University of Texas Professor Art Markman has written a good column for Fast Company about job interviews. He offers some good advice for how to handle the challenging interview question that has you stumped. His advice boils down to three key ideas:
1. Don't try to BS your way through an answer if you are clueless about the subject matter. You will do far more harm than good with this approach. You will be much better off acknowledging what you don't know, while demonstrating an eagerness to learn quickly on the job.
2. Make the interview a conversation. Ask questions for clarification if you are stumped. Probe to learn more about the interviewer's intent with the question that he or she has posed. Sometimes initiating that conversation will make things much clearer for you, while also building rapport with the interviewer. In many cases, a reframing of the question will spark a thought for you that will help you provide a thoughtful response.
3. Remember that the interviewer may have asked a very tough question with a clear purpose in mind... namely, he or she may want to evaluate your ability to handle adversity and to navigate a difficult conversation. Keep your cool in these situations and remember that you don't have to knock every question out of the park to get the job. Focus on the big picture... explaining why your skills and capabilities will benefit the organization.
I would add one other key piece of advice. If the question is technical in nature, be ready for the topic to come up in a second or third round interview. Be sure that you have done your research and are prepared to answer the question in a subsequent interview. That type of good follow-up will be viewed very positively by most organizations.