The only clue in this sentence is that the woman has an endless supply of "tiresome" (boring) stories. This suggests that the blanks must somehow relate to the boring or uninteresting or plain nature of the woman. This should help you solve for "austere" as the adjective used to describe her dress and "stolid" and "monotonous" to describe the woman. "Austere" means severe, grim; "stolid" means impassive, unexciting; "monotonous" means boring, one-dimensional. To provide additional help, "taciturn" means quiet, not talkative; "gregarious" means sociable; "amiable" means friendly; "cerebral" means intelligent or thoughtful; "comely" means cute, attractive; "paltry" means too little of; "licentious" decadent, sinful; "winsome" means charming, appealing; "obstinate" means stubborn; "harrowing" means very scary, terrifying; "pious" means deeply religious. 

From context you know that the subject had to win over his workmates. This suggests what they previously considered him to be was negative and perhaps related to insincerity, it also tells you that the subjects sincerity must have been genuine. So the correct answers are “artless” (without deception, genuine); “hackneyed” (unoriginal and trite); “spurious” (false, fake). To provide additional help, “blatant” means obvious; “somber” means serious and sad; “lachrymose” means constantly crying; “boorish” means not interesting; “caustic” means harsh, severe; “pecuniary” means related to money; “hollow” means empty, meaningless; “craven” means cowardly; “inchoate” means immature, not developed; “belligerent” and “hawkish” both mean warmongering, aggressive; “despotic” means autocratic, tyrannical, ruling without challenge.

You are told that the falling apart house is in stark contrast to the mansion across the street. So the house must be “dilapidated” (in a state of disrepair, falling apart) and the mansion must be the opposite. This means the mansion is “ostentatious” (fancy, showy) and “extravagant” (luxurious). To provide additional help, “deleterious” means harmful; “beneficial” means helpful; “doggerel” means a poem with an irregular rhythm; “convivial” means friendly and lively; “outlandish” means bizarre and unorthodox; “irresolute” means uncertain; “mettlesome” means full of courage; “circumspect” means careful and wary; “assiduous” means diligent, attentive; “consummate” means accomplished; “immutable” means not changeable.

The best clue for starting this sentence is the fact that the second and third blanks are opposed to each other. The old woman seems to have noted something in the young man's attitude that is positive (to be encouraged, at least). The young man also seems to have a certain attitude regarding difficulties. When something is "insuperable" it is unable to be overcome. (The prefix "in-" here means not, and "super" generally means over or over top of.) When someone has a "sanguine" attitude, he or she is very optimistic. Thus, a sanguine person is not too likely to think that many difficulties will be insuperable. The old woman's advice was likely offered out of kindness, so it is understandably referred to as being "benevolent" or coming from a good will.

The clearest clue in this sentence is the fact that the first and the third blanks are opposed to each other. This is indicated by the use of "however" in the second independent clause. Likewise, the description of the old man given in the second blank is likely to be related to the word chosen for the third. The words "trite" and "perceptive" are well opposed to each other. Something "cursory" is made in passing, often with little thought. (It is related to the Latin word for to run, "currere," which we find in other words like "current" and "course." Something "cursory" just "runs by" in discussion and perception—missing the details.) A "perceptive" remark is one that truly notes the details involved in the matter at hand. Thus, "perceptive" is a good word to oppose to "cursory." Finally, someone who is perceptive is likely wise. The word "sage" can describe a person who is wise—either as a noun or an adjective.

In this sentence, the first and second blanks are clearly contrasted to each other. In addition, the final subordinate clause gives us a description of the events hosted by Nigel, thus also hinting at his personality. If he invited many neighbors to events, it can be inferred that he liked their company—at least from what we know in this sentence. Thus, he was likely a sociable person. Someone who is "gregarious" is just that—an interesting word coming from the Latin for a flock (e.g. of sheep) or herd. In contrast to this, a "curmudgeon" is an unpleasant person (likely also implying that such a person is not sociable, at least for our purposes closely enough). Finally, it is quite fine to describe these events as "communal," for the general idea is that Nigel is actually a rather friendly person who likes gatherings. Thus, the sentence draws attention to the communal nature of the events.

Clearly, Eggbert has a very upbeat personality, and Wilbert's personality is negative and depressive. We see at the end of the sentence that Eggbert had an "exceedingly optimistic disposition." When something is "saccharine," it is overly sweet—often describing an overly optimistic personality. The contrast is clearly between being depressive and being so very positive. For this reason, the best pair of words for the second and the third blanks are "melancholic" and "doleful." A "melancholic" person is someone who is generally sad. A "doleful" remark is one that expresses sorrow.

The best clue for this sentence is that the younger colleague's essay is said to be "little more than a patchwork of sources." This hints that the younger colleague merely gathered together a bunch of sources without doing sufficient work to order or connect them together. Such an approach can be called "eclectic," which means drawn from various sources. This is the best option for this sentence. (While the work might have been poor, we are not 100% guaranteed of that from our context clues.) The work seems to have lacked internal cohesion or unity. Thus, it is understandably called "disunified." In contrast to this, a "systematic" approach is one that follows a careful plan. This is an acceptable contrast to the "eclectic" method mentioned in the case of the younger colleague.

The general idea of the sentence is that it is often simpler to avoid disagreement completely rather than to choose topics that could possibly be disagreeable to someone in a large group. An "anodyne" remark is chosen to be very inoffensive. "Peculiar" things are ones that are unique to a given person, group, or object. Finally, someone chooses to make such anodyne remarks in contrast to the much more difficult task of making carefully chosen, but substantive, remarks that will be acceptable to all. Such latter attempts would require careful balancing. That is, they would require deft action, meaning quite clever and (metaphorically speaking) nimble action.

The best clue in this sentence is the word "irregular." The two types of quakes are being contrasted for being regular and irregular. Thus, the small quakes (since they are the irregular ones) are best called "sporadic." In general, both of these types of events are "seismic," meaning related to earthquakes and such movements. Finally, we do not know much about the size of the fractures, but we can guess that they did destabilize the building. Thus, this is the best option, given the details provided in the sentence.