I look for a couple of things in an RCG (recent college graduate):
1) have they ever had a job of any kind? You'd be amazed at how many haven't EVER had ANY job. These are bad risks IMO; they don't understand that an 8:00 start time means damn it, you're HERE at 8:00, not 8:15, not 8:30! The kind of job is a factor, but I don't expect too much in the way of relevant experience. Working a customer service job is a bonus -- shows they can interact with grownups. If they worked their way thru college, double bonus points.
2) Why are they applying to your company? (and not someone else) Are they doing it because your office is near a ski area? Or the ocean? or because their interests professionally align with the type of work you do. (I had an applicant who really wanted to work in the Northeast because of the amateur hockey opportunities; I pointed out that New Mexico is not the center of the hockey universe. How long would he stick around?!).
3) A tough one is finding out if they have any motivation to do a quality job, to grow professionally, and give the company their undivided attention. No on-the-side jobs, no internet business. Are they a socety member (ASHRAE, ASME, etc) and active? Did they take the Fundamentals?
4) Do they consider their education over? This is one of the hard ones too. A lot of them think they're done. I know how good that feels, after maybe 18 yrs of school, but it's just the beginning! If they don't want to embrace that, they are destined to be losers.
MikeHalloran, your ploy of not telling the answer rings home! I interviewed Dow Chemical in Chicago in '75, and the interviewer asked a "test" question that has been driving me crazy for 30 years! He did it to others in my class, all of us will remember him for a long time!