diegoasaavedra wrote:if a.b.k, and m are positive integers, is a^k a factor of b^m?
1- a is a factor of b
2- k=<m
answer is C, could somebody explain me this?
Thanks
(1) a is a factor of b
Let a=2, b=6
2 is a factor of 6
2^2 (= 4) is a factor of 6^2 (= 36)
2^3 (=8 ) is not a factor of 36
INSUFFICIENT
(2) k<=m
Does not tell us anything about a and b.
(You can also test this using numbers).
INSUFFICIENT.
Combining
a is a factor of b and k<=m
a^k = a*a*a*a... k times
b^m = b*b*b*b... m times
b^m/a^k = (b*b*b*b...m times)/(a*a*a*a... k times)
For every b in the numerator, there is atleast one a in the denominator (k<=m)
Since a is a factor of b, all those a's in the denominator cancel out. Hence, b^m/a^k is an integer.
SUFFICIENT.
Answer is (C).
So It Goes
