When we describe something as being "manifold," we mean that it involves many different aspects or elements. Thus, the word "numerous" is the best synonym. When we say, "The requirements for the position were manifold", we mean, "There were numerous requirements for the position."

When something is exhilarating, it is exciting or thrilling. This does not mean that it is dangerous, though dangerous things are often exhilarating precisely because of their dangerous nature. Thus, the best option is "invigorating." "Vigor" is energy or enthusiasm. To say that something is "invigorating" is to say that it fills one with energy. Something that is exhilarating does this insofar as it is exciting. Thus, this is the best option among those provided.

When something is "inferior," it is beneath something else. (That "higher" thing is said to be "superior.") The word can be used to describe people. Thus a worker is the "inferior" to his or her boss. The word can also be used to describe things that are deficient in quality. Thus, you could say, "The corn that I bought yesterday was of inferior quality." This means that it was not as good as it could be. The options "minimalistic" and "simple" attempt to have you choose incorrectly. Something that is inferior is subpar or sub-standard. Neither "minimalistic" nor "simple" express this kind of deficiency. Hence, "deficient" is by far the best option among those provided.

Something that is "revolting" is disgusting. Now, this could also be the present participle of the verb "revolt," meaning to rebel, but none of the options presented match that meaning. Therefore, we are looking for something that is akin to "disgusting." While something that is "rotting" is likely to be disgusting, this is not the same being revolting, as "rotting" refers to a specific process of organic decay, not the feeling produced by that process. The only option that provides a direct synonym is "nauseating," which describes something that is sickening (in the way that something revolting is sickening).

The word "progressive" can be used as an adjective to describe a process that changes one step at a time. To make progress literally means "to step forward." (The word "gradual" comes from the same Latin root.) Additionally, the word can also be used to describe something that has already made such progress—a progressive idea is one that is forward-thinking. For this question, the only option that functions as an adequate synonym is "developing." If someone has a progressive disease it is "developing" (in the sense of increasing in its strength and the damage that it is doing).

When something is "mutual" it is held by multiple people. For example, three people could have a "mutual hatred" for corn on the cob. This hatred is common to each of the members of the group. We also speak of a "mutual enemy". This very clearly means "common enemy." Thus, "common" is the most obvious choice for this question.

The adjective "extensive" describes something that covers a large area—whether literally or metaphorically. An extensive plot of land is a very large plot of land. An extensive collection of books "covers" many topics and authors. Extensive knowledge "covers" many topics. (You can think of it meaning that each of these "extends" over a large area.) Now, this does not mean that something that is "extensive" completely covers its given "area;" however, it can seem close to being complete. The word "exhaustive" means comprehensive. At least among the options provided here, this is by far the best.

The word "fragile" means weak or easily broken. Now, most of your options are likely tempting, for they remind you of glass, which is easily broken, but the only option that directly indicates a kind of fragility or weakness is "delicate." When something is "delicate," it is not very strong. Sometimes, we speak of "delicate health" in someone who is sickly. We can also speak of a "delicate situation," meaning that the situation could fall apart easily.

When something is tainted, it loses its purity. For instance, a water supply can be tainted by having small amounts of paint poured into as well as small amounts of soda. In both cases, the water supply loses its purity. Tainting does not have to do with poison necessarily, so be careful not to choose an answer based on this. Instead, the best option is "polluted," which can apply to any kind of the actions mentioned above as examples of tainting.

The word "superfluous" comes from Latin roots that literally mean overflowing. (The "super-" prefix means "over or above" and "-fluous" clearly means "flowing.") When something is "superfluous," it is excessive or beyond one's current needs. While such things could be "overwhelming" or even outragous / exorbitant, they are always unnecessary. Thus, this simple word is the best option for this question!