Does integer n have a factor f such that 1 < f < n?

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
The question "an integer n has a factor other than 1 or n" means n is a composite number.

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)
23 < n < 37 means 24 ≤ n ≤ 36.
If n = 24, then n is a composite number and the answer is 'yes'.
If n = 31, then n is a prime number and the answer is 'no'.

Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)
31 < n < 41 means 32 ≤ n ≤ 40.
If n = 32, then n is a composite number and the answer is 'yes'.
If n = 37, then n is a prime number and the answer is 'no'.

Since condition 2) does not yield a unique solution, it is not sufficient.

Conditions 1) & 2)
We have 32 ≤ n ≤ 36.
Then 32, 33, 34, 35 and 36, all of them are composite numbers.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.

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.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.