The key word in this sentence is “mistakes.” The only contrast being implied is that George did not seem to think that he could make mistakes (though his friends knew better). When someone is “infallible” that person does not make mistakes. The word “fallible” means “capable of making mistakes” and is related to “false” as well as “fallacy” and “fallacious.” The “in-” functions here as a negative, making “in-fallible” to mean “not-fallible.”

The only thing that we can say about Nathanael is that he is avoiding any waste of time. Any other description might hold (that it is amazing, insightfully done, etc), but that goes beyond what we are given. The best answer is “efficiently,” which describes someone who is very productive while using the least amount of resources (money, time, etc).

The teacher explains that the axes of a graph "[cross] at a right angle," so we need to pick out an adjective that describes the relationship between two lines that do exactly that. "Parallel" cannot be the correct answer, then, because "parallel," when used of lines, planes, surfaces, or objects, means " side by side and having the same distance continuously between them," so "parallel" is the antonym of the word we're looking for. "Perpendicular," an adjective which means "at an angle of 90° to a given line, plane, or surface," best describes the orientation of the two lines, so "perpendicular" is the correct answer.

We can infer that because the footnotes allow room for various types of information of which "none . . . are absolutely necessary to the text itself," we can infer that we need to pick out an answer choice that means something like "extraneous" or "extra." "Crucial," then, cannot be the correct answer, because "crucial" is an antonym of "extraneous" and "extra." "Ancillary," however, is an adjective that can mean " additional; subsidiary," and because it best describes the nature of the information the book's footnotes contain, "ancillary" is the correct answer.

For this sentence, we can infer that the knitter must have been pretty smart to "[predict] the fashion trend toward homemade goods." So, we need to pick out an adjective to describe the knitter that means something like "smart." "Undiscerning," then, cannot be the correct answer, because "undiscerning" means "lacking judgment, insight, or taste," making it the opposite of the word for which we're looking. "Astute," however, is an adjective that means "having or showing an ability to accurately assess situations or people and turn this to one's advantage," and because "astute" best describes the knitter's profitable assessment of the fashion trend, "astute" is the correct answer.

The choice that makes the most sense is assiduous: showing great care and perseverance; diligent.

The choice that makes the most sense is contentious: quarrelsome; causing or likely to cause an argument.

The choice that makes the most sense is craven: contemptibly lacking in courage; cowardly.

The choice that makes the most sense is wary: feeling or showing caution about possible dangers or problems.

The choice that makes the most sense is vituperative: bitter and abusive; scolding.