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.

"Inconceivable" means impossible to comprehend or grasp fully, while "mundane" means concerned with the world rather than with spiritual things or commonplace.  Evidently, for many, Robert's concern with the world makes his life incomprehensibly commonplace, so "inconceivably . . . mundane" is the correct answer.

The key is to realize that Catholic law was not organized, which could be described as “ad hoc”—i.e. not collected and pulled together only from case to case as needed. (The expression “ad hoc” literally means for this in Latin, indicating that something applies only “for this or that”—but not according to a universal, organized rationality); therefore, it was not gathered together into a single “code” in which all the statutes were organized. Thus, the word “codified” fits well for the first blank.

The first part of the sentence says that Maggie is not usually afraid, but the "but" is the key word that lets us know that the blanks describe her being afraid in the second half of the sentence. Starting with the second blank, "tentative" makes the most sense because it means hesitant or uncertain. This is confirmed as the correct choice by the first blank, "dilapidated," which means in bad condition because of lack of care. While "ramshackle" and "nervewracking" also would work, their partner words do not fit the context as well.

The opening word "though" tells us to expect a change in the relationship between these two siblings—either they were close as children and no longer are, or they didn't get along when they were young and do now; we are looking for antonyms. Three of the answer choices offer two words with very similar meanings: "docile" and "agreeable" (both depicting a fairly-pleasant relationship), "volatile" and "bellicose" (both describing a combustible or even warlike relation), and "strained" and "turbulent" (both telling of a relationship marked by tensions and fighting). Only the pairing of "tempestuous" (stormy) and "amicable" (friendly) provides the antonym pair we are looking for.

For the first blank, we need an adjective that describes how many films the filmmaker is able to create in a short amount of time. Both "hardworking" or "prolific" emphasize how many films the filmmaker is producing, so either word could work in the first blank. For the second blank, we're looking for an adverb that conveys how consistently the filmmaker is working; in choosing between the remaining answer choices "diligently" (industriously) and "ludicrously" (ridiculously), "diligently" is the better option, making the correct answer "prolific . . . diligently."

For the first blank, we're looking for a word that means "not likely," as the teacher knows that Billy's family doesn't have pets, but he is claiming that a dog ate his homework. Either "implausible" or "unbelievable" could work. For the second blank, we need an adjective that means something like able to be seen, or obvious. Either "palpable" (easy to perceive) or "tangible" (able to be physically touched) could work. Looking to see which of the possible answers we've identified match up, we can pick out "implausible . . . palpable" as the correct answer.

The sentence implies that Bryce has an aggressive personality and that he will fight over any topic, whether large or small. Some of the options for the first blank are tempting, such as “tempestuous” and perhaps even “overbearing.” However, “aggression” best matches the notion of fighting, and—even more importantly—none of the other options match the second as does the word “trivial,” meaning small or unimportant.

We can infer that because "many people [are] choosing to install fake, manmade grass," we need to pick out a combination of words that either means "real lawns have become rare" or "fake lawns have become common." While "artificial" and "manufactured" are both similar in meaning to "fake" and "manmade," only "artificial" lines up with a word for the second blank that means "common" - "commonplace." "Manufactured" lines up with "uncommon," so it can't be the answer, because if many people are installing fake lawns, manufactured lawns cannot be uncommon. Similarly, "authentic . . . pedestrian" cannot be the correct answer either, because if many people are installing fake grass, authentic lawns are not likely in the process of becoming "pedestrian," or commonplace. The correct answer is "artificial . . . commonplace" because it best fits the context of the sentence.