There are three kinds of unexpected questions for which you need to prepare.
First, are standard questions for which you didn’t prepare. This might be something great research would have prepared you for, but you didn’t have enough time to prepare with that much depth. For example, “You probably saw the results of our ABC project on our website. We did that with software tool A. I saw on your resume you know how to use software tool A and B. How could we have done it better if we had used software tool B?”
In a case like this, if your research didn’t get far enough that you saw this, you can’t really answer the question as asked, so you need to change your approach.
A good first step is to admit that you missed this part of their website during your research and immediately ask a question: “I love software tool B! I went through your site quite a bit a few days ago but I didn’t see the ABC project. Can you tell me a little more about it and why you used software tool A?”
Once they have answered your question you are now in a better position to give a great answer to their original question—don’t forget to do that when they are done!
Second are behavioral questions for which you have no prior experience. They ask you to “tell them about a time when you managed a large team on a project” and you’ve never worked on a team with more than three people. The best way to approach this situation is to answer in the hypothetical, but drawing on any related experience you have.
“I haven’t had an opportunity yet to manage a really large team. In managing small teams in the past I’ve found communication to be really important. If it was hard sometimes with three people I’m sure it would be even harder with a larger group. I’ve always tried to make sure there was a process in place to make communication easier, for example in my last internship my three-person team was managing a project and we only saw each other in person once a week so…”
Asking a question is also a great way to re-frame this question, allowing you to give a better hypothetical answer:
“I’ve worked with a number of small teams, but I haven’t had an opportunity yet to manage a really large team. Could you tell me a little more about some of the challenges team leaders have seen here in the past?”, then armed with their response about specific challenges you can try to give examples of how you would meet those in the future if given the chance, always remembering to back up your answer with related examples from your past.
Third are the “wild card” questions that some interviewers will throw in to test your reaction to the unexpected, or how you handle pressure. If you read the section of the guide on different interview types, the “stress interview” is often contains several of these types of questions. They are typically “unanswerable” in the sense that you can’t come up with a specific, accurate response based on the question itself.
For example, “How many cars are on the road in the U.S. right now?”
Do they mean cars physically in use and driving? Cars mechanically capable of being driven, but parked? Registered vehicles? And by “right now” do they mean right this second? In a typical day? You could start to ask clarifying questions like these, but in most cases the interviewer won’t answer. Part of the reason for questions like these is to see how you handle pressure and how you deal with limited information, so they probably won’t answer clarifying questions—because the goal isn’t to come up with an actual, final, factually correct number—it’s to see how you would approach determining the number. Do you use logic? Do you consider all the angles? Do you jump to conclusions without thought? There are many versions of this question. The trick is to recognize the question for what it is—ultimately unanswerable—and logically work through a thought process to find an answer based on lots of assumptions, being sure to share your assumptions and thought process as you go.
Often these questions do require, and therefore help reveal, if you have broad general knowledge about the world, so be careful, don’t get nervous, and be sure to think things through. For example, a good starting point for this question might be starting with an estimate of the total population of the U.S. While it literally varies minute by minute as people are born and die each day, there is a common agreed upon estimate based on the census, give or take a few million. What is it? As long as you state your initial assumption you could still come up with a logical answer if you were way off on your U.S. population estimate, but it might be embarrassing if you are off by a lot (the answer as of right now is about 325 million). Giving an estimate of 300 million might be forgivable. Panicking and saying 30 million might raise some alarms.