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If K is a positive integer, how many factors does 12*K have?
(1) K is prime.
(2) K is not divisible by 2.

We can answer the question with the first statement alone. If K is a prime, say, p, then 12K can be written as 2^2*3*p, this will have (2+1)*(1+1)*(1+1) factors. The answer can be obtained from statement 1 alone.

Am not sure about the formula.

If K is a positive integer, how many factors does 12*K have?
(1) K is prime.
(2) K is not divisible by 2.

Statement (1): K is prime.
When K = 2, 12 *K = 24; when K = 3, 12* K = 36; 24 and 36 have different number of factors.
INSUFFICIENT

Statement (2): K is not divisible by 2.
When K = 1, 12 *K = 12; when K = 3, 12* K = 36; 12 and 36 have different number of factors.
INSUFFICIENT

Combining: 12*K = 2^2 * 3* K
K is a prime number greater than 2.

NOTE: A positive integer R when written in the form a^p *b^q where a and b are prime will have (p+1)(q+1) factors.

When K = 3, 12* K = 2^2 * 3^2. Number of factors = (2+1)(2+1) = 9
When K = 5, 12* K = 2^2 * 3* 5. Number of factors = (2+1)(1+1)(1+1) = 12
INSUFFICIENT

Answer: E

Guess i walked into that trap. K can be a prime number can mean K can be 2 or 3 as well.