The first blank of this sentence indicates that the doctors would like to slow the growth of the tumor, perhaps stopping it. The most tempting wrong answer here is "invert," for you might interpret it as "reverse" (as in, making it shrink); however, this is a bit of a stretch, and the sentence hints that they are looking merely to reduce the pain for the time being, which would begin by stopping this growth. The verb "to check" can be used in this way, though we do not often think of this meaning immediately. The option "provide" is quite acceptable and requires very little explanation. Clearly, the patient as been suffering. To be "afflicted" means to experience suffering, which is a good option for the final blank.

The clearest clue in this sentence is the description of the man as being known for procrastinating, meaning that he puts things off to the future. ("Procrastinate" comes from Latin roots meaning on behalf of / for ("pro-") tomorrow ("-cras").) When someone "defers" something, he or she puts it off for a later date. Clearly, the decision to be made is important (for it is related to a troublesome matter). The man's delay is likely annoying to his wife. To be "piqued" can mean either to be interested (e.g. "piqued his curiosity") or to be irritated. The latter is the case for this sentence. Finally, to overcome his wife's annoyance, it makes sense for the man to deal with the issue. Thus, he should "resolve" it, meaning that he should find a solution to the problem. 

It is important to note that the elders in question were able to serve as examples of virtue and success. This means that they not only succeeded in overcoming their difficulties but likely managed to do very well in life after that. Hence, the best pair for the second and third blanks are "overcome" and "flourishing." This, of course, indicates that they were well respected. To "venerate" someone is to hold him or her in high esteem. Often related words are used in the context of religion, as when someone "venerates" a statue.

The word "enigmatic" describes something that is mysterious or difficult to understand or interpret. The students were unable to decipher its meaning. To "unravel" something can also mean to explain that thing. (This meaning of the word is clearly a metaphorical extension of its more literal meaning.) To "decrypt" is quite akin to "decipher," for both words deal with translating something out of an encoded form. (To "encrypt" a message is to encode it.) Finally, insofar as they could not solve this problem, they were defeated (so to speak) in finding their answer. To "confound" someone can mean to frustrate him or her. It can also mean to defeat that person, preventing him or her from reaching a given objective.

The implication in this sentence is that the people being considered are trying to enter into culture that is not their own. Thus, they are trying to become acclimated or accustomed to this new way of life. To become "assimilated" means both to understand something (e.g. to assimilate knowledge in a given subject) as well as to become similar to something else. In this latter sense, we can see how a person would become "assimilated" to the norms of a given foreign culture over time. The second sentence indicates that this is best done by taking part in day-to-day life as well as by investigating the self-awareness of the given culture. While one might think that "working" or "laboring" are particularly good answers, they are too specific. "Engaging" works best, as it means more broadly to take part or participate.

The major problem with the people mentioned in this sentence is that they are unable to give a firm and fixed commitment to the tasks they need to undertake. To "consign" oneself to something is to do just that—as opposed to making a less firm declaration of commitment. To "vacillate" means precisely to waver between options in the manner described in the sentence, so it is by far the easiest blank of the three to fill in. Finally, although we use "evaporate" to describe a physical process involving liquids and gasses, the term can also have the extended meaning of to disappear from existence entirely. This latter meaning is what is indicated in this sentence.

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.