If they want to make it a real competition they can ask a question that at least people need to resort to google to answer or a riddle type question. Particularly annoying if the prize is tickets to see a sold out event, instead of favouring hard core fans with a tough question they give a question that a 4 year old could answer.
Part of their thinking is likely to be market research, guessing trends in listenership from the number of answers, if everyone always knows the answer then it makes it easier to spot the trend.
Some of it could be profit motivated, depending on how the answer is required to be sent in (rarely via email). There's some high profile RTE tv programs that run quizzes that almost certainly result in a profit for someone, since the entries are 1 euro a call. Wouldn't happen at the beeb.