The subject stands in contrast to "his much more proper wife."  This means his manner, which is also described as "embarrasing," is decidedly not proper. "Gauche," meaning awkward or tacky, is the correct answer choice.

The key word in the sentence is "traditional," as the sentence is constructed to contrast the missing word with it.  All of the other information, about football, coaching, and training methods, is unnecessary to find the correct answer. "Heterodox," meaning unorthodox and against tradition, is the best choice among the answers.

The subject has a careful approach to her appearance, with "every article of clothing in place." This indicates she was always making sure to look appropriate. "Mannered," meaning stylized and affected, is the best choice among the answers.

Although the sentence discusses rivals and "a history of conflict," the construction of the sentence indicates the subject was acting against that history. The correct answer must indicate avoiding conflict or backing down from a fight. "Deferential," meaning showing respect, is the best choice among the answers.

The sentence contrasts the missing word with the theory's reliance on "stories from a handful of individuals."  This means the correct answer will mean not relying on stories, or small samples. "Empirical," meaning experiential and observed, is the best choice among the answers.

The answer to this question is fairly straightforward, as "the wrestler" is called "The Fox."  "Vulpine" means fox-like, making it run in parallel with the other answer choices. ("Avian" is bird-like; "bovine" is cow-like; "porcine" is pig-like; "equine" is horse-like).

The sentence describes an injury on top of "wrecking a car" by the teenager.  The missing word needs to indicate that the teenager has run into a good deal of misfortune. "Hapless," meaning unlucky, is the best choice among the answers.

Look for clues as to what kind of word completes this sentence. The word “although” hints that there is some seeming contradiction between concepts in this sentence; in this case, between the short time of the speaker’s acquaintance and the intimacy of their bond. Note that this intimacy is characterized as “growing;” this allows you to know that the correct answer should be a word that implies growth. This words is “burgeoning,” which means growing or flourishing.

The word however clues you in that there is a contradiction between the first clause of the sentence and the second. In this case, the contradiction exists between students who feel the professor's approach is . . . the word you're looking for, and "classic." The word classic tells you the professor's style is probably old-school; the contradiction, then, would be between students who feel this is a positive and those who think it is negative. The word "antediluvian" means outmoded or ancient—the best fit for a description of an "out-of-date" teaching style.

The dash lets you know that the sentence's second clause should help explain what came before it (in this case, the word you need to figure out). The description "not even the learned presenters fully understood their topic" lets you know that the topic was confusing and possibly obscure. The closest word choice to match that meaning is "esoteric," which means intended to be understood by only a few.