If this restaurant's popularity has increased, we would expect it to be difficult to reserve a table for the same night; conversely, if its popularity has declined, it would be relatively easy to get a same-day reservation. The end of the sentence ("we were able to") tells us that the latter scenario (diminished popularity/ better odds of getting a reservation) is the case here. For the first blank, either "waned" or "ebbed" would fit, as these are synonyms meaning decreased. "Secure" and "procure" in the second blank would both mean that you were able to obtain a reservation. "Proffer" (offer) would not make sense. Thus, the pairing of waned/secure is the correct answer.

For this sentence, the general sense is that the gold was removed from stones in which it was mixed with other metals. Of all the possible options, the “melting, mixed” pair is perhaps the most tempting. This is a trap, for the sentence provides no hints regarding the process of this removal. The best option is “extracting” for removal, for it literally means “to draw (or drag) out.” The word “tractor” comes from the same root word in Latin, and there are many other related English words like “attract,” “detract,” and “contract.” The word “alloyed” means “mixed” as in the metal brass, which is an “alloy” of copper and zinc.

The best clue in this sentence is the word "upon," which indicates that the monks apparently came to the city in protest. Likewise, it is important to notice that they came as a "group." Thus, we should say that they gathered together, not that they fled together. The general idea is that they gathered and then all "stormed" the city in protest. The word "congregate" means come together in a crowd.  A church "congregation" is called such because it is a gathering of people.  Based upon its Latin roots, it is literally a "flocking together." The monks gathered and then all together "swarmed"—i.e. moved as one large group—upon the capital city in protest as a swarming group. Swarming insects are so called because they act as a group made up of many individuals.

The astronaut had for a while planned his potential action. Upon choosing to undertake this plan he “executed” it. Although we might think of “execute” as meaning to kill, its primary meaning is to carry out or put into effect. This meaning is almost a direct translation of the Latin roots of the word: “ex-” (out / out of) and “sequi” (to follow). The latter is found in words like “consecutive” and the direct Latin phrase, often used in English, “non sequitur”—something that does not logically follow.

Drilling out of the craft would clearly cause a hole in its hull.  Therefore, it would “rupture it” – a word with Latin roots meaning “to break” and found in similar English words like “disrupt”, “corrupt”, “interrupt”, and “erupt” (among many others).

Given that neither party is remaining silent, clearly the argument is happening in the open. Therefore, the options for “simmering” and “smoldering” are likely inapplicable for the specific needs. Now, the sense is that each party in the argument is trying to outdo the other one by way of insults. Such an argument, continually becoming more heated and worse, is best said to be “escalating.” The word is related to “escalator,” indicating that something is “going upward,” generally in the metaphorical sense of “becoming more intense.”

The sense of the sentence is one of opposition (because of the word “however”). The pair “invigorated  . . . languishing” captures this best. To be “invigorated” is to be given energy. Looking at the word, you can see the two parts: in + vigor, which roughly could be translated to put strength into. To “languish” is to lose strength or vigor. It comes from a Latin root that is likewise found in words related to “lax,” in the sense of being “loose.” Another related word is “languid,” meaning showing little energy for exertion.

For the first blank, we can infer that we're looking for a word that means something like "declared." Either "decreed" ("ordered something by decree") or "announced" ("make a public and typically formal declaration about a fact, occurrence, or intention") could be potentially correct. For the second blank, we need to pick out a word that means something like "increase," because we know that the king plans to order the addition of new trebuchets and increase the walls' height. Either "bolster" ("support or strengthen; prop up") or "supplement" ("add an extra element or amount to") could be potentially correct. Of the possible words that we've identified as potentially correct for each blank, only "decreed" and "bolster" appear in the same answer choice, so the correct answer is "decreed . . . bolster."

One clue as to which word should go in the first blank is that the daughter fears not having long talks but will still be able to. This tells us that the word that goes in the first blank should somehow involve relieving fears. "Mollify," "dissipate," and "assuage" could each work. "Assuring" is the only word choice for the second blank which involves positive reinforcement, though, so "assuaged . . . assuring" is the correct answer.

The first blank requires one to consider what people do at work. "Accomplish" means achieve or complete, and a lot of jobs involve completing tasks, so this makes sense. In the second part of the sentence, "reunited" is the answer choice that makes the most sense because the holiday break would give Charles some time off to see his family.

"Bristle at" means show anger or indignation in response to something, while "bilking" means cheating, defrauding, or swindling. Because Elizabeth was not a thief, it is natural that she would be indignant at the idea of swindling her clients our of their money.