The sentence states that "outlandish stories" were widely believed. The correct answer will indicate a similar absurdity of the "rumors." "Specious," meaning false or unreliable, is the best fit among the answers.

If the "formerly religious" feel the groups they left have a "problematic concern," it is reasonable they view the sins lightly. The correct answer should mean minor or unimportant, the definition of "venial."

The critic's review was "scathing," so we can infer that it was negative in tone. The responses from fans of the director are implied to be similar in tone to the critic's original review, and thus "condemnatory" is the correct answer, as it means condemning in nature or speaking poorly of a subject.

The sentence implies that Humbert believes this work to be dull, and "prosaic" means common or uninspired, which makes it the best choice to finish this sentence, as it most closely aligns with the word "dull." 

The key word in this sentence is same. The fact that "mass consumer culture" leads every person to idolize "the same commercial values" tells you that what many fear, in this case, is a society where everyone acts or thinks in the same way.  Although it could also be described as vapid, a better descriptor would be "homogeneous," a word that means made to be the all the same or uniform.

Since no one could understand the professor's theorem, we know that the answer cannot be "lucid," which means clear. Similarly, it can't be "loquacious"—which means talkative or long-winded and is used to describe people, not ideas. We're not given any information to suggest that it is "ambiguous," meaning open to multiple interpretations, and while "erudite" (demonstrating great learning or knowledge) sounds like it could be correct because the sentence is talking about a professor in a classroom, the remaining answer choice, "esoteric," is most appropriate for describing a theorem that only the professor understands, as "esoteric" means able to be understood by few people with a specialized knowledge or interest.

There are several clues here, but a double shift is going on. The word "however" illustrates a contrast with the first clause of the sentence, and then the word "hardly" gives us a second shift back the other way. Thus, we are looking for two words that mean "favorable." "Auspicious" may sound negative, but it actually means pertaining to good fortune.

We know from the sentence that the traces of cyanide aren't enough to harm the body, so we are looking for a word that means "harmless," and that is what the word "innocuous" means. Notice that it is closely related to the word "noxious" but the prefix "in" lets us know that it is not noxious, or not harmful. 

We are looking for a word that means all style and no substance, and our word is meretricious. This word is tricky because it reminds us of meritorious (a positive word), but remember that the "e" instead of "i" alerts us to the fact that something else is going on. Meretricious means the opposite of of meritorious: it is something that seems attractive but is really empty.

The contrast here is betwween the efforts of the two campaigns. The opponent's campaign has not begun to mobilize, while the incumbent's campaign has already done the hard work of canvassing the neighborhood. So we are looking for a word that means hard-working, zealous, or busy. Sedulous is a tricky one, perhaps because it sounds sinister (like seductive) or lazy (like sedentary). It actually means the opposite of sedentary, and that might be a helpful way to remember that it is not what it sounds.