The philosopher seems to have expressed his or her theory in some manner. It would also be possible to say that he or she held the opinion. None of the options are about the actual having of the opinion. Therefore, it is better to focus on words pertaining to expressing it.

Now, "divulged" and "promulgated" both have to do with expressing something. Divulging something deals with telling private information, and promulgations usually happen in official affairs (or at least with more fanfare than is indicated in this sentence). Thus, the word "propounded" is the best option, as it means expressed for consideration.

As regards reality being a shadow that will pass away, the word "evanescent" describes something that will fade away in this manner. Something that is "evanescent" is something that will not last for a long period of time.

For this sentence, stay as close to the clues as possible. A number of the potential answers are a little too specific, so you should not choose them. Instead, note that the inhabitants are fleeing. Therefore, the best option for the first blank is "vacated." This is related to the word "vacuum," which describes a space in which there is nothing whatsoever.  Whenever an area is "vacated," everything is taken out of it (especially people). The fumes are apparently dangerous, though we do not know how. The word "pernicious" is a good general term for being dangerous, so this is the best option among those provided here.

The first blank of this sentence does not necessarily have to do with the woman being masculine in any way whatsoever. It merely expresses the idea that she is courageous. Hence, the only option that is acceptable is "intrepid", meaning without fear. Indeed, it even can indicate an adventurous spirit. (The word "pusillanimous" means timid—quite the opposite!) For the second blank, all we know is that she travelled across many miles. Hence, it is best to stay with the rather direct option, "traversed."

Follow the clues very closely for this sentence. It is said that the old man is able to walk. It is most likely that this state of affairs is what surprised him after his surgery. The word "ambulatory" comes from the Latin ambulare, meaning to walk. An ambulance, which we tend to think of only as a transport, actually is given its name because it is a kind of "walking hospital." To be "ambulatory" means that one is able to walk. The second blank, in its simplest sense, appears to mean require. The word "necessitate" is a good synonym for this.

At first glance, “mortified . . . censured” might seem like a good fit, but note that “censure,” which means to chastise, does not work as well as “emasculated,” which means to make less manly. It is implied that he feels less manly; maybe his sister criticizes him for it, or maybe she does not. “Abashed . . . emasculated” form the only correct answer.

“Exculpate” means to find not guilty, so this choice would not work given the context. “Rankle” means to aggravate, which is also not quite right. “Abbreviate” means to shorten, and this can apply to sporting events. “Dubious” means doubtful. Together, these two form the correct choice.

The first blank is a sentence shift: We can assume that the word has an opposing meaning to “visionary talk.” “Myopic” means shortsighted and is an extremely good fit. “Abnegate” and “abdicate” are very similar. Both mean to give up some position of power or responsibility, but “abdicate” is usually reserved for higher positions, such as a king or ruler. “Myopic . . . abnegated” is the correct response.

To be “amenable” to a thing means you are willing to go along with it, which is not the definition we need in the first blank. For the second blank, we are looking for a word that warrants a proper response to “the latest fiasco.” Thus, “redressed” and “amended” will not suffice. “Ambiguous . . . abolished” is the correct answer.

“Genuine” and “bona fide” do not work when we consider the second part of the sentence about “foreign” and “from a neighboring country. Though “mitigated” is similar to “migrated,” note that these two have very different definitions. “Mitigate” means to make less severe. “Aboriginal . . . appropriated” is the correct answer.

If someone is “captious,” they tend to find fault with everything. “Complacent” means overly content. These could possibly describe the judge, but these do not inherently apply. “Discretionary” means to have the power to act according to one’s own judgment. “Discretionary . . . absolve” is the correct answer.