Solution:

Since k has only two prime factors, 3 and 7, k = 3^m x 7^n where m and n are positive integers. In this case, the number of factors of k is (m + 1)(n + 1). Since we are given that k has 6 factors, we have:

(m + 1)(n + 1) = 6

Since both m and n are integers greater than or equal to 1, we see that m = 1 and n = 2 OR m = 2 and n = 1.

Statement One Only:

3^2 is a factor of k

We see that m = 2. So n = 1 and therefore, k = 3^2 x 7^1 = 63. Statement one alone is sufficient.

Statement Two Only:

7^2 is NOT a factor of k.

We see that n ≠ 2. So n must be 1 and m must be 2. Again we have k = 3^2 x 7^1 = 63. Statement two alone is sufficient.

Answer: D
_________________