What does a burnt resistor result in?
When answering exam questions you unfortunately have to make assumptions. If no numbers are given then you generally are expected to assume an extreme case, the extreme cases would be open-circuit or short-circuit, the question makes no sense with the short-circuit assumption, so open-circuit it is.

Open-circuit is certainly one plausible outcome of a resistor "burning out", but I would not assume during actual circuit design that it was the only possibility.