dfenton, Allen's approach is nice, but an interviewer doesn't want to see how you know have you a scheduling problem. He wants to see you handle your OWN scheduling problem.
My answer is simple:
If I'm the boss I delegate one of the conflicts to one person and the other conflicted event to another person.
If I'm not the boss then I ask the boss which one is more likely to get me fired if it is late.
If they ask why I didn't suggest that I would do overtime, I would point out that we hadn't talked about company rules on overtime yet. Believe it or not, in my job with the government as a contractor, I am not allowed to work overtime without explicit approval for every separate event!
Vassago, I used to love to conduct fishing expeditions. I would tell folks I was going on one, then ask them what they knew about finite state automata or Monte Carlo methods or simplex optimization. Not because I expected them to know anything but I wanted to find someone who knew just enough to get in trouble with it. The ones who HAD to have an answer were suspect. The ones who would admit that they didn't know about some particular topic were honest. Those, I hired. Because kids don't understand that it isn't what you learned in college that counts. Your bosses will teach you the particulars of your job anyway. It is attitude and the ability to adapt that gets you hired.