If n is a positive integer, what is the value of n?

[Max@Math Revolution]

[GMAT math practice question]

If n is a positive integer, what is the value of n?

1) n(n-1) is a prime number
2) n(n+1) has 4 factors

[Max@Math Revolution]

=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

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)
Only n =2 makes n(n-1) a prime number.
Thus, condition 1) is sufficient.

Condition 2)
Integers with four factors have the form p*q or p^3, where p and q are prime integers.
It is impossible to have n(n+1)=p^3, where n is an integer and p is a prime number.
The only time n(n+1) = pq is when n(n+1) = 2*3 and n =2.
Condition 2) is sufficient since it yields a unique solution.

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.