Bunuel wrote:

Which of the following numbers is the least positive integer that is not a prime and is not a factor of 15!

(A) 14

(B) 22

(C) 19

(D) 34

(E) 38

Remember that 15! = 15 x 14 x 13 x 12 x 11 x 10 x … x 2 x 1. Let’s consider each answer choice:

Choice A. We see that 14 is not a prime number, but it is a factor of 15!, so A is not correct.

Choice B. We see that 22 = 11 x 2, and both 11 and 2 are factors of 15!, so B is not correct.

Choice C. We see that 19 is NOT a factor of 15!. However, it is a prime number, so C is not correct.

Choice D. We see that 34 = 17 x 2, so 34 is not a prime. Furthermore, since 15! does not have a prime factor of 17, 34 cannot be a factor of 15!.

Thus, 34 is the least positive integer that is not a prime and is not a factor of 15!. Thus, choice D is correct.

Answer: D

_________________

Jeffery Miller

Head of GMAT Instruction

GMAT Quant Self-Study Course

500+ lessons 3000+ practice problems 800+ HD solutions