The word “vivid” is related to words like “vivacious,” “survive,” and “revive,” all of which have to do with being alive or liveliness. While the word can mean “lively,” it is often used to describe brilliant colors. The word “radiant” best captures this sense, for the word “radiant” means “shining” or “emitting energy.”

The word “diffuse” comes from roots that literally mean poured away from. The “di-” prefix means away from or down from, and the “-fuse” means to pour. This latter is found in words like “infuse” (meaning, literally, to pour into) and “effusive” (meaning pouring out, implying that someone “pours out” a great amount of something like praise). As a verb, the word “diffuse” means to scatter or to spread out, as when one diffuses a smell into a room or when an idea diffuses through an entire population. The word can likewise be used as an adjective, basically having the meaning of the past participle of the word, namely “scattered.”

"Desolate" comes from the same roots as "sole" (alone), so it makes sense that "desolate" means stark and deserted, so "bleak," which can mean bare and gloomy, is the correct answer. 

As for the other answer choices, “archaic” means ancient, outdated, old-fashioned; “discreet” means wary or purposely subtle; “resigned” means accepting of one’s fate; and “explicit” means obvious and not subtle or hidden.

"Liber-" is derived from the Latin term for free, so it makes sense that a “libertine” is a person who behaves without regard for moral or societal rules about sexual relationships; most often, this word is used to describe men. This means that “philanderer" is the best answer choice, as a “philanderer” is a man who has casual sexual relations with women. As for the other answer choices, a “philosopher” is someone who studies philosophy, that is, questions that concern the nature of being and knowledge; an “instigator” is someone who provokes or starts conflict; an “imitator” is someone who copies someone else; and “testament” means evidence, proof, or something that serves as evidence of a fact.

The word "divisive" clearly comes from roots related to "divide," meaning to cut up. When someone makes "divisive remarks," that person ends up dividing himself or herself from a group of people. Indeed, he or she often causes the very group to break apart because of how people take sides in response the comments. Thus, a good synonym for "divisive" is "alienating," which describes something that causes similar rifts and anger.

The word "vitality" comes from the same roots as "vital," which means either "essential" or "having life." The root word vita is found in Latin and means life. Now, the "vital signs" for someone in a hospital are the signs that indicate how healthy that person is. Thus, "vitality" is the state of being healthy. The word "energy" is the best option among those given for a potential synonym to "vitality."

The word ardor comes from the Latin for to burn. It is related to "ardent," which describes someone who is passionate. (An ardent person "burns" with devotion and passion.) We would use ardor to mean a state of passion, as in the sentence, "He was filled with ardor for the woman whom he loved." This indicates a kind of intensity. Thus, "intensity" is the closest synonym among the options provided. The words "difficulty," "trouble," and "exertion" all try to get you to confuse "ardor" with "arduous". The latter means difficult, but that is not the meaning of "ardor."

The word "mutable" comes from Latin roots that mean to change. A genetic mutation is a change in a gene in a cell. While such mutations can have very negative effects, these are not the same as the mutation itself. To be mutate is to change. Therefore, the best option among those provided is "fluctuating" which alone among the possible answers indicates change.

The word "dismiss" comes from two Latin roots that are familiar. The "dis-" means away from and is related to the "de-" that we find in "descend" and "deconstruct." The "-miss" portion is the same as that found in "missive" (mail / letter) or "missile." Thus, to "dismiss" means in its roots to send away. The English meanings therefore include things like to reject, to send away, and even to fire from a job. It is this last sense that is most important for this question. If an employee is dismissed, he or she is fired. To be "terminated" is to be brought to the end of one's service. ("Term-" comes from Latin meaning "end", as we see in the word "terminal" used in airports.)

The word "arcane" comes from the Latin for closed up. The word "arc" comes from similar roots. When something is described as being arcane, it is mysteriously closed up from people's knowledge. Often, this has connotations of being magical. This is not, however, the primary meaning of the word. Thus, the best option here is "mysterious." Be careful not to mistake "arcane" for "archaic". The latter means, Ancient or out of date. These are not the same, even though some archaic things might be arcane because of their age!