Question

if k m and t are positive integers and 6k + 4m = 12t 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.

Answer 1

hii mate!!

2(3k+2M)=12t

3k+2M=6t <-- stem

1) K=3N

9N+2M=6t, if N=1 then 9+2M=6t if M and t are positive integers then, 2M=6t-9 or 2M=3(t-3)

then t-3 has to be even, so suppose t=5, then M=3, if t=5 and 12 have no factor greater than 1..

if 2M=3(t-3), suppose 2M=18, the t-3=6 t=9, then 12 and t have factors, 1 and 3 in common..insuff

2)I just picked example above of M=multiple of 3..
6K+4*3N=12t

3(2K+4N)=12t -> 2k+4N=4t -> 2(K+2n)=4t ; k+2n=2t ; then we know K has to be even, 

suppose K=2, n=2, then 2+4=2t or 6=2t t=3 then 12 and 3 have factors 1 and 3 in common

suppose K=4, N=2 4+4=2t, 8, t=4 then 12 and t have 1 and 2 and 4 in common..

B is sufficient

hope it helps !!☺☺☺☺