There is a lot of cynicism about these types of questions in this thread, but I suspect a lot of it is coming from programmers and not data scientists. As a DS candidate I always find these kinds of interview questions a valuable learning experience and a positive challenge. It also provides me some insight into the kinds of problems they're interested in, and the kinds of approaches they use.
When I mean "right approach", I mean that there are several possible approaches, but only one of them is doable in a few hours in the afternoons, where as the others might take a research team and several weeks. Being able to recognize the right approach, and to ask the right clarifying questions, is important for data scientists, in the same way that being able to choose the correct algorithm or data structure is important for (certain types of) software engineers.