This analogy uses adjectives that decrease in intensity. "Illustrious" contains the root "lustr" meaning shine. It is being compared to "impressive." While something "impressive" is "nice," we attribute more value to things that "shine." Take for example, gold or jewels.  Following this relationship, we want a word that has the same basic meaning as "offensive" but with more intensity or strength.  

Of the choices, only "abhorrent" is correct. All the words in the analogy are adjectives, meaning the answer must also be one. Additionally, "abhorrent" contains the prefix "ab" (away) and the root "horrere" (horror, tremble at). Put together, these mean something that is so horrible, we turn away in hate and disgust.

Malicious (adj), root word "mal" (bad, evil). While something "evil" could be "offensive," it is not directly related in meaning to "offensive."

Luminous (adj), root word "lum" (light). This word is related to "illustrious," not "offensive."

Graceful (adj), means full of grace, smooth of disposition and well-mannered. Again, this is the opposite of "offensive."

Dissecting (verb), refers to the act of cutting (a body) into two for study. While some might find the act offensive, it is subject to personal opinion, and is not an adjective.

The word "pungent" means strong smelling. "Pungent" is a particularly intense word that relates to smell. So, to solve this analogy you are looking for an answer that is a particularly intense word that relates to sound. The correct answer is "deafening" which means very loud. Additionally, "harmonious" and "melodious" both mean pleasant sounding; an "aspirant" is someone with goals, someone who aspires to something in particular.

"Infinitesimal" means very small, tiny. So, to solve this analogy you are looking for the answer choice that means very large, giant. The correct answer is therefore "gargantuan." Additionally, "illicit" means illegal, against the rules; "humiliating" means embarrassing, causing shame; "abstruse" means hard to understand; "obtuse" means stupid.

To begin with to "meander" is to move slowly, in an indirect fashion. And, to "hurtle" is to move very quickly, in a chaotic fashion. Both words relate to movement, but "hurtle" is a much more intense form of "meander." So, to solve this analogy you need to determine which of these is a much more intense form of "trickle." To "trickle" means (of a liquid) to fall in very small quantities. So, the correct answer is "cascade" which means to fall rapidly. Additionally, "orate" means speak in public; "galvanize" means motivate, inspire to action; "bolster" means support, reinforce; "loft" means throw up high.

"Miserable" is a more intense version of being "sad." So, to solve this analogy you need to determine which of these is a more intense version of being "happy." The correct answer is "blissful" which means full of bliss, deeply and profoundly happy. Additionally, "irate" means furious, very angry; "celestial" means heavenly; "prostrate" means lying flat; "monotonous" means boring, unchanging.

To "hound" means to pursue relentlessly. ("The criminal was hounded across the country by law enforcement and finally captured.")

Is to "badger" to harass relentlessly? Yes, by definition, that’s exactly what it means. ("James badgered me every day for a week until I paid him the five dollars I owed him.") So, "badger is to harass" is the correct answer.

Does "efface" mean to approach relentlessly? No. To "efface" means to erase or to make seem insignificant. It has nothing to do with approaching someone or something.

Does “to bug” mean to defeat relentlessly? Nope. To "bug" is to annoy.

Is “to faze” to mollify relentlessly? No. To "faze" means “to disturb or unsettle” someone, whereas "mollify" means to reduce the anger of someone. They are basically antonyms, so they have a connection, but it isn’t the  connection that the stem words have.

Lastly, "rat" does not mean to edge relentlessly.

A "gale" is a very strong wind. A "downpour" is a very heavy rainfall. This question asks you to identify a change, in this case an increase, in intensity.

A "breeze" is a light wind and a "gale" is a very strong and powerful wind. So, to solve this analogy you need to determine which of these is a more intense version of a "trickle." Well, a "trickle" is a slow-moving stream of water. So, the correct answer is "torrent," which means a very powerful and fast-moving stream of water. Additionally, "gust" refers to a sudden and powerful flow of wind; "drizzle" means (of rain) to fall slowly and weakly.

A dog is a domesticated canine, while a wolf is a wild canine. So, because a cat is a domesticated feline, we need to pick out an answer choice that describes an animal that is a wild feline. “Lion” is the only answer choice that refers to a wild feline, so “lion” is the correct answer.

Hound dogs bay; it is a very specific sound associated strongly with this type of dog (canine). A howl is a specific sound associated strongly with a wolf (also a canine). "Cat is to purr" and "Snake is to hiss" also make some sense, but the BEST fit is "wolf is to howl" as both animals are canines.