This is a Sufficient Assumption question so our job is to add a premise to make the existing argument valid.
It's a very difficult question because you had to realize that they fed you the definition of "prudent" in the premises. The definition is "forming opinions of others only after cautiously gathering and weighing the evidence."
If you can't get over that hurdle, you're likely getting this question wrong.
Assuming you made that connection, then replace that long definition in the premises with the word "prudent" and you should see that this is like any other SA question.
Premise in English: being prudent will make people resent you.
Premise in Lawgic: P --> R
Conclusion in English: appearing prudent is imprudent
Conclusion in Lawgic: P --> Imp
What's the missing SA?
SA in Lawgic: R --> Imp
SA in English: making people resent you is imprudent.
That's (E)
The Iliad and the Odyssey were both attributed to Homer in ancient times. But these two poems differ greatly in tone and vocabulary and in certain details of the fictional world they depict. So they are almost certainly not the work of the same poet.
Summarize Argument
The author concludes that the Iliad and the Odyssey were almost certainly not written by the same poet. She bases this on the fact that the two poems differ greatly in tone and vocabulary and in their depictions of the fictional world.
Notable Assumptions
The author assumes that, just because two works differ greatly in tone, vocabulary, and other details, they were almost certainly not written by the same person. This means the author assumes that the same writer cannot or would not write two works that differ greatly in these respects.
A
Several hymns that were also attributed to Homer in ancient times differ more from the Iliad in the respects mentioned than does the Odyssey.
We don’t know if Homer actually wrote these hymns that were attributed to him. So, (A) doesn’t tell us anything about whether the same writer could or would write separate works that differ in tone, vocabulary, and other details.
B
Both the Iliad and the Odyssey have come down to us in manuscripts that have suffered from minor copying errors and other textual corruptions.
Just because the Iliad and the Odyssey have suffered from “minor copying errors” doesn’t change the fact that the two poems differ greatly in tone, vocabulary, and other details. So the question of whether they might have been written by the same author remains.
C
Works known to have been written by the same modern writer are as different from each other in the respects mentioned as are the Iliad and the Odyssey.
By presenting works by the same modern writer that differ greatly in tone, vocabulary, and other details, (C) proves that the author’s assumption (that two works that differ in these respects can’t be by the same writer) cannot be true. So, the author’s conclusion doesn’t follow.
D
Neither the Iliad nor the Odyssey taken by itself is completely consistent in all of the respects mentioned.
The fact that parts of a work vary in these ways doesn't answer the question of authorship. Perhaps, for example, the work had multiple authors. We need an answer that addresses the assumption that works with such differences can't have been written by the same person.
E
Both the Iliad and the Odyssey were the result of an extended process of oral composition in which many poets were involved.
By suggesting that many poets contributed to the poems, (E) further argues against the idea that the Iliad and Odyssey were written by a single author. So it doesn't weaken the author's conclusion.