Economist wrote:

A drawer contains 36 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?

(1) The probability is 4/9 that the first sock is black.

(2) The number of white socks in the drawer is 4 more than the number of black socks.

Total # of socks 36.

(1) P(B)=4/9 --> B=16 --> P(BB)=16/36*15/35=4/21. Sufficient.

(2) W=B+4, as we don't know whether drawer contains only white and black socks, or there are also some other color socks, we can not determine the # of B. not sufficient.

Answer: A.

This was how I analyzed it! And if I'm doing what you're doing, I'm finally getting somewhere..