Interesting question. A really important exam would be one that's crucial to passing in a class that's necessary to graduate, especially where the class is a pre-req to other essential classes required to graduate.
I've gone in to exams without studying at all leading up, relying on what I remember from class and using every available logical inference from the test material to minimize the portion I would have to guess on randomly.
And when I've been forced to guess randomly in these scenarios, I've hedged guesses between questions that share plausible answer choices (chosem the same answer to different questions to ensure that I locked in points). It's interesting how tactics come into play on exams that don't require free writing type of answers. The typical test provides enough information to deduce freebies. It's like a cushion you enjoy from carefully studying the test itself.
These situations happen in life all the time. If you remain calm and play to beat the situation, you should be able to get some slack.