I'm not sure that can be an interview question, only if the question is partial.
Did you ever considered to put such a question in an interview?
in order to estimate how many functional test cases you could/should develop for any application/functionality you need a lot more data:
- posible actions and inputs;
- posible inputs values;
- inter-relations between those actions;
Even when you know all these, there is a lot of work to estimate them...
... Not even me.
A good question and difficult to answers. So to say how many test cases are required, you may convert your requirements into function points. Using IFPUG's standard formula for minimum number of test cases i.e FPs raised to 1.2 you may have approximate minimum number of Test cases.
If you do not know how many FPs are there then take the LOC and using the standard conversion table to convert LOC to FP arrive at the funtion points. This table is again publised by IFPUG. Once you get application FPs arriving at minimum number of TCs is easy.