1) n = 20k, where k is an integer.oxvt wrote:Is the integer n a multiple of 15?
1) n is a multiple of 20
2) n+ 6 is a multiple of 3
n is a multiple of 15 only if 20k is divisible by 15. For this to be true, k must be a multiple of 3, but we can't establish this fact, hence insufficient.
2) n + 6 = 3m
n = 3m - 6, where m is an integer.
n is a multiple of 15 only if 3m-6 is divisible by 15. For this to be true, m must an integer value such as 7, 12, 17, etc. We cannot determine anything about the value of m, hence insufficient.
1+2)
3m - 6 = 20k
m - 2 = 20k/3
Clearly, k must be divisible by 3 because m-2 must be an integer. If k is divisible by 3, then 20k (=n) must be divisble by 15. Hence sufficient. Choose C.
-BM-
