NandishSS wrote:If n and m are positive integers, is m a factor of n?
(1) n = 5(3^k), for any positive integer k
(2) m = (3)^k-1, for any positive integer k
We are given that n and m are positive integers and need to determine whether m is a factor of n, i.e., whether n/m = integer.
Statement One Alone:
n = 5(3^k), for any positive integer k
Since we do not have any information regarding m, statement one alone is not sufficient to answer the question.
Statement Two Alone:
m = 3^(k-1), for any positive integer k
Since we do not have any information regarding n, statement two alone is not sufficient to answer the question.
Statements One and Two Together:
Using statements one and two, we can create the following equation:
n/m = 5(3^k)/3^(k-1)
n/m = 5(3^k)/(3^k)(3^-1)
n/m = 5/(3^-1)
n/m = 5 x 3 = 15
Thus, n/m IS an integer.
Answer:
C
