From the context of the question you can infer that the Prime Minister had no time for advisors who were not honest and uncompromising. Of the five possible answer choices only sycophants refers to someone who is dishonest. A sycophant is literally a person who flatters someone powerful for personal gain. Vagabonds are homeless people; merriment refers to great happiness; rancor is resentment; theologians are people who consider the nature of God and religion.

The sentence implies a contrast between the answer and the word “enrage.” It is not a complete contrast but a case of intensification, for the answer is said to be “nothing more” than something (i.e. something relatively small in comparison with being enraged). While a number of the options pertain to anger, the word “irritant” best captures the sense of “making someone slightly angry.” The word generally is applied to something causing a bodily sore but it also can be applied to people in the sense of being annoying.

Since citizens had to take “all precautions,” they had to exercise great care and indeed awareness of any potential personal data that might be placed into the trash. When one exercises awareness, he or she is said to be “vigilant.” The word is related to “vigil,” which is the act of staying awake in order to wait for someone or something. Someone who exercises “vigilance” does not “fall asleep at the wheel”—metaphorically speaking—and does not overlook dangers.

The key expression in this sentence is “for favoring any party . . .” The answer must be a word that describes the act of such favoring (which the leader must not show or do). When someone shows partiality or is partial to something, he or she shows a bias in favor of that thing, often for reasons that are not adequate. It often can merely mean “favoritism.” You can think of it as one “taking the part (or side)” of some favored person.

The key thing to note is that the arsonist must totally repay the value of the organ. When someone restores stolen or damaged property, such a payment is called “restitution.” The “-stit-” portion of the word comes from the Latin for “to stand,” though it takes on the meaning of “returning to a state in which something stood before.” (As you can see, the sense is metaphoric.) This base word is found in many English words like “institute,” “substitute,” and “statue.” Note that “restitution” can also be repaid for general losses and injuries, not merely property damage.

Since the politician’s fortunes had changed so greatly, it is fair to say that he has gone from being “on the top of the world” to being on the “lowest rung.” When one is at his or her “nadir,” he or she is at the lowest point of his or her fortunes or accomplishments. Do not be tempted to think that the best option would be “ruination” or “unraveling,” for while these may indeed be true, the focus of the sentence is clearly on the fact that this is a low point in comparison with the rest of his career.

The key thing to note here is that the appointee is being assigned to a colonial office and that said person will be acting as a representative, not as a replacement. Such a person is called a “viceroy.” The prefix “vice” means “in the place of,” as one sees in the case of “vice president.” The ending “roy” is related to the French for king, “roi,” which ultimately is related to other words from the common Latin base meaning king or ruler, as founding words like “regal,” “reign,” and “interregnum.”

The pivotal clues for this sentence are “initial evidence” and “potential research project.” This implies that the person has not yet started the project. While perhaps he or she could be presenting "opinions," the general implication is that he or she is undertaking some new research. When we start projects of this sort, we often lay out a thesis or hypothesis, upon which we will further elaborate with the passage of time.

The wall stands between two areas, functioning as the means by which sound passes between rooms. Though some medieval men had intriguing reasons for misunderstanding this phenomenon, we know better now. The word “medium” means middle or between. It can be used as a noun meaning the substance traversed by something like light, electricity, or (indeed) sound.

The key thing to note is that the butler serves in such a way as to often overlook his own desires. This does not necessarily imply love or even uprightness, but it does imply that he is unwavering in his service. Such a spirit is one of “dedication.” The word comes from the Latin base for the word for “consecrating” and is also somewhat related to words like “dictation,” “diction,” and so forth.