ishtmeet wrote:
If k, m, and t are positive integers and k/6+m/4 =t/12 , do t and 12 have a common factor greater than 1 ?
(1) k is a multiple of 3.
(2) m is a multiple of 3.
(1) k is a multiple of 3, so k=3n for some positive integer n
k/6+m/4= 3n/6+m/4= (6n+3m)/12
Thus t=6n+3m=3(2n+m)
Since n and m are both +ve integers, t is a multiple of 3, and t and 12 have a common factor of 3.
SUFFICIENT
(2) m is a multiple of 3, so k=3p for some positive integer p
k/6+m/4= k/6+3p/4= (2k+9p)/12
If k=p=1, t=11 and the only factor 11 and 12 have in common is 1
If k=1 and p=2, t is a multiple of 2, so t and 12 have a common factor of 2.
NOT SUFFICIENT
Answer: A