Statement 1: n is a multiple of m/2.Ramit88 wrote:If a, m and n are positive integers, is n^(2a) a multiple of m^2 ?
1. n is a multiple of m/2
2. n is a multiple of 2m
Hence, n^(2a) = (m/2)^(2a) = (m²/4)^a
Now, there may two possible cases,
- 1. m has a single 2 in its prime factorization. Thus n has none. Hence n^(2a) is NOT a multiple of m^2.
2. m has more than one 2 in its prime factorization. Thus n has at least one 2 in it. Hence n^(2a) may be a multiple of m^2.
Statement 2: n is a multiple of 2m
Hence, n^(2a) = (2m)^(2a) = (4m²)^a = (m²)*[m^(2a - 2)]*[(4)^a]
a and m both being integer, we can conclude that n^(2a) is always a multiple of m^2.
Sufficient
The correct answer is B.
