1) 8k is divisible by 16 . means that k can be 2 or 4 or 6. So may or may not be divisible by 4. NS

2) For 9k to be divisible by 4 , k can be 4 or 8 or 12 ..... so is divisible by 4. Sufficient.

Therefore Statement 2 alone is sufficient to answer.

These problems can get really confusing so I always like to think of them in terms of a prime "box" filled with the prime factors, and which prime factors can or cannot belong in it! (MGMAT strategy!)

The question rephrase -- does K have at least 2 two's in it's prime box?

In statement 1, we are told that 8k is divisible by 16. That means 8k has a prime box with 2,2,2,2 (all the prime factors). But these 2's can belong to 8 or to K- we don't know! Insufficient.

In statement 2, we are told that 9k is divisble by 12. So 9k's prime box has a 2, 2, and a 3. But the 2's can only belong to K, because 9 doesn't have any 2's as prime factors. So we have --- sufficient!