the question asks me to describe the writer's style (serious, sarcastic, etc.)

Question

what could be some other answers to this question?

Style has to do with HOW writers use words and sentences, as well a how they construct sentences, paragraphs, etc.

Style can be formal, informal, succinct, wordy, flowery, plain, and many others.

http://www.unc.edu/depts/wcweb/handouts/style.html
There's a good discussion of style here. The idea that it's rather subjective is a good idea to keep in mind.

If you need to look up any words, here is a good dictionary website: http://www.answers.com

Please re-post if you have further questions.

=)