The relationship in "eating is to feasting" is that while "eating" and "feasting" both mean consuming food, the word "feasting" has a more intense meaning that that of "eating." "Eat" means to take in for nourishment while "feast" means to eat a lot, often at great expense. There is an increase in degree between the words "eat" and "feast." The pair that shares this relationship is "walking is to running," so it is therefore the best choice. "Sprinting is to running" has the appropriate relationship but is in the reverse order and shows a decrease in degree, because "sprinting" is a less intense action than is "running". Because of this, it is not the appropriate choice. Considering the other choices, the "sky" is made up of "air", "nice" and "kind" are synonyms, and "hopscotch" is a type of "game."

Since a mountain can be thought of as a really large hill, we need to pick out a word that can be thought of as a really large pond. While "lake," "river," and "rain" all have to do with water, "lake" is the best answer because a river involves flowing water, which a pond doesn't, and rain involves water falling from the sky, which a pond doesn't either. Since a lake can be thought of as a large pond, "lake" is the best answer.

“Gale” is a noun that means “a very strong wind,” so we need to pick out an answer choice in which the first word represents a very strong version of the second word. While “ashes are to fire” and “downpour is to rain” might each look like a potentially correct answer, “ashes are to fire” cannot be the correct answer because “ashes” are defined as “the powdery residue left after the burning of a substance,” not “a large or powerful fire.” “Downpour,” however, when used as a noun, means “a heavy rainfall,” and because a downpour is a heavy rain just as a gale is a strong wind, “downpour is to rain” is the correct answer.

“Ravenous” is an adjective that means extremely hungry. Since “hungry” and “ravenous” are synonyms, and “ravenous” has a greater intensity than “hungry,” we’re looking for a pair of words that are synonyms, in which the second word has a higher intensity than the first.

 Since “fever” is a symptom of the “flu,” the words have a cause-and-effect relationship. The words aren’t synonyms. We can rule out this choice. 

 “Guzzle” is a verb that means to eat or drink something greedily. Although “guzzle” has a higher intensity than “thirsty,” the words aren’t synonyms. We can rule out this choice. 

 “Satisfied” is an adjective that means pleased or content. Though “happy” and “satisfied” have similar meanings, they intensity is about equal, so we can rule out this choice. 

 “Furious” is an adjective that means extremely angry. It is a synonymous with angry” with a higher intensity.

Of the answer choices, “ANGRY is to FURIOUS” is the best choice.

“Abhor” is a verb that means to hate or detest. Since “like” means to find agreeable or enjoyable, we’re looking for a pair of words in which the second word is opposite in meaning and higher in intensity.

“Compliment” and “insult” are antonyms with equal intensity, so we can rule out this choice.

“Hero” and “villain” are antonyms with equal intensity, so we can rule out this choice.

Although at times one might “like” their friends and “abhor” their family, “friend” and “family” are not antonyms. We can rule out this choice.

“Miserable” is an adjective that means wretchedly unhappy or uncomfortable. It is an antonym to “happy” with a higher intensity.

Of the answer choices, “HAPPY is to MISERABLE” is the best choice.

"Eradicate" means to completely destroy, to 'wipe something out.' It is a more intense version of the word "destroy." So, to solve this analogy you need to determine what "trounce" is a more intense version of. The correct answer is that "trounce" means to rout or to heavily "defeat." Additionally, "rectify" means to repair a situation, to fix a problem; "mend" means to repair a breakage, to fix something that is broken.

A "knoll" is a small hill. So, to solve this analogy you need to determine which of these answers means something like small river. The correct answer is therefore "stream." Additionally, an "estuary" is the mouth of a river, the place where a river runs into the ocean.

A "grove" is the name given to a small "forest," a small wooded area. So, to solve this analogy you need to determine which of these words could describe a larger "principality." Well, a "principality" is a small, independent nation ruled by a prince. So, the correct answer is "kingdom."

A "pebble" is a small rock or stone. So, to solve this analogy you need to figure out which of these a "hamlet" is a small version of. The correct answer is that a "hamlet" is a village, or a small "town." 

A "dinghy" is a small "boat." So, to solve this analogy you need to determine which of these is a word that describes a small "lake." The correct answer is "pond."