The key words in this sentence are "discrete points," particularly "discrete." This word means separate or distinct. Each point drawn is a separate whole on its own. To this is contrasted the line, which the passage implies is the opposite to this, being some kind of whole. When something is "continuous" it is unbroken, without the spaces that we find between discrete things. A line is like this. While you can divide it into points, no amount of points will ever add up to a line. This option is by far the best because it is directly contrasted to "discrete." Words like "mathematical" might be true in a sense, but they do not convey wholly what the sentence intends.

If the subject is afraid of the dark and tight spaces, he is likely to also be afraid of caves. He would, therefore, presumably, approach a cave with worry, fear, and hesitation, or “trepidation.” “Jubilation” means great happiness; “illiteracy” is the inability to read; “incentive” is motivation; and “aptitude” is skill or talent for something.

The fact that the man needs to learn "to control his puffed-up arrogance" says that he could best be described as “brash.” “Brash” means arrogant, self-important, bold, and careless; “meek” means shy and quiet; “hesitant” means unsure and slow in taking action.

It is clear from the context that the claims made by the man were "vague and unclear"; this tells you that the correct answer is “nebulous,” which means hazy, indistinct, or vague. “Intelligible” means able to be understood; “lucid” means expressed clearly; “comprehensible” means able to be comprehended or coherent; and “unambiguous” means not ambiguous, clear, and not able to be confused. In this instance, the four incorrect answer choices are all synonyms of one another and antonyms of the correct answer.

The author of this sentence seems to be expressing frustration and dismay about missing the bus in the morning, so you can say he or she is “infuriated.” “Infuriating” means frustrating, annoying, or making one angry; “placating” means soothing; “vigorous” means robust, strong, and fit; “trite” means cliché; and “repugnant” means disgusting or revolting.

The use of the word “except” suggests that although the friends agree about most things, they do not agree about baseball. So, baseball must be something “divisive” between them. “Divisive” means causing disagreement or hostility. As for the other answer choices,“aghast” means shocked; “indignant” means outraged or offended; "minor," in the context of the sentence, means relatively unimportant; and “hackneyed” means trite or clichéd.

If the demand of the customers is “ravenous” (insatiable or very hungry), then you can infer that the store would want to be well-stocked or full of copies of the video game to meet that demand. The correct answer is therefore “replete,” which means full of. As for the other answer choices, “nimble” means agile; “palatable” means edible or appetizing; “gaunt” means too skinny, thin, and bony; and “unkempt” means messy.

The context of the sentence suggests that the runner was unaffected by pain and fatigue, so the best answer is “impervious.” “Impervious” means not affected by or unable to be penetrated by; “kinetic” means related to movement; “robust” means strong and sturdy or healthy and tough; “hoary” means old and gray or cliché; and “congenial” means agreeable or pleasant and likable.

From context, you can tell that the underlined word must mean something like important or crucial. This should lead to the correct answer, which is “imperative.” “Imperative” means necessary. As for the other answer choices, “senseless” means without sense or pointless; “approachable” means friendly-looking and able to be approached; someone who is “opportunistic” seizes and takes advantage of opportunities; and “deleterious” means hurtful or harmful.

Because the old man is able to save money and yet has a small and limited (“meager”) income, you know that he must lead a very “frugal” existence. “Frugal” means thrifty, economical, or sparing of expense. As for the other answer choices, “affluent” means wealthy; “prosperous” means wealthy and successful; “morose” means sulky and in a bad mood, and "jumbled" means physically disorganized.