paresh_patil wrote:if a, b, k & m are positive integers, is a^k a factor of b^m?
1) a is a factor of b
2) k<= m
Statement 1: Let us assume b = a*p ---> b^m = (a*p)^m = (a^m)*(p^m)
As we don't know the relation between k and m, we cannot say whether a^k is a factor of b^m or not.
Not sufficient.
Statement 2: As we don't know anything about a and b, we cannot say whether a^k is a factor of b^m or not.
Not sufficient.
1 & 2 Together: Now, we know that a^m is a factor of b^m and k ≤ m.
Hence, a^k must be a factor of a^m.
Hence, a^k must be a factor of b^m.
Sufficient
[spoiler]
The correct answer is C.[/spoiler]
