The word "obsequious" means excessively eager to please or obey someone in authority. Therefore, the word that is most nearly the opposite in meaning to "obsequious" is option B, "brusque."

When someone is "obsequious," they are overly deferential and submissive, whereas someone who is "brusque" is blunt, curt, and often appears rude. The two terms are essentially opposites in meaning, with "obsequious" describing someone who is excessively compliant, while "brusque" describes someone who is dismissive and impatient.

Option A, "quick-witted," means having a sharp and clever mind, which is not directly related to "obsequious." Option C, "sharp-tongued," means critical or insulting in speech, which is also not directly related to "obsequious." Option D, "luxurious," means extravagant or indulgent, which is not directly related to "obsequious." Therefore, B is the best choice as the opposite of "obsequious."