First, you must note that "the latter" refers to the "latter person", namely Lee. Therefore, we could read the sentence: ". . . he was unable to prove Lee's __________."  From what we have been told, Thompson is certain of Lee's guilt. The best answer is the one that states that he cannot prove this (i.e. the guilt). The word "culpability" means guilt. It comes from the Latin "culpa", which means fault or blame. Someone who is "culpable" ("culp-able") is able to be blamed ("blame-able").

Since George believes himself to be a righteous man, he must believe that he does good deeds. However, the sentence indicates that this opinion is not held by others. This is indicated by the key word "although," which indicates the contrast of perspectives. While George thinks that he is rightesous, many others found his actions to be less than perfect. The word "conduct" can mean manner of behaving, so "conduct" is the correct answer.

When we cannot explain the reason for our belief, we are said to have a "hunch." Sometimes, we just "feel" that something "has to be the case." For instance, you know that someone is a liar and likewise has often been nasty to old women. Suppose that person came to your house, and at some point soon thereafter cookies came up missing. You might have a "hunch" that the person stole them—particularly if your other visitors were all virtuous people. Of course, it would be a good idea to investigate the facts related to this hunch.

When someone has "deep convictions," that person is very convinced of his or her beliefs. When such a person defends such "personally important" positions and beliefs, he or she will likely be very passionate. Such passion will be a mark of the strong feelings that he or she feels regarding the topic or belief.

The two key things to note are the introductory clause that begins with "although," and the fact that Thomas does decide to attempt the task. When someone has little hope for success, it is possible that such a person would be a "pessimist," that is, someone who thinks the worst about a situation (or even life in general).  However, the sentence indicates that while Thomas does have little hope, he has not completely given up hope. Therefore, he is not an absolute pessimist. (In contrast to pessimism, there is "optimism," which is the belief that things will work out for the best. It is related to words like "optimum" and "optimal," all coming from the Latin for "best.")

This sentence contains several context clues. First, the key word "despite" tells us that Austin's attempts to stay awake were unsuccessful. If that information weren't enough, the second part of the sentence outrightly states that Austin fell asleep. So, the feeling that overcame him must have been one of exhaustion. The only word that fits this sentence is "fatigue," which is the great tiredness that generally follows activities that require great effort.

In the main clause of the sentence, we are told that Brandon's friends did not know either his likes or his dislikes. Therefore, they did not know what types of things he preferred in comparison with other things. The idea of "preferences" includes the notion of ranking or ordering the things that are preferred, so this is the best option among those provided.

What do we know about Mary's view of her new job at the law firm? First of all, we know that she did not accept the job due to its high salary. This eliminates "affluence," which refers to the possession of wealth. "Dereliction" means abandonment or neglect, so it is clearly not the correct answer; we can assume that Mary would not want to work for a law firm because it is being neglected. Similarly, "culpability" is too negative to properly complete the sentence. This word refers to a person's guilt or knowledge that they are responsible for a mistake or wrongdoing. The only remaining answer is "prestige," which describes the respect and admiration that often comes with a highly coveted job and thus makes the most sense in the sentence.

The subject of this sentence has made an assumption that he is above average at basketball; however, the author’s use of the word “but” suggests that the subject’s assumption was incorrect and that he is in fact average or below average. When someone is considered average in a negative way, we call them “mediocre.” So, the correct answer is “mediocrity.” To provide further help, “supremacy” means dominance; “ascendency” means rising up or improving; “misery” means great sadness; and “frivolity” means playfulness.

This sentence contrasts the unified groups that the parties used to be with their apparent state of being split into non-unified groups. When a group breaks into smaller groups within the larger whole, such smaller groups are called "factions." Likewise, "factions" often are in disagreement with the larger party, so this word is by far the best option for this sentence.