Ummm ….to my knowledge @DroidsLookingFor , private boarding schools are not interviewing students for employment but are interviewing them to join their community as residential students. 
The most annoying set of questions (mentioned on CC in previous years) were those that asked my student to rank schools on their list and to name other schools applying to. This was done at multiple schools . This can be tricky for any kid to answer.
There are a couple ideas to tackle this type of question. There are smarter people than I on CC (eg @skieurope) who have good strategies for answering questions about other schools you’re applying to. Here is what we learned to do a while back during the interview process.
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Try to deflect the question to one of what you are looking for in a BS, rather than naming a specific school. “I am very interested in schools that offer XY, WP, and QRS…and your school offers all 3”
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Do be careful with answers if you are applying to both single gender schools and Co-ed schools. For example, when interviewing at single gender school and have just mentioned how important it is for you to be at an all -XYZ school….you may then be asked later what other schools are you looking at or applying to? If you list all co-ed schools, it sounds disingenuous.
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AO’s are interested in yield - that is why they ask some of these questions.