Understanding whether the question is asking for a "yes/no" answer or the solution to the problem is an issue of implicature.
Implicature is a technical term in the pragmatics linguistics, coined by H. P. Grice, which refers to what is suggested in an utterance, even though neither expressed nor strictly implied (that is, entailed) by the utterance.
In other words, when people say something, we have to use context and our knowledge of the conventions of language to determine what is meant.
For example, if you are out for a drink with a friend and he says, "Do you have any money?" he is probably not really concerned about your financial situation but perhaps suggesting that he hasn't got any and hopes you will pay for the drinks.
So, in this case, although they could just be asking if you are able to solve the problem it is far more likely that they are asking you to actually solve it.