common factor

[ska7945]

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.


answer A

[parallel_chase]

Simplify the equation

k/6 + m/4 =t/12

2k+3m=t

Statement I

k is a multiple of 3

From the above simplification we know that m is a multiple of 3

if k and m both are multiples of 3 then t will always be a multiple of 3.

Therefore, common factor between 12 and t greater than 1 will be at least 3.

Sufficient.

Statement II

m is a multiple of 3.

We already know that and it does not tells us anything about k. Therefore, insufficient.

Hence Answer is A.


Remember the below rule, it will help you solve these kind of questions.

if A is multiple of 5
and B is also multiple of 5
then A-B & A+B will also be multiples of 5

The above rule is true for any integer.

Hope this helps.