The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of k?

1) 3^2 is a factor of k.
2) 7^2 is NOT a factor of k.



Let's say you have 'M' number of 3's, and 'N' number of 7's.
this means there are M + 1 possibilities for the number of 3's in a factor of k (no 3's, one 3, ..., 'M' 3's), and, likewise, there are N + 1 possibilities for the number of 7's (no 7's, one 7, ..., 'N' 7's).
therefore, the total number of factors is (M + 1)(N + 1). (this formula generalizes to more than 2 prime factors as well, although it's unlikely the gmat would hit you with a problem involving such generalizations)
if there are 6 factors, this product is either 2x3 or 3x2, meaning that there are either one 3 and two 7's, or two 3's and one 7. (you can't have zero 3's and five 7's, because then 3 isn't a prime factor at all; likewise for five 3's and zero 7's.)
this means the only possibilities for k are 3x3x7 and 3x7x7, before you even examine statements (1) and (2). go from there.

Ans - D