Something “astonishing” is very surprising (and perhaps also amazing). The sense of this analogy is, “Something astonishing is very surprising, as something X is very easy.”   Among the options, “vapid is the best.” The word originally comes from a usage meaning “having little flavor.” However, it has come to mean, “being completely unchallenging or not stimulating.” Sometimes, we will refer to “vapid music” that really just repeats several very simple chords over and over. It is “easy” for the listener, requiring little musical knowledge or thought. We could say by extension that something that is “vapid” is something that is very easy.

Something that is “overwhelming” is so extremely challenging that it “defeats” the person attempting it (or overcomes them by its force / difficulty). The bridge sentence is a bit difficult here, for you need to read “dislike” not as a verb but as a noun. We do this when we say something like, “He had a strong dislike for pizza.” A “strong dislike” is an “aversion,” which is one of our options. None of the other potential answers capture the same sense of disliking something greatly.

A “bellow” is a very strong type of speech, often loud and caused by pain. The general sense of this analogy is that a bellow is a louder and stronger type of enunciation than speech. A way to form a bridge sentence would be, “As bellowing is much stronger and louder than speaking, so too is X much stronger than crying.” Among the options, “lament” best describes this kind of “extreme crying,” for a “lamentation” (an act of lamenting) is a very passionate kind of crying. All of the other options are too weak and do not express this sense of “really crying.” “Rage,” though strong, does not deal with crying but instead with anger.

Something “exhilarating” is often thought of as being very “fun” or “exciting.” In general, the term means “something causing great joy or pleasure.” In the parts of speech provided, we can say that the analogy’s sentence form is, “As something exhilarating is very pleasing, so too is something X very thin.” Among the options provided, “emaciated” means “very thin” (perhaps malnourished). The other options do not express this sense of extreme thinness.

Someone who has expertise in a given subject has a great deal of ability in it. Therefore, we are looking for a word that will express the state of having a great deal of strength.   Although the word “puissance” is a bit out of date, it does mean “having great power.” It is related to words like “potent” and “potentate,” which indicate power. Even if you did not know this word, you should be able to tell that none of the other options express either great strength or even (in the case of “weakling” and “fastidious”) anything related to strength (except perhaps negatively in the case of “weakling”).

Dolor is an emotion of great sadness. Therefore, the analogy represents a stronger form in comparison to a more general term. The bridge sentence could be constructed like, “As dolor is a type of great sadness, so X is a type of great or strong feeling.” When someone “vehemently” does something, he or she does it with great force or passion. Sometimes, we will say, “I vehemently disagree with you,” meaning by this, “I totally disagree with you and believe you are utterly wrong!” The option “vehemence” is thus the best option, as it means “having a strong feeling.”

Avarice is excessive or extreme greed, so the bridge sentence for this analogy would be something like, “As an avaricious person is excessively greed, so is a(n) X thing excessively fat.” To be obese is to be exceedingly fat. For this reason, this is the best option among the others, which either do not connote excess or are totally unrelated.

Something that is ancient is very old. When someone speaks of “ancient times,” he or she means “long ago.” For that reason, we are looking for a word that means “very large.” Although something very large might be “impressive” or “magnificent,” neither of these mean “very large” in a strict sense as does the word “gargantuan,” which is the best option among those given. Big is merely synonymous, not giving the additional sense of “to a great extent.”

When someone “exults,” he or she or she expresses great joy. The word “exultant” is the an adjectival form of this verb. We could thus say that someone who is “exultant” is “extremely happy.” Thus, we are looking for a word that means “extremely good.” Among the options, only “excellent” has this sense of “extreme goodness.” Both “desirable” and “fine” are not strong enough to answer to the needed notion of “great” or “extreme.”

To “inquire” after something is to look into it or to ask questions regarding it. Likely, you know the word “inquiry,” which means a process of formal questioning (perhaps in a legal case, though other options are possible). When someone “delves” into something, he or she “digs” into it very deeply. The word’s first meaning is “to reach into,” though it is often used metaphorically to mean “to dig into” or “excavate.” It likewise can mean “to research very thoroughly.” Thus, our bridge sentence is, “As delving is a form of deep and detailed inquiry, so too is X a deep and detailed form of reflecting (or reflection).” To “mull over” something is not merely to dally and consider it. It means “to think deeply and for a long time over something.” For this reason, it is the best option among those provided.