Although we often think of “negotiations” as the interaction between two parties attempting to come an agreement, it can also have the sense of “finding a way past an obstacle.” For instance, one can say, “She managed to negotiate the winding passes of the mountain, only to realize that she had many more miles to travel.” For this reason, do not be tricked by any of the wrong answers, all of which mean to tempt you into choosing in accord with your sense of “negotiation” as an attempt to come to an agreement. None of those other options express the very act of negotiating (in which there is “back and forth”). The best option is “overcome.”

“Whet” means physically sharpen or encourage and stimulate, as in the phrase "whet one's appetite." “Persevere” means persist; “defiant” means noncompliant, showing resistance and stubbornness; “overwrought” means hysterical or in a state of agitation; and “compassionate” means kind and loving.

The word "faint" can be used to indicate the physical act of passing out (as well as the feeling that often precedes this). The word also can indicate something that is almost too weak to be sensed at all. Thus, a "faint sound" is one that is very soft, and a "faint pencil mark" is one that is very lightly written on a piece of paper. This last example indicates that the writing is very light and likely vague—meaning that it is indefinite in shape. Likewise, "faint memories" are ones that are very vague and indistinct. Thus, do not be tricked by options like "sickly" and "unhealthy" (or even "underweight"). These options are trying to lure you into thinking that "faint" must deal with passing out, but this is not always the case. Even if this were the meaning for this question, being sickly only leads to fainting. It is not the same as the act of fainting itself. Thus, the best option is "vague."

The word "pellucid" comes from Latin roots that mean light. This is the "-luc-" root that comes from "lux, lucis." To be "pellucid" means, literally, to let light shine through. Thus, the word can be a synonym for "translucent," which also contains the lux root. Often, the word is used to describe someone's ability to communicate ideas clearly and understandably. Such a person lets the ideas "shine through." Thus, the best option among those offered is "understandable." Something that is "pellucid" in this latter sense is something understandable—like a "clear idea", as many say.

The word "fabricate" comes from Latin roots roughly meaning "to make or create." A related word is "fabric", which is a carefully crafted type of cloth. The word "fabricate" can have a negative connotation too, and this is the case for this question. A "fabrication" can be a lie—something that is "made up", as we often say in day-to-day speech. To "fabricate a tale" means to craft and tell a lie or false story. When we "counterfeit", we make something that is false—such as false money, which we most often describe by the adjective "counterfeit" (though "counterfeit" can also be used as a verb).

The word "modest" has several meanings, though all of them have to do (in general) with being in the "middle" or "moderate." Modesty is the character trait of not bragging but, instead, having an accurate idea about one's abilities. A "modest income" is an acceptable income—not too much, not too little. The word does, however, emphasize the fact that it is not too much. Thus, it has a shading of meaning that indicates that it is a smaller amount. Still, the general idea is to express that it is not a large amount. For this question, "modest" is used in yet another sense. When a young lady has on a "modest dress", she is wearing something that is not overly revealing of her physique. Thus "modest" can mean proper,  as in suitable.

The word "devolve" comes from two well-known Latin roots. The "de-" prefix means down from or downward, as in words like "descend" and "delegate." The "-volve" portion of this word is the same as the root found in "revolve", meaning in general to roll. Thus, when something "devolves" it goes downward. Sometimes, this indicates that a situation becomes worse, as when we say, "The meeting devolved into a lot bickering, hateful remarks."  It can also mean to delegate or to transfer authority from a higher level of command to a lower one. Thus, a commander might devolve his authority to smaller groups of troops and their commanders. (Thus, the power "rolls downward", you see?) Therefore, the best option is "transfer", as none of the other options match the other meanings of "devolve." 

The word "rustic" is used to describe something that is in the country. It could indicate that the thing in question is merely in a rural location. It also can be used in a positive manner to describe a kind of simple beauty that is involved in the thing. The word does have a negative connotation, for it can be used to imply that someone is uncivilized or uncultured because he or she does not live in the city. Thus, the option "unsophisticated" matches this last meaning. (The word "impoverished" does not, as "rustic" does not primarily have to do with being financially disadvantaged.)

The word "sophisticated" can be used to describe a number of things that are related. The general meaning that applies to the various uses is highly developed, intricate, or refined. A sophisticated machine is a complex one that takes much skill to create. A sophisticated person is someone who is very knowledgeable about the complex matters of the world. Now, this does not mean that the person is "scholarly," "reflective," or "haughty." These are perhaps things that we associated with some sophisticated people, but the best meaning provided here is the most direct one, namely "intricate," which means complex.

The word "irrelevant" means no longer applicable. Now, it is possible that you have heard the term be used to describe something that is boring or even tedious; however, these are reactions that people have to irrelevant matters. For example, if someone does not care about learning logic, he or she will find a philosopher to be pretty boring—precisely because the philosopher is irrelevant to the given person. The irrelevance causes the boredom. It is not the same as it, however!

Thus, the best option is "immaterial," which is a direct synonym for irrelevant. (The word also can mean non-material or spiritual, but this is not of direct interest to this question.)