k/6+m/4 = t/12

(2k+3m)/12 = t/12

2k+3m = t

3m is a multiple of 3, we only need information about k.

St 1: K is a multiple of 3

k = 3*a, where 'a' is an integer which when multiplied by 3 gives a product of k.

2(3*a) + 3m = t

3*[2a + 3m] = t

So t is also a multiple of 3. Hence the answer to the question is yes
St 1: SUFF

St 2: m is a multiple of 3.

3m is anyways a multiple of 3. We don't know if 2k is a multiple of 3 or not.

If k=1, m=5; t = 17, the only common factor between 17 and 12 is 1. Hence answer to the question is No.
k=2, m=4; t = 16, the answer to the question is Yes.

So answer is A.

Excellent solution Mals24!

Thank you cramya

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PS: When someone appreciates your effort, thanking that person is considered POLITE.