SeanWest

Maybe this strategy makes sense:

Tally up each answer letter have already chosen, then choose the least used letter for the unknowns. Assuming the answers are completely random, each letter has a 1 in 3 chance of being picked. In the long run, each letter should be right a third of the time. In this case, the sample size is small (60 questions) so it probably wont be anywhere near this. Nonetheless, I think there should be a slight statistical advantage to picking the least represented letter. Obviously try and adjust the choices for the letters you know are incorrect.

My stats knowledge is fairly limited so maybe a math guru might want to chime in on this.