since n and 210 = 2*3*5*7 are relatively prime, we must have n = 11*13 = 143.
Both conditions 1) & 2) together are sufficient since they yield a unique solution.

Therefore, C is the answer.
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.