A “colloquialism” is a type of expression that is used in conversation though it is not used in formal speech. It comes from a form of the “cum-” or “con-” prefix (here “col-”) being placed on the “-loq-” base that means speech and other related meanings. (The “-loq-” comes from a Latin base meaning to speak and found in English words like “locution,” “eloquent,” and “colloquy”). For our purposes, merely note that a colloquialism is a specific type of expression. “Expression” is a general class into which “colloquialism” can be placed. Thus, we are looking for the general class into which “pension” can be placed. Strictly speaking, a "pension" is the payment that one receives, generally for retirement. It is not per se a savings, but instead is a payment promised by some organization or government to another person. We use the word to describe such payments as being used for retirement, though it used to be used to describe the types of payments that a patron would give to some artist or scholar to allow that person to continue his or her work.

Although “coin” might at first glance appear to be synonymous with “money,” it is better described as being a type of money. Coins can be created for a number of reasons—commemorations, decoration, etc.—and money can come in many forms—paper, coins, electronic forms, checks, etc. The bridge sentence for the analogy could thus be expressed as, “As coins are a type of money, so are letters a type of X.” While several options might be tempting, “document” is the closest thing to a class into which letters can be assigned. Letters are written on paper, perhaps by calligraphers, but they are neither types of paper nor types of calligraphers.

A king is a type of ruler, thus the correct answer for this question will be the word that tells us what is the general type into which “reed” fits. You might know the word from being in band, for it is used to describe instruments like the clarinet and the saxophone. These instruments are called “reed instruments” because of the small wood-like portion used for producing the initial sound. The small item is actually part of a type of grass, which is called “reed.” Thus, the general class into which “reed” falls is the simple word “grass.”

Someone “embezzles” when he or she steals or misuses money that had been put in his or her control (generally for the good of some organization). Such a person is a specific type of criminal; therefore, we are looking for the general category into which “professor” can be placed. Although professors do research and review books (among other things), they are best placed in the general class “educator.” All of the other options are related in some way to what it is to be a professor; however, none of them give the general class of which the professor is a specific instance (as embezzler is a specific type of criminal).

A representative is person in a legislature, which is a law-giving body in a government. Thus, we could translate this analogy as stating, “As a representative is a member of a legislature, so is a earl a member of X.” The aristocracy is the upper class in a society, often by hereditary title, though there is such a thing as an aristocracy of excellence (a meritocracy). An earl is a type of high-raking noble in England. Thus, an earl is a member of the aristocracy. All of the other options are trying to make you answer based on non-essential properties. You need a word like “aristocracy,” which is an appropriate, broader class of which earls are members.

A compendium is a small, though detailed, collection details regarding some topic. For instance, Thomas Aquinas wrote a little “compendium of theology” as short guide to theological questions in the thirteenth century. Here, it is best to read the analogy as stating, “As a compendium is a type of collection, so is a harangue a type of X.” A harangue is an angry and likely nasty type of speech. The other options might describe “harangue,” but none of them are general classes into which it might be placed.

A camera is said to “capture images.” The implication is that it takes pictures and stores them in some medium. For this reason, the implication of the analogy is that a microphone also captures something, namely sounds. While “waves” might be tempting, note that cameras also capture light waves. The analogy is speaking more of the representation that is recorded by the instrument—images, not merely waves. The waves could be recorded as a chart of scientific data if one so wished, and that would not be exactly the same as saying that an “image was captured.”

When someone smirks, he or she smiles in a self-satisfied manner, generally because he or she is smug, that is, prideful in some accomplishment. The bridge sentence could be written, “As someone acting smugly would smirk, so would someone acting exuberantly X.” Exuberance is the state of having a great deal of energy, often in a cheerful manner. Such a state would likely lead one to grin.

Something that is oscillating swings back and forth in a regular pattern. A pendulum does just this—as in the pendulum in a grandfather clock. The simple word “swinging” must therefore be paired with something that has a swinging movement (just as a pendulum has an oscillating movement). Among the options provided, only the word “hinge” denotes a “thing.” This alone weighs heavily in its favor. Likewise, the word does describe the small joint of a door that is the tiny origin of the swinging motion of the larger door surface.

One can "advance" in a "forward" direction, just as one can "retreat" in a "backwards" direction.