From the context of the sentence you know that whichever aspect of Achilles is being described relates to the difficulty encountered when trying to restrain him. Nonchalant means not caring; ineffectual means not effective; equivocal means ambiguous or hard to understand; magnanimous means noble-spirited. Of these four options only magnanimous could possible match; however there is a better match. Irrepressible means not able to be controlled and directly references the difficulty one would encounter trying to restrain Achilles.

Because we know that Carly thought "[the poem's] treatment of its subject was far too simplistic" and "none of its other features caught her interest," we can infer that she thought the poem to be dull. So, we need to pick out a word that means something like "too simple" or "dull." We can rule out "exciting" as a potential answer because "exciting" is an antonym of the word that we're looking for. "Jejune," however, is an adjective that means "naive, simplistic, and superficial" or when used of ideas or writings, "dry and uninteresting." Because "jejune" is the answer choice that best fits the sentence's context, it is the correct answer.

We can infer from the sentence that we need to pick out a word that means something like "stubborn," because "some people assume that the breed has a[n] . . . intractable personality," and "intractable" is a synonym of "stubborn." So, "meek" cannot be the correct answer because "meek" is an antonym of "stubborn," not a synonym. "Obdurate," however, is an adjective that means "stubbornly refusing to change one's opinion or course of action," and because "obdurate" is the answer choice which best fits the context of the sentence, it is the correct answer.

The important thing to note in this sentence is that, in his experiment at least, the physicist is unconcerned with the question of the soul’s immortality. The question could be said to be “outside” of his concerns or irrelevant for his considerations. When something is called “extraneous” it is being described as being thus unrelated. The word comes from the Latin for “external” or “foreign.”

Because the customers considered themselves superior, they were most likely arrogant while talking down to me, making them "haughty."

The key word in this sentence is “settling.”  The opening phrase of the sentence stands in contrast to the second clause, and the missing word needs to be the opposite of “settling.”  Only “peripatetic” is an antonym of “settling.”

The key expression here is “insignificant matters.” Therefore, she found John’s critiques to be rather small or insignificant. The best word to describe such things would be “petty,” which means “small” or “trivial.” It is related to the French “petit,” meaning small, and which is often used in English in the same sense.

The idea here is that Caesar never wasted words, so that should mean his dispatches were short. So, we need to pick out an answer choice that means something like short. "Effusive" is the opposite of short; it means overflowing, unreserved, and exuberant.  "Dreary" means boring or uninteresting—it doesn't fit with our expectation of being short.  Neither does "noble," which means upstanding or righteous, nor does "bellicose," which means warlike. The best answer choice is "laconic," which means terse, concise, or using few words.

The best word here is “auspicious,” thought “felicitous” is a very tempting trap word. The latter indicates that something is pleasing or very appropriate for the given circumstances. When something is “auspicious” it is not merely a “happy chance” but moreover indicates (or at least forecasts) future success, something for which Zachary was hoping, as indicated by the interpretation of these signs as hopefully indicating “a positive turn of events.” The word “auspice” literally means a token of prophecy, coming from the Latin word for one who looks at birds to discover the will of the gods. When one says that something was “done under the auspices of X,” he or she means that X supported the given undertaking.

When something fluctuates, its changes in an irregular manner, making it hard to predict that which is fluctuating. That this is the case in our sentence is hinted by the fact that the “volatility was too great” for any kind of forecasting. The word is derived from the Latin verb for “to flow,” and has related English words like “flux” and “influx” as well as “influence” and “fluid.”