The answer is 3. I also interviewed here and the question states that you are in a dark room and cant see the socks that you are picking, how many do you need to pick before you are guaranteed to have picked out a pair
24. Count all multiples of 5, so 100/5=20, and multiples of 25(give you an additional 0) 100/25=4. This means 24 zeros. All other explanations are basically complicated ways of this fact.
An elaboration of the above: You are looking to build ten's since each time ten is multiplied by ten, the number of zero's increases by one. The prime factorization of ten is 5*2. In 100!, the determining factor in the number of ten's you can build is the number of fives (since two's are plentiful)...hence you are counting the number of fives in the prime factorization of 100!