Hard questions come in many forms and contexts, in business and in life. Brett and Kate McKay write a lengthy primer on how to handle all of these questions. Here is a taste of it.
No More Questions on Questions
For starters, panicked impulse answers are seldom ideal. A moment of silence before answering can be powerful, because it shows you are really reflecting deeply on the question. Another thing to do is seek clarification when asked vague questions. If you want to really get certain, ask them to define the language they are using, or even define a word or qualify a point yourself. A third point of business discussed in the article is how to respond when, for various reasons, you outright do not want to or cannot give a full answer. In this case, you can choose to give a partial answer, perhaps try to reframe the question more favorably, or even discuss the nature of the question itself as opposed to giving a direct answer.
That is your taste. For the full meal, you can view the whole primer here: http://www.artofmanliness.com/2015/04/08/thinking-on-your-feet-how-to-answer-difficult-questions/