The key to linking these words is to look at their prefixes. “Overwhelmed” is to be overcome with feelings, whereas “underwhelmed” is to have a lack of feelings for something. The equivalent of pair of words for "educated" would be “overeducated” and “undereducated.” To further help you, if something is “educational,” it can be used to teach something, “uneducational” is the opposite of this. A person who is “educated” has learned information to a significant degree. If you are “re-educated,” you are taught the same information again or you are taught new information which is different from what you had previously been taught.

A “diameter” is a line running through the center of a circle from one side to the other. A “radius” is half the diameter, so to solve this analogy you have to determine which answer choice means half a circle. The correct answer is “semicircle.” The prefix "semi-" means half and the prefix "dia-" means through, across, over. To provide further help, the “circumference” is the length around the outside of a circle; a “sphere” is a three-dimensional circle; “parallel” means running alongside, having the same slope; “perpendicular” means running on opposite slopes and is the opposite of "parallel." 

“Infancy” is the state of being a baby. Similarly, "adolescence" is the state of transitioning from childhood to adulthood, or the state of being a "teenager."

The prefix "arachno-" means related to spiders and the suffix "-phobia" means fear of, so “arachnophobia” is a fear of spiders. The prefix "aqua-" means related to water, so “aquahobia” is a fear of water. 

The word fragment "-athl­-" suggests a sporting or exercise term and indeed a “triathlon” is a sporting competition with three events. The prefix "tri-" means three. Similarly, the prefix "dec-" means ten, so a “decathlon” is a sporting competition with ten events. 

The suffix "-archy" means ruling, so in a “patriarchy,” the people are ruled by a man or a group of men. In a "matriarchy," the people are ruled by a woman or a group of women.

The prefix "dys-" is a negation prefix; this means it takes the original meaning of the word “functional” (working) and causes it to mean the opposite, so “dysfunctional” means not working. To solve this analogy, then, you need to determine which of the answer choices means the opposite of “endorse.” “Endorse” means give support to, so the best available antonym is “undermine,” a word that means work to prevent someone from succeeding or something from occurring or working. None of the other answer choices work as antonyms of "endorse": "support" is a synonym of "endorse"; “demonstrate” means show someone or a group how to do something by example; “pretend” means fake; and “harangue” means rebuke, scold, or tell-off.

The “medieval” period of history occurred between the ninth and fifteenth century CE in Europe and Asia. As it is a period of history, it can be said to be an “era.” To solve this analogy, you have to determine which of these categories “Mediterranean” fits into. It is worth noting that the prefix "med-" means middle, so the “medieval” period was so named because it was a middle period between antiquity and the modern day, while the Mediterranean sea was so named for being in the middle of Europe and Africa—that is, between the two continents. So, because the Mediterranean is a sea just as "medieval" is an era, "sea" is the correct answer.

A “century” is one hundred consecutive years, so to solve this analogy, you have to determine how many years a “millennium” is. The correct answer is a "thousand.” The prefix "cent-" means hundred, and likewise, the prefix "mil-" means thousand. Just think of "centipedes" and "millipedes" if you think you might get these confused. The key here is not to be confused by the fact that "millennium" does not refer to a span of a "million" years, despite "million" also beginning with "mil-."

You use scissors to cut, so to solve this analogy, you need to pick out an answer choice that is a verb that describes what you do with a needle. The correct answer is to “inject” something. The prefix "in-" means put into, so “inject” means to put something, usually a liquid, into something else. To provide further help, “induce” means force or cause to be, and “imply” means suggest.