Since Barbara gathered a large collection, the best term to select is “amassed.” The other two tempting options are likely “heaped” or “piled,” but while these two words do partially imply a respectable number of items, (in order to create a heap or a pile), they primarily signify the act of creating the piles or heaps. The word “amass,” on the other hand, primarily means “to gather together,” usually implying a large number as well. The word is indifferent to the manner by which these items are gathered together.

Since even the most perceptive philosophers misunderstand analogical predication, it “escapes” them. When something “eludes” someone, it “escapes” him or her in the sense of not being understood. The word comes from Latin roots literally meaning “to play away from,” though it takes more nuanced forms in English. It is related to words like “illusion,” “elusive,” and even “prelude."

"Avow" means to declare openly. The sentence provides the exact definition of the correct answer choice, making this question a quiz of the test-taker’s vocabulary. If you know the definition of “avow,” you’ll be quick to choose the correct answer.

The sentence implies that the employees were left to their own devices after the incident in question, and “marooned” means to be left isolated and alone and without means of escape. “Marooned” is the correct word choice to describe the feelings of the employees.

“Officiate” most closely means to perform a ceremony or duty in an official capacity. As a marriage ceremony, in this context, would be an official ceremony, "officiate" is the best answer choice.

The law’s effort, as mentioned in the second part of the sentence, is to prohibit certain actions. Of the given answer choices, only “proscribe” is a synonym for prohibit.

The professor’s habit of discussing topics not related to his subject shows he wanders around various topics. Of the answer choices, only “meander” is a synonym for wander.

The structure of the sentence indicates that the grandmother did not like her grandchildren's behavior. Look for an answer that means dislike or even hate. Of the answer choices, only "abhorred" has the appropriate meaning.

The best clue for the answer lies in the word "democracies," as "enfranchising" means enabling voting rights. Another clue is the fact that the other four answer choices all indicate some sense of hurting people; identifying synonyms among answer choices is a good way to eliminate some choices.

The key word in the sentence is "rival." With rival in mind, look for a word that would indicate a sense of harm or impairment.  Of the answer choices, only "hamper" has the appropriate meaning.