If n = 3k, is k an integer?
(1) n is an integer.
(2) n/6 is an integer

statement (1),
if k = 2, then 3x2 = 6 = integer
if k = 1/3, then 3 x 1/3 = 1 which means that n = 1 = integer
since k could be 2 or 1/3, then this statement is not suff

statement (2), if n/6 = integer, then a good question to ask yourself is, what can n be? the only way for n/6 to be an integer is if n = an integer. so n must equal some multiple of 6. when you plug any multiple of 6 into the equation n=3k, then k = integer.

n/3=k

The question asked is whether k a integer or not

statement 1 tells that n is an integer...

Therefore n=1,2,3....etc
n/3=1/3,2/3,1...etc

So statement 1 is not sufficient

statement 2 tells that n/6 is an intege

Therefore n must be divisible by 6( i.e any multiple of 6 should satisfy this condition)
n=6,12,18,24...etc
n/6=1,2,3,4...etc

Therefore n/6 is an integer and hence statement 2 is sufficient..