zachlebo 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








OA says A

i do not understand why 2 is not sufficient

k/6+m/4=t/12;
2k+3m=t;

1) k=3p; here p=1,2,3,4,,,

2(3p)+3m=t;
3(2p+3m)=t;
now since t is a multiple of 3 thus t and 12 have 3 as a common factor which is greater than 1 hence 1 alone is sufficient to answer the question..!!

2)m=3p;
2k+3(3p)=t;

now since this doesn't give any information about the nature of t; hence 2 alone is not sufficient to answer the question hence it should be A

Thank you!! now it makes sense!

zachlebo 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

when we simplify equation it looks like this
2k+3m = t

statement 1: if k is a multiple of 3 then we can do something like this 2*3*x+3m=t . so we can make equation like this 3* ( 2*x+m) = t . from here we can see that 3 is factor of t and 12.
statement 2: here as we see, m being a multiple of 3 is no make any differcen, it's already is a multiple of 3.

so because you can factor out a 3 in statement one and not in statement two makes it sufficient?