Problem Solving - 23

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

Answer: C

x is divisible by 15 -> x is divisible by 3 and 5
x is not divisible by 20 -> x is not divisible by 4

Now because x is divisible by 15, it has 3 and 5 as factors and because x is not divisible by 20, it definitely does not have 4 as a factor .

In the given options only 12 is the number with 4 as a factor.

Thus x will not be divisible by 12. Hence C is the answer.