If you "trudge," it means you walk slowly, so you need to pick out an answer choice that describes your speed when you "sprint." If you sprint, it means that you run very quickly, so as trudged is to slow, sprinted is to “fast.”

Plugs fit into sockets, so we are looking for an answer in which the first word fits into the second word; thus, the best answer choice is "key is to lock," because a key fits into a lock.

Since you use a hoop to play basketball, we need to pick out another pair of words in which the second word describes something that you use to play the game that the first word describes. While "tennis" and "baseball" are each sports, "catch" is not something you use to play baseball—it can't be, as it's not a noun. "Racket," however, is something that you use to play tennis, so "tennis is to racket" is the correct answer.

“Walking” is an action undertaken by a cat when it wants to get from one place to another. To solve this analogy, you need to figure out how a fish moves from one place to another. The correct answer is “swimming.” The key to solving analogy questions is to figure out the relationship between the first two words and then use that same relationship to figure out the missing word.

A “priest” is a religious leader, and someone who would be likely to be “preaching.” “Preaching” means speaking forcefully and giving advice on how to live one’s life. To solve this analogy, you need to figure out which of these answer choices is an action associated with being a “professor.” A “professor” is a well-educated teacher who works at a university, so you can assume that a “professor” is associated with “teaching.” To provide further help, “clergy” is a name for the group of all priests considered together, particularly in Christianity.

Students learn, so you need to pick out an answer choice that is a verb and describes what teachers do. Teachers "instruct," which means teach, so "instruct" is the correct answer. While the other answer choices are all words that you might use when talking about teachers and students, none of them are verbs, and because "learn" is a verb, we know that the word that goes in the blank needs to also be a verb. The incorrect answer choices are all nouns.

"Oral" is an adjective that means related to the mouth. To solve this analogy you need to pick out a noun that relates to the adjective "nasal." The correct answer is “nose," because "nasal" means related to the nose.

Syrup is commonly put on top of pancakes, so we are looking for an answer in which the first word is a popular topping put on the second word. Thus, the best answer choice is "icing is to cake" because many cakes have icing on them!

Blue is a component color of green. (Green is created with a combination of blue and yellow.) Thus, the correct answer would be one in which the first word is a color that when combined with the color yellow, results in the second color. 

When red is combined with yellow, the resulting color is orange. Therefore, "red is to orange" is the correct answer.

In this problem, a tadpole is the stage that a frog is in before it becomes a frog. Similarly, batter is the stage that a cake is in before it becomes a cake. While a tadpole must grown and develop, a cake must bake. In both cases, there is a developmental stage that has to happen between each of the two pairs of words. 

A tempting wrong answer is "addition is to division." While division is more complex than addition, there is not a stage of growth causes addition to become division.