"Egalitarian" means having to do with the idea that all people deserve to be treated equally, so the answer choice closest in meaning is "equal." As for the other answer choices, none are close in meaning to "equal": "equestrian" means having to do with riding horses; "crinkled" means wrinkled; "ideal" means conforming to one's idea of perfection or the best possible; and "swift" means speedy or quick.

"Impromptu" means unplanned, extemporaneous, off the cuff, or not scheduled in advance, so "unrehearsed," which means not rehearsed in advance, is the correct answer. "Planned" is an antonym of "impromptu"; it means organized or scheduled in advance. None of the other answer choices are close in meaning to "impromptu"; "athletic" means physically fit or having to do with athletes; "greedy" means overly concerned with the accumulation of money or other resources for oneself; and "faithful" means loyal and devoted.

If someone is “divisive” they cause a lot of disagreement between people and cause them to separate into different groups. "Divisive" shares a root with "division" and "divide." If you are “factious” then you are inclined to create and maintain small groups or factions. Do not mistake it for “fractious” which means causing trouble or hard to manage. To clarify, “undermined” means to make weaker or less effective, usually in a secret way; “determined” means working hard to achieve something; “regretful” means wishing you had not done something. 

"Intriguing," means to arousing curiosity or interest, so "interesting" is the best answer.

If a business is “lucrative,” it makes a lot of money or it is able to make a lot of money. “Profitable” also means able to make a lot of money or profit. If something is “hindering,” it prevents something from moving forward. You can tell the meaning of the word "hindering" from its root word "hind-," which means back. An animal’s “hind” legs are their back legs. “Recreational” refers to something done in one's spare time. “Sensational” means shocking or amazing.

"Formidable" is an adjective that means "inspiring fear or respect through being impressively large, powerful, intense, or capable." So, we need to pick out an answer choice that means something like "inspiring fear or respect." "Afraid" may look like a potentially correct answer, but "afraid" does not mean "inspiring fear," but rather "feeling fear or anxiety; frightened," so it cannot be the correct answer. "Accomplished," however, is an adjective that means "highly trained or skilled," and because "accomplished" is the answer choice that is closest in meaning to "formidable," "accomplished" is the correct answer.

"Potent" is an adjective that means "having great power, influence, or effect," so we need to pick out an adjective that means something like "powerful" or "having a strong effect." "Frail," then, cannot be the correct answer, because "frail" is an adjective that can mean "of a person: weak and delicate," "easily damaged or broken; fragile or insubstantial," or "weak in character or morals," making it an antonym, not a synonym, of "potent." "Mighty," however, is an adjective that can mean "possessing great and impressive power or strength, especially on account of size" or "of an action: performed with or requiring great strength." Because "mighty" is the answer choice closest in meaning to "potent," "mighty" is the correct answer.

"Potent" means powerful; Unfortunate means unlucky; Immortal means able to live forever; Memorable means easily remembered; and Critical means important.

"Drowsy" means sleepy or tired.

Something that is "intricate" is complex and complicated. For clarification, an "outlier" is something or somebody that is outside of the norm; "serendipitous" means owed to good fortune.