I'd say so. The "assuming time encoded"-bit is important though - I rather think starting with the data is valuable:

Can I assume the times are in a sane date format/datatype? If not, start with e1 = toSaneDateFormat(endtime1), s2 = toSaneDateFormat(startime2) (Fill in if interviewer is interested).

Then, as you say, a check for overlap is easy - but maybe one wants to be more fancy, like: if (timeDelta(e1, t2) < timeToWalkFromAtoB, or < 5 minutes -- they should be considered an overlap? If they are on different continents, maybe < 24 hours should be an overlap?

At any rate, I'm guessing (hoping) this leads to discussions about representing dates, and what the business logic is (eg: physical meetings - you can't teleport from one location to another).

[ed: And as others have touched on, if you deal with timestamps/raw number types - be careful that you don't end up with appointments in "wrong" order - I'd say a sort() aware of date-objects might be your friend here.

ed2: In fact, if you can assume a sane date-type, and timeDelta, you could probably assume an "interval" type, and simply ask for overlap?(appointment1, appointment2) ... ]