Largely agree with Rob but having faced this question and discussed it with associates and senior associates, the resounding takeaway that I’ve heard is that they want to know whether you can effectively communicate and delegate. In the first place you need to check with the partner about your conflicting deadline. If the work has been given by two different people (say, a partner and an associate), seniority pulls rank. You do the urgent work for the partner first (after having discussed the deadline with them) and then revert to the associate about the deadline to see whether 1) you’ll still be able to meet it, 2) there’s any flexibility, 3) there’s anyone available to jump in and help out.
As Rob said, different firms will have different “best answers”. If it’s not a multiple choice question, I’d try to set out the different points to take into account and then reason why you’d act one way over another (and whether particular factors might influence how you act).
Other people likely disagree but I think as long as you can demonstrate those key competencies (communication, delegation, organization), you’re on the right path.
