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Stmt 1

8 is comprised of 2*2*2
16 is comprised of 2*2*2*2

if 8K is divisible by 16 then k must have at least one occurrence of 2 in its prime factor set. But in order for k to be divisible by 4 (=2*2) we need two occurrences of 2

--> insufficient (k could or could not be divisible by 4)

Stmt 2

9 is comprised of 3*3
12 is comprised of 2*2*3*3

if 9k is divisible by 12 then the K must have two occurrences of two in its prime factor set. Hence K is divisible by 4 ---> sufficient

Ans B

[gmat_nov_2008]

(1)
Since 8K/16 = 2*2*2*K/2*2*2*2 = K is divisible by 2.
So insufficient.

(2) 9K/12 = 3*3*K/3*4 = K is divisible by 4.
Sufficient.

Hence B.