The word "affluent" does have roots that mean to flow. While this meaning was once upon a time reflected in the word, it no longer is used in this manner. Instead, the word means wealthy—as though someone is "flowing" with money. Thus, the only option that is appropriate is "prosperous."  (Note that "mobile" is not the same as flowing. A walking person is mobile—yet is not flowing, strictly speaking.)

Something that is "opulent" is very expensive, to the point of being showy. Thus, the word "lavish" is the only option that matches this meaning. Note, however, that "opulent" can be used as an adjective that means wealthy more generally as well.

As probably is obvious to you, the word "impassioned" is related to "passion," but this does not necessarily indicate being in love or anything of that sort. It merely can mean being moved greatly. Think of a "passionate attitude." This describes someone who experiences a great amount of emotional attachment to something. To say, "Paul is passionate about politics," is to say, "He really is devoted to and excited about political matters." Thus, the best synonym for "impassioned" is "ardent", which means enthusiastic. It actually comes from Latin roots meaning to burn. (A passionate person burns with enthusiasm, so to speak.)

Someone who is "infirm" is weak or sick. This has nothing to do with rigidity (as though it were like a "firm mattress"). Several options—elasticity and flexibility—attempt to have you misread the word in this manner. We often speak of the elderly as being "infirm" because of their weakness; however, "infirmity" is not the same as senility. The only option that is correct, therefore, is "malady". Inasmuch as an infirmity can be a sickness (in addition to a more general weakness), it is synonymous to "malady", which means disease.

Something that is "drastic" is extreme and often surprising. A drastic reduction in work output means that the amount of work being done has reduced significantly. The word "radical" comes from Latin roots meaning, to the root. A radical change is one that alters something significantly. This is the best option among those provided. Do not be tricked into "thrilling." A drastic event might be exciting or thrilling; however, this is not the direct meaning of "drastic."

The word "latent" comes from roots meaning hidden. A "latent" ability is one that is unknown and hidden to the one who possesses it. When something is "dormant" it is hidden in this way as well. The word "dormant" comes from the Latin for to sleep. It is as if something that is "dormant" is hidden because it is sleeping. (Think of a "dormant volcano," meaning one that is not active. Its power is hidden, so to speak.)

The word "culpable" comes from the Latin "culpa," meaning guilt. A culpable person is a guilty person. Thus, the best answer is "responsible." This is meant in the sense of saying that someone is guilty, as when we say, "He was responsible for the crime." Now, "condemned" and "imprisoned" may be tempting, but culpability is first and foremost about guilt. Whether or not it causes condemnation or imprisonment is secondary. Culpability is a matter of inherent responsibility, not the results of the action for which the person is responsible.

For this question, you need to be very exact when considering potential options. Often, we hear the word "heinous" used to describe a crime. This means that the given crime is extremely wicked or horrible. Among the options provided here, only "atrocious" is an appropriate synonym. Many "heinous" things are "illegal," "criminal," and "terrifying;" however the word first and foremost describes something that is extremely terrible and immoral.

Something that is "ludicrous" is ridiculous, amusing, and utterly foolish. While such things could be considered illogical, the word "illogical" does not exactly capture the ridiculousness expressed by the word "ludicrous." Thus, among the options provided, the only one that is appropriate is "preposterous," which means completely insane or crazy.

To "lament" something means to express sorrow or grief over that thing. Something that is "lamentable" is something that causes grief or sorrow for an understandable reason. Now, while it may cause sorrow, the primary meaning of a lamentable event or thing is horrible or extremely bad. Because it is so bad, it causes grief, but "lamentable" first and foremost indicates such a terrible situation. Thus, the best option among those given is "wretched", meaning horrible.