The AI might not need to play dumb. There's no reason I can think of that an AI must be good at math or embed encyclopedias. Asimov had a short story, whose name I can't remember, about an AI that believed it was human.
I think it isn't so much that an AI has a good reason for that but rather that there is no good reason to have an AI incapable of it.
Of course, an alternate solution may be just around the corner--imagine talking to a person who has some sort of direct interface to Wlfram|Alpha (maybe Google glasses or something like that)--he would be able to answer those questions as easily as a computer, for the same reasons.
