LIC AAO Model Paper 8

Prolix (Adjective) means (of a speech, writer, etc.) using too many words and so boring to listen to or read : a prolix speaker.
Her style is tediously prolix. Prolixity is the Noun form of the word prolix.
So, the word prolixity and brevity are clearly antonymous.
Brevity means shortness or briefness; conciseness.
For example,
He is very famous for the brevity of his speeches.