"Keen" means either eager or sharp-witted. So, "sharp-witted" is the correct answer. For clarification, "banished" means sent away, and is an antonym of "welcomed," which means amiably received. "Ill-tempered" means crabby or cranky, and "jocular" means jovial, playful, or funny.

"Mercurial" means unpredictable, capricious, or mysterious, so "unpredictable" is the correct answer. For clarification, "fey" means supernatural, "notorious" means infamous, "profane" means rude and disrespectful or worldly as opposed to spiritual, and "magical" means of or related to magic or extraordinary.

"Ostentatious" means showy or pretentious, so "showy" is the correct answer. For clarification, "parsimonious" means stingy or not generous, "destitute" means very poor or having no possessions, "abstinent" means refraining from doing something, and "messy" means unorganized or dirty.

Someone who is "astute" is smart, shrewd and quick-witted, so "shrewd," a word that means clever, is the correct answer. For clarification, "imprudent" means not prudent or rash, as you might be able to infer from the word being a combination of the root "im-," which means not, and "prudent." "Daft" and "harebrained" can each mean absurd or foolish, and "thoughtless," as you might guess, means done without thinking, and specifically done without thinking about the emotions of others, or in other words, inconsiderate. 

Someone who is "imperious" is very arrogant and self-assured, so "arrogant" is the correct answer. For clarification, "pious" means deeply religious, and "sanctimonious" means self-righteous or smug.

Someone who is "pugnacious" is aggressive, hostile and belligerent, so "belligerent" is the answer choice closest in meaning to "pugnacious" and the correct answer. For clarification, a "rendezvous" is a secret meeting, "devout" means very religious, "repugnant" means gross or unpleasant, and "munificent" means generous or plentiful.

Someone who is "rancorous" is merciless, relentless or implacable. For clarification, "noxious," "toxic," and "poisonous" are all synonyms.

"Bombastic" means long-winded, insincere, or verbose, and is often used to describe speech. "Verbose" refers to unnecessarily long speech, so it is the answer choice closest in meaning to "bombastic" and the correct answer. For clarification, "forlorn" means sad and hopeless, "banal" means mundane or boring, "umbrage" means offense, and "prophetic" means predicting what will happen in the future.

Someone who is "wily" is crafty and cunning and possesses guile, so "cunning," an adjective that means shrewd, is the correct answer. For clarification, "fortunate" means lucky, "excessive" means too much or extreme, and "opulent" means wealthy or fancy.

"Gregarious" means friendly and sociable, so "sociable," an adjective that means cordial or affable, is the correct answer. For clarification, "fulsome" means flattering or excessive, "vicarious" describes something that is experienced through another person, "introverted" means shy, and "lonely" means isolated or friendless.