Bunuel wrote:

If x is an integer divisible by 15 but not divisible by 20, then x CANNOT be divisible by which of the following?

A. 6

B. 10

C. 12

D. 30

E. 150

Since x is divisible by 15 and not 20, and 15 = 5 x 3 and 20 = 2^2 x 5, we see that x will never be divisible by a number with two 2s in its prime factorization. Thus, x will not be divisible by 12, because 12 = 2^2 x 3^1.

Answer: C

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