The unusual thing about online purchases, is that in addition to the #, the name on the card and the expiration date, the good online sites will also ask for your Security Code - which is a 3 digit number near your signature.
It doesn't appear on statements b/c it is not part of the cards electromagnetic info and it is illegal for any website/company to store that # (except for the credit card companies themselves). It has to be verified and then immediately discarded. This # also does not appear on any receipts or statements, also by law. But again, not everyone uses it/requires it.
AND, they also ask for your address, as the credit card companies use that to verify online purchases. I think this person probably had all this info, but how they got it, who knows.
I'm not sure what they were doing at Monster, but I would think they should be able to find out...
If they were using it to post resumes, then look at the resume info and contact phone numbers. If they were using it to post jobs, then again, look at the contact info. If they were using it to buy merchandise (I know, people buy t-shirts here?), then where was it shipped? Maybe Monster recorded the IP of the person who used your card, etc. - and the credit card people MIGHT be interested in this info.