"Gainsaid" is the past tense of "gainsay," which means to contradict; this means that Alfred's answer was wrong, so he would not be relieved. If we were to choose "derided," the professor would have made fun of Alfred's answer, and Alfred would once more probably not be relieved. "Denigrated," meaning criticized, also seems unlikely. We might be tempted to choose "ignored," but "corroborated," meaning made certain or attested to the truth and reliability of, is a much better choice. 

The semicolon separating the two clauses tells you that the second clause will further explain the first clause. In this case, you want to know what happened to the man's political views; the second clause tells you that he became "set in his ways." This lets you know to look for a word that means became inflexible. The best choice here is "ossified," which means hardened like bone into an unyielding substance.

The hiring process is sped up for the candidate, despite the "usual requirements." The correct answer will show the requirements were eliminated in the candidate's particular case. "Waived," meaning let go or dismissed, is the best choice.

The key word in this sentence is "annoyed," indicating the author disagreed with the conspiracy theories. He would not attempt to support any of their claims, so the correct answer should indicate criticism or skepticism. Of all the choices, only "debunking," meaning exposing false ideas, makes sense in the sentence.

The young man's attempt to avoid trouble with his parents means he was not telling the truth or avoiding difficult subjects. "Equivocate," which means speak ambiguously, is the only answer choice with that meaning, as all the other choices indicate either excessive speaking, forthrightness, or both.

A "contrarian nature" means the subject of the sentence would support causes because they are unpopular. "Debunk," "criticize," "obviate," and "mock" would all mean he was going with the popular opinion. "Advocate," meaning to support or argue for, is the correct answer choice.

We need a word that describes an action that is opposite of what people do when they are blunt and honest. They are unclear and speak ambiguously, meaning they "equivocate." "Castigate" means harshly criticize, while "titter" means giggle quietly.

The reference to an "executive board" and "bylaws" indicate an official process is taking place in the organization. The correct answer will not only indicate that, but also the approval given by the "executive board." "Ratify," meaning to approve officially, is the correct answer.

The "clue phrase" in this sentence is "not only . . . even . . ." This indicates an intensification from the first portion to the second portion of the phrase.

Let us consider each of our options. The first two that we can eliminate are "derided" and "spurned." These both imply a negativity that doesn't make sense given the clue phrase.   "Lauded" might seem to fit, but it really would prevent us from having an intensification from the first to the second part of the phrase.  We are left with "accepted" and "considered." This is a tricky last set. The intensified word in the second half of the phrase is "hailed;" therefore, it is more appropriate to choose "accepted" as being the word to be intensified since it is least ambiguous regarding the scholars' approval of the conclusions. "Considering" can merely mean thinking about the topic, not necessarily accepting it (though that could—but not necessarily—be the case).

Even if the word "filibuster" is unfamiliar, the phrase "delaying votes" gives a good enough definition to find the answer. The correct answer will in some was mean delaying.  "Hindered," meaning to obstruct, is the best choice among the answers.