Since the sentence is not general about the kind of math problem involved, the best answer will be that one which is most general. Therefore, the option “elements” best fits, for it can mean merely “the smallest part” of something, unable to be broken down any further. This can apply to anything, not merely the so-called chemical elements. All of the other options imply more specificity than is needed here.

Since Scott realizes that he should have listened to stories about previous generations, he is interested in those who preceded him, that is, his ancestors. Therefore, the best option is “ancestry” which applies to the generations that precede a person. The word literally means “those going before (someone).” The “cest-” portion is related to English words like “secede” (or “secession”) meaning “to go apart or away” (e.g. when the South seceded from the North during the Civil War). The “an-” prefix of “ancestry” comes from the Latin “ante-”, which means “before.” The word “antebellum” is often used to describe the southern states of the United States before the civil war. It literally means “before the war.”

The only thing implied by this sentence is that the country experienced a reduction in certain services. While this might mean poverty or a bad economy, the closest word is “austerity,” which generally means “plainness” or “sternness.” When applied to government actions, it can carry the additional meaning of “cutting services.” Think of it as “making the government services plain or simpler.”

The key word to the contrast is “several small” found in the main clause. This implies that most of the evidence was centered on the fateful night of the crime. The word “bulk” can mean “the majority” in addition to “a large mass.” It is therefore better than the other options, which do not reflect this contrast as well.

Although Diane might be said to be insane or perhaps even irrational because of her refusal to change, we cannot go beyond this stated fact. Therefore, he is best described as being “rigid,” meaning that she is “unbending” or “inflexible” in the sense of not deviating from her positions. The word is related to “rigorous” and “rigorist.”

Here, the only way to choose the correct answer is to find the one that most directly matches the key expression “he must believe that nobody else actually exists.” While many of the options deal with “self-centeredness,” only “solipsist” means “someone who believes that only oneself can be known.” The word comes from the combination of the Latin “solus,” meaning “alone” and “ipse,” an intensifying pronoun meaning “him/her/itself.” The first can be found in words like “solitary” and “solitude.” The latter can be found in odd English words like “ipseity,” meaning “selfhood,” as well as the Latin expression used in legal parlance, “res ipsa loquitur,” meaning, “The thing (event, data) speaks for itself.”

The explicit statement in the sentence refers to the production of milk. Therefore, the option “lactation” is the best answer, for this is the word for the secretion of milk from a mammalian mother to its child. The “lact-” prefix comes from the Latin for milk and is found in English words like “lactose,” a type of sugar found in milks and “lactic acid,” which is found in sour milk but also in the body after exercise, causing soreness.

The key expression is “eat nearly any type of food.” Note that this does not say that Ken eats large quantities of food. Therefore, any of the options that imply gluttony (and so forth) are not acceptable. The sentence is a bit playful, using a word as an affectionate title. Based on the context, we can tell that the title must mean something like “eats everything.” To this end, “omnivore” fits well. The word literally means “eating all things.” The “omni-” prefix (meaning “all”) is found in many word like “omniscience” and “omnipotent.” The “-vore” comes from the Latin for “to swallow,” though it is used in words like “voracious” (desiring much food) and the other “-vore” words like “herbivore” and “carnivore.”

The key thing to note in this sentence is that the vegetarians are described as eating more than plant products. The implication is that they cannot be called properly “animals eating only plant products.” Such animals are “herbivores,” a word constructed from the parts “herb-”, meaning “grass,” and “-vore,” literally meaning “to swallow.” The prefix is found in words like “herbicide” (something that kills grasses) and “herbal.” The latter is found in words like “voracious” (desiring much food) and the other “-vore” words like “omnivore” and “carnivore.”

Since the sentence is very vague regarding exactly what the crown matched on the King, the word to be chosen must likewise be vague. Although it is a bit old-fashioned, the word “raiment” means “clothing.” It is often used literarily, so the application to a king is perhaps somewhat understandable.