"Vacillate" means to waver, hesitate or be indecisive. "Interject" means to say something abruptly, especially as an interruption. The word "between" provides a strong clue that the boy was having a hard time deciding, and the end of the sentence provides a clue that the second word should involve interrupting the boy. So, "vacillated . . . interjected" is the correct answer because it best fits the context of the sentence.

That the Emancipation Proclamation resulted in energy tells us that the word should involve inspiring someone. "Galvanize" means stimulate or stir to action. That the British were considering doing something on the Confederate's behalf tells us that the second word should involve doing something for someone else. "Intercede" means intervene on behalf of someone else. So, the correct answer is "galvanized . . . interceding." 

We can infer from the sentence's context that we need to pick out a word for the first blank that means something like "made" or "encouraged" since we know that Harriet's apprehension likely made her do something. Either "convinced" ("persuaded someone to do something") or "compelled" ("forced or obliged someone to do something") could be correct. For the second blank, we need to pick out a word that means something like "not participate in" or "stop," given that Harriet saw other kids getting hurt in the snowball fight and that she was apprehensive about it. Potentially correct answer choices include "avoid," "stop," and "forgo" ("refrain from"). Of the possible words that we've identified as potentially correct for each blank, only "compelled" and "forgo" appear in the same answer choice, so the correct answer is "compelled . . . forgo."

The word “arbitrator” means a person who mediates between two parties to settle a dispute. So, the arbitrator would hope to reconcile the disputing parties. We can eliminate "castigate . . . exterminate" because "castigate" means criticize or reprimand severely. The second blank requires a word that means take away; therefore, "reconcile . . . eliminate" is the right answer.

In an old usage, “meet” meant “to be proper or just.” When one “metes” a sentence, he or she issues a judgment. The sentence implies that the judge does not like giving (meting) out such sentences because it is difficult see and interpret all of the details in the midst of life’s ambiguities. To attempt to see and discern such details in an exact manner would be to “ascertain” them. The word is derived from the Latin word for “sure or settled” and is related to English words for “surety” such as “certificate” and “certitude.”

For the first blank, we need to pick out a word that means something like get or buy. Either "obtain" (acquire) or "afford" (have enough money to be able to buy) could be correct. For the second blank, we need to pick out a verb that means something like last or be used. Either "serve" (be adequate) or "suffice" (be enough) could be potentially correct. Of the possible words that we've identified as potentially correct for each blank, only "obtain" and "suffice" appear in the same answer choice, so the correct answer is "obtain . . . suffice."

In sentences with two blanks it is important to ensure that the meaning of the two blanks work with one another, as well as with the sentence as a whole. From the context of the sentence it is clear that the second blank must be a form of behavior that would get Alice fired. Comely means cute and mandatory required so those two answer choices could be ruled out. Histrionic means dramatic, but being fired from her job would be unlikely to make Alice feel reinforced so we can rule out that option. Merciless means cruel and without mercy, but again being fired is not going to make Alice feel jubilant. That leaves us with only despondent and debauched. Despondent means upset or disappointed, which is a normal reaction to being fired and debauched means wicked or lurid. This answer choice fits.

This sentence explains the relationship between the two blanks by saying that the second opinion is much stronger than the first opinion. This means that the two blanks both have to focus on the same general principle and that the second is an exaggeration of the first. The correct answer is insufferable . . . reprehensible. Insufferable means annoying and unbearable,and reprehensible means very bad and immoral;both are negative implications and the second is stronger opinion than the first. Petulant usually refers to someone ill-tempered, but worthy means someone deserving of praise so that does not fit. Erratic means difficult to predict, which does not match with regressive. Cursory which means done superficially does not fit comfortably into the sentence. Prosaic means ordinary,which also does not fit comfortably.

The contrast in this sentence is between “rigid logic” and the second blank. The word “heuristic” (particularly in computer science) means a loose rule—often explained as being a “rule of thumb.” Such devices help to simulate some scenario but not with the certainty of mathematical logic. For those who are used to such rigid logic, the development of such “heuristics” can be very difficult and perplexing—hence the choice word for the first blank.

A "sophisticated" work is one that is very complex, requiring much experience and knowledge to navigate. Although the word is distantly related to the Greek root “sophia,” meaning wisdom (and found in words like “philosophy”), “sophisticated” had a long development through more negative connotations (partially related to usages like “sophistical”). These are not reflected in our usage here. 

“Colloquial” means related to ordinary speech. Its root is derived from the Latin for “to speak or talk,” which has many derivatives in English, not only including those with the “c” that we see in “interlocutors” (e.g. "locution," "allocution"), but also the more common (and phonetically related) “q” (e.g. "eloquence," "loquacious," "colloquium"). The prefix “col-” really is derived from the Latin “cum,” meaning with. Colloquial language is the language one uses to “speak with” others of similar backgrounds and upbringings.