Factors Problem-2

[leumas]

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 6.

[knight247]

Firstly, multiplying throughout by 12. We have,
2k+3m=t

(1)k is a multiple of 3 so 2k has to be a multiple of 3. Remember one ground rule,
If two multiples of a certain number are added/subtracted then the resultant number is also a multiple of the same number. So we have Multiple of 3+Multiple of 3=Multiple of 3. Hence, t is a multiple of 3. And, 12 is also a multiple of 3. So, t and 12 do have a common factor greater than 1 i.e. 3. Sufficient

(2)m is a multiple of 6 i.e. 2*3. So m is a multiple of 2 and 3. So obviously, 3m is a multiple of 2
multiple of 2+ multiple of 2=multiple of 2 hence t is also a multiple of 2. Sufficient.

Answer is D