“Nemesis” is a noun that can mean either “the inescapable agent of someone’s or something’s downfall” or “a long-standing rival; an archenemy.” So, a superhero and a nemesis form a pair of rivals, and we need to pick out an answer choice that also consists of two nouns which form a pair of rivals. While “ally is to friend” and “competitor is to rival” might each look like a potential correct answer, “ally” is a synonym of “friend,” so the two words cannot represent a pair of rivals and “ally is to friend” cannot be the correct answer. “Hero” and “villain,” however, do form a pair of rivals like “superhero” and “nemesis,” so “hero is to villain” is the correct answer.

“History” is a noun associated with time that has passed, while “future” is a noun associated with time that is yet to pass. So, we need to pick out a pair of nouns in which the first noun is associated with the past and the second noun is associated with the future. While “present is to past” and “yesterday is to tomorrow” might each look like a potentially correct answer, “present” is not associated with the past and “past” is not associated with the future, so “present is to past” cannot be the correct answer. “Yesterday,” however, is a noun associated with the past, while “tomorrow” is a noun associated with the future, so “yesterday is to tomorrow” is the correct answer.

Mirthless means not happy or amused and is therefore an antonym of amused. To solve this analogy you must therefore identify the best antonym for jaunty. Jaunty means carefree or without worries so the best answer choice is “troubled.” For clarification unabashed means shameless; nondescript means unremarkable; jumbled means mixed-up; something done in jest is something done for a joke.

Serendipitous is an antonym for unfortunate so to solve this analogy you must find the best available antonym for upbraid. Upbraid means scold, chastise or reproach so the best antonym is “praise.”

"Tropical" is a type of climate that would generally be very hot, and frigid means very cold; to solve this analogy you are looking for the opposite of the type of temperatures that would be associated with a polar climate. A polar climate would likely be very cold, so the correct answer is the antonym of cold, “hot.”

"Doleful" means very sad, and "jubilant" means very happy, so to solve this analogy you know you must identify the best available antonym for "tentative," which means to be unsure and careful as a result of that uncertainty.

"Inconspicuous" means difficult to notice which is an antonym for "obtrusive," which means highly noticeable. You must therefore identify the best available antonym for "glacial," which describes something very slow moving (like a glacier); thus the best antonym is “very fast.”

"Prohibited" means forbidden and is an antonym of "encouraged;" therefore, you must identify the best available antonym for "circumspect," which means prudent, considerate and thoughtful, so the best antonym is “inconsiderate.” For clarification, "judicious" is a synonym for "circumspect;" "extroverted" means outgoing; "utopian" describes a vision or representation of an ideal of perfection.

Excessive and minimalist are antonyms. Excessive means to have or be too much; minimalist means providing only the least needed. So to solve this analogy you have to determine which of the answer choices is the best available antonym for discordant. Discordant means in disagreement or incompatible. So the best antonym is “harmonious” which means in agreement or peaceful. For clarification, "cantankerous" means bad-tempered; "ineligible" means not allowed or qualified to do something; "portentous" means self-important; "ludicrous" means ridiculous.

Absence is the antonym of presence so to solve this analogy you have to identify the best antonym of conceal. To "conceal" something is to hide it so the correct answer is “reveal” which means to show something.