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If you have an offer expiring about a week after an upcoming CB interview at your top choice, should you notify the interviewing firm a few days before the interview to give them a heads-up, or should you wait until immediately following the interview?

Also, if a firm inquires about what firm the competing offer is from, should you tell them? I assume there's no harm in doing so, right?

Is your CB at a firm you'd rather be at? If so, I'd tell them about the offer, at the interview, and tell them you have an offer but you kept the CB because you are VERY interested in the firm. Everybody wants to be desired, and some firms like that a lot more than others, but it won't hurt. When I was asked what firm, I generally told them.