The contrast in this sentence is between advanced studies and the basics necessary for them. The basic principles of a subject are called its “rudiments.” Something “rude” is something that is “uncultured” or (closer to its Latin bases) “unshaped” or “unmade.” When something is “rudimentary,” it is basic, not having been subjected to much elaboration and further development.

Since the students are said to be exploring the unknown tunnels and not merely doing research on them, the best option for this sentence is “expedition.” An expedition is a trip organized for a particular goal. It is often used to describe scientific and military outings of this sort, though it has a more general sense as well.

A “bout” of something is an abrupt incident of some kind of illness or activity. The word “vertigo” is the best option, for it is a condition resulting in a loss of balance and the feeling that the world is spinning. The word “spins” really is just a flippant trap word. Do not be tricked by it. The other options are too general, given that we have the very specific “vertigo.” The word comes from the Latin for “to turn.” A close relative is “vertiginous,” which means “causing vertigo” (such as a high cliff that overwhelms someone looking over its edge). Since it is derived from “to turn,” “vertigo” has many other relatives in English like “convert,” “divert,” “introvert,” and many others.

The argument is said to be complex, but nothing in the sentence should lead you to think that it is an incorrect argument; therefore, the words “assumptions,” “presuppositions,” and (especially) “conjectures” all convey more than is necessary for completing the sentence. Strictly speaking, the “premises” of an argument are the statements upon which it is based. Since the sentence only implies that there are many such foundational statements, the best option here is “premises.”

Each of the multiple paintings are considered “derivative” works, meaning that they are “taken from” some preceding work. In this sentence, it is clear that they are all imitations of a single original. Therefore, the most appropriate word here would be “archetype,” meaning (among other things) such an original exemplar from which other like things are derived. The “arche-” prefix means “ancient” or “original,” and “type” means more generally “figure, model, or example.” We sometimes say things like, “The herring is a type of fish,” meaning, “The herring is an example of a fish.”

Do not be fooled by this sentence into thinking that it calls for “carnie.” The man does not work in the carnival but instead follows it to make a living. When someone does not have a regular job but instead travels about to make his or her living, that person is called a “vagrant.” The word is ultimately derived from the Latin for “to wander.” When something is called “vague,” it is implied that it cannot be understood because it “wanders around the topic” without being explicit and direct.

The key thing to note here is that the “rules” that Otho does not obey are described as being “conventions.” Propriety is the characteristic that one has when he or she follows the generally accepted norms of a society. Such generally accepted norms are said to be “conventional” in nature. The word “proper” has a very strong sense in meaning “strictly conforming to something’s form or nature.” This is derived from much older Latin terms in logic and philosophy. Here, “propriety” (which is related to “proper”) is “conformity with the standard of society.”

The key expression for this sentence is “without influencing.” In light of the “and not merely,” it is clear that Samantha wishes to have an influence on her students’ lives. Expressed in another manner, she could be said to want to “impact” their lives. By its most direct usage, “impact” means “to strike or hit.” For instance, when a meteor is said to impact the earth. More generally, the word means “to have a strong influence on something else.” This is how the word is being used in the sentence.

The parallel in this sentence is between the notion of “depriving” and the needed word. When someone deprives himself or herself, he or she is said to deny himself or herself of a given good thing. The word “mortification” does not necessarily have the strong sense of “killing” as might be suspected by the “mort-” portion of the word (meaning death, as found in “mortal,” “immortal,” and “morgue”). “Mortification,” might merely mean the process of eliminating or subduing (in a sense “killing off”) the passions of the body. This meaning is used with particular frequency with regard to religious acts of this type, though one can find them in a number of other walks of life as well.

For this sentence, the most specific answer is the best one. Many of these options might be acceptable, for even lumps and bruises can also bleed (in addition to being lumps and bruises). The best option is “lacerations,” which are deep cuts in the flesh, which would be wounds almost completely guaranteed to bleed. All the other cases may or may not bleed.