The relationship between "green" and "blue" is an uncommon one: they are both types of colors. Since "sad" is an emotion, we must look for another word that is an emotion. The only choice that shares this relationship with "sad" is "angry." "Blue" is a color and unrelated in this regard. "Smile" and "frown" are facial expressions that accompany certain emotions. "Tears" can also be considered an expression of sadness, but is not an appropriate choice because "tears" are not an emotion themselves.

"Fog" and "hail" are both varieties of weather, so we're looking for a word which fits into the same category as "red." While both "blue" and "color" may look like potentially correct answers, "color" is the category into which "blue" and "red" both fit, and "blue" an example of something that fits into that category along with "red," so "blue" is the correct answer, because as fog and hail are both types of weather, red and blue are both colors.

"Gold" and "silver" are both elements and precious metals, so to solve this analogy, you have to figure out which answer choice is grouped with "oxygen" in a similar fashion. Oxygen is an elemental gas, so the answer choice should also be a gas. The correct answer is therefore “nitrogen.” The answer cannot be "gas," "atmosphere," or "breathe," because although these words are related to oxygen, their relationship is not comparable to the relationship between "gold" and "silver."

Since a sail is the part of a sailboat that propels it forward, we need to pick out an answer choice that describes what part of a carriage propels it forward. While "horse," "door," and "axle" are each components of a carriage, it is a horse that propels a carriage forward by pulling it, so "horse" is the correct answer.

Words are the constituent parts of sentences, so we need to pick out an answer choice in which the first word is the constituent part of the second. While "paragraph is to sentence" and "book is to page" might each look potentially correct, sentences make up paragraphs and pages make up books, not the other way around as the answer choices are listed, so neither of those answers can be correct. Letters make up words just as words make up sentences, however, so "letter is to word" is the correct answer.

A shoelace is part of a tennis shoe, so we need to pick out an answer choice in which the second word is a part of the first word. Of the potential answer choices, "beak is to bird" and "blubber is to walrus" might each look like potentially correct answers, but because each of those answers's words are in the wrong order, neither can be the correct answer—birds are not part of beaks, but the other way around, and neither are walruses part of blubber. "Computer is to keyboard," however, is the correct answer, because just as shoelaces are part of tennis shoes, keyboards are part of computers.

A chapter is a subdivision of a book, so we need to pick out an answer choice in which the first word is a subdivision of the second. While “week is to month” and “day is to hour” might each look like a potentially correct answer, a day is not a subdivision of an hour, so “day is to hour” cannot be the correct answer. A week is a subdivision of a month, however, just as a chapter is a subdivision of a book, so “week is to month” is the correct answer.

An "army" is a group of soldiers lead by a general, so to solve the analogy, we need to pick out an answer choice that describes the person who leads a "team." A "captain" leads a "team," so "captain" is the correct answer.

The relationship in "sleeve is to shirt" is part to whole. The best choice is "branch is to tree" because a branch is a part of a tree. The choice "car is to wheel" demonstrates the same relationship, but the words are in the reverse order of whole to part rather than in the order of part to whole as the question is worded. As such, it is an inappropriate answer. Remember, the order of the words in the answer must appear in the same way as the question. Considering the other choices, "human is to mammal" has a categorical relationship in which humans are a type of mammal. "Spark is to fire" holds a cause and effect relationship and "ugly is to hideous" represents an increase in degree.

An engine is a part of an airplane. Likewise, a window is a part of a wall, making the choice "wall" the best answer. The choice "glass" would make the relationship whole to part or characteristic of, as you can think of glass as being a part of a window or describing one type of window. A "window" is an opening in a wall and does not necessarily need to have glass in it, though it usually does. Another word for "drapes" is "curtains," both of which cover a window. "Clear" is another characteristic of a glass window. "Wood" is unrelated unless you consider that a frame for a window may be made out of wood. In that case the relationship would be whole to part.