The key here is to pay heed to the description “burden” in the subordinate clause. The word we are searching for will best match that notion. While a burdensome task might be "remarkable" or "outstanding" (or even perhaps the other more negative choices), it most definitely is “onerous,” which means excessively burdensome. (This is further supported by the adjective “greatest” describing the perceived burden.)

The word “onerous” is derived from the Latin "onus," which means burden or load. Our English is derived from a form of the word that has the base “oner-.”

The necessary word describes a strengthening of the activity of standing. (The key to this interpretation is the phrase “but also”); therefore, the best fit is “ambulatory,” which means able to walk.

It is derived from the Latin "ambulare," to walk, which has derivatives not only in words like "ambulate" but likewise in the more familiar “ambulance,” which is indirectly derived from the Latin via a French expression for a type of moving (in a broad sense, "ambulating") field hospital.

Frederick’s frustration with the unmerited members of government and society imply that he wishes for the country to be ruled by those who have talent and ability. While we generally think of “aristocracy” as being rule by titled nobility. While this is often the usage, more generally, the term means rule by the noble in the more fundamental sense of “noble” (i.e. as being truly excellent). The “aristo-” portion of the word is derived from the Greek for “best.”

All of the answer choices are a type of speech, but the contrast in the sentence with "motivational tools" and the adjective "nasty" leads to an answer choice with a negative tone. "Harangues," which indicates loud, aggressive attacks, fits the rest of the sentence best in context.

Here, Peter’s character is contrasted with the taciturnity appreciated by his friends. When one is taciturn, he or she uses words sparingly. Therefore, the best contrasting word would be “prolixity,” a word meaning that one speaks too many words. It is derived from the prefix “pro-” for “forward or outward” and “-lixity” from the same root from which we get “liquid.” Therefore someone who is prolix is one whose words can be said to “pour forth” like too much water.

If someone is the opposite of being understated, he or she would draw too much attention to himself or herself. When one is “ostentatious,” he or she displays things in a gaudy manner, particularly in order to draw attention to himself or herself and be noticed.

The implication here is that the work of astrophysicists has been more capable and effective in bringing forth practical advances (in comparison with theoretical mathematicians). When one can bring forth results in an effective manner, such a person (or institution) is unsurprisingly called “efficacious.” This word has many relatives, as might be surmised, such as “efficient,” “effect,” and “efficacy.”

This sentence works by way of contrast, as you can tell from the word "although" in the second clause. The description in that introductory clause is implied with regard to the wealthy people mentioned in the first clause. If someone does not give even a penny of money, he or she gathers all of his money for him- or herself. While perhaps the money is invested, the general sense of the sentence is merely to point out such acts of gathering and keeping money. To "hoard" things is to do just that. The word can also be used to describe the things that have been gathered together and amassed in this fashion.

The second clause furnishes the clues that we need. It implies that without the ability to cope with changes, a healthy psyche is likely impossible. This means that you must have this skill—it is not optional. Such things are "essential." In much older philosophical language, "essential" things were contrasted with "accidental" ones. The latter were not "accidents" in the sense that we generally use that word; they were things that just happened to come along with something. For instance, it is essential to a person that he or she be able to think (or at least potentially be able to do so). It is wholly accidental if he or she has black or blond hair. In this sentence, it is said that it is a necessary and essential aspect of psychological health to have the ability to cope with changes.

The best clue for this sentence is the expression "that was soon to assault them." This implies that there is going to be an even stronger storm soon. The option "trickle" might seem like a good way to characterize the weaker first storm, but that really does not fit the sentence—neither in style nor really in grammar. A "prelude," however, is something that introduces another thing, generally being less important than that later thing. For instance, a "prelude" before a musical show lets the audience here some of the music but does not really give them the whole show at once. That comes later. The word literally means to play before. In the sentence, the first storm is said to be a mere prelude to the one that is soon to come.