“Value” is a synonym of “worth;” both words have the same meaning, so to solve this analogy you have to determine the best synonym for “vacant,” which means not in use, available, empty. The correct answer is therefore “empty.”

"Sly" means the same as thing as "sneaky," just as "cunning" means the same as "clever," so "sneaky" is the correct answer.

A “crusade” is a major effort to change something or one of several medieval religious wars where Europeans tried to retake the Holy Land from Muslims. A “campaign” is similar to a "crusade" in that it is a connected series of operations designed to bring about a particular result that often relates to war. “Infinite” means lasting forever; it is the opposite of “finite,” which means lasting for a certain period of time. So, since you need to look for a word that means the same as “infinite,” the correct answer is “forever.” To help you, “resurrected” means brought back to life after being dead.  

"Difficult" and "challenging" are synonyms because they have very similar meanings. So, to solve the analogy, you need to pick out an answer choice that consists of two words that mean the same thing. "Gullible" and "naive" both mean easy to fool, so "gullible is to naive" is the correct answer.

"Vex" means make angry, just as "anger" can be used to mean make angry. So, the two words are synonyms because they mean the same thing, and to solve the analogy, you need to pick out an answer choice that also consists of a pair of synonyms. "Cheery" and "gleeful" both mean happy, so "cheery is to gleeful" is the correct answer.

You likely know that “brave” and “bold” mean roughly the same thing. A “pariah” is a person who is rejected by other people. A “pariah” is generally someone who is cast out by society or an “outcast.” To further help you, to “curry” means to seek to gain favor by flattery or attention.

Big and tall have similar meanings, just as hard and tough do.

"Monarch" is a noun meaning " a sovereign head of state, especially a king, queen, or emperor," so "monarch" and "king" are synonyms. That means we need to pick out a pair of words that are also synonyms. While "duchess is to duke" may look like a potentially correct answer, "duchess" means "the wife or widow of a duke," or "a woman holding a rank equivalent to duke in her own right," so the two words are not synonyms; however, the word "tale" means "a fictitious or true narrative or story, especially one that is imaginatively recounted" or "a lie"; since its first meaning is the same as that of "story," the two words are synonyms, just like "monarch is to king," and "tale is to story" is the correct answer.

"Aroma" is a synonym of "smell" because they mean the same thing, so to solve this analogy, you need to pick out the answer choice that is closest in meaning to "fragment." Both "fragment" and "piece" refer to a portion of a whole. So, a slice of cake is a "fragment" or "piece" of the whole cake. So, "fragment" is a synonym of "piece," and "piece" is the correct answer. To help you, "fragrance" means the smell of something.

"Sanitary" means free of germs or contaminants, so "sanitary" and "clean" are synonyms because they mean the same thing. So, to solve this analogy, you need to pick out an answer choice that means the same thing as "fallible." "Fallible" means able to fail or make mistakes, so the answer choice closest in meaning to "fallible" is "imperfect," which means not perfect or able to make mistakes. None of the other answer choices are close in meaning to "fallible."