common factor greater than 1

[apuso]

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.

[itsratul]

Ans :only (1) is sufficient to answer

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

divide throughout by 3 ,

(2k)/3 [ k is a multiple of 3,(2k)/3 is an integer ] + m [m is an integer] = t/3 [Integer + Integer = integer]

Therefore one of the other common factors of t and 12 greater than 1 is 3 .

[sreak1089]

We know, k/6 + m/4 = t/12

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

1) says k is multiple of 3
Let's say k = 3p (p is constant)

=> t = (2*3p + 3m)
= 3(2*p + 1)
=> t is a multiple of 3 or t has 3 as its factor.

12 = 3 * 2^2 Hence 3 is a common factor > 1. Hence SUFFICIENT.

2) says m is multipe of 3
Let's say k = 3q (q is constant)

=> t = (2k + 3*3q)
= 2k + 9q

We know that m is multiple of 3 but we don't know anything of k. Hence 2 is NOT SUFFICIENT.

Answer is A.