Hello Everyone!
Let's tackle this question, one issue at a time, to figure out which option is the correct choice! Here is the original question, with the major differences between each option highlighted in orange:
A professor at the university has taken a sabbatical to research on James Baldwin's books that Baldwin wrote in France while he was living there.
(A) on James Baldwin's books that Baldwin wrote in France while he was living there
(B) about the books James Baldwin wrote in France
(C) into James Baldwin's books written while in France
(D) on the books of James Baldwin, written while he lived in France
(E) the books James Baldwin wrote while he lived in France
After a quick glance over the options, two major differences become clear:
1. How they begin
2. How they end
If we start with how each option begins, we need to focus on the idiomatic structure with the phrase "to research."
Whenever we research something, we have to ask the question: WHAT are we going to research? In English, we follow the structure "to research X," with X being the topic at hand. Let's see which options use the idiomatic structure correctly, and rule out those that don't:
(A) to research on James Baldwin's books that Baldwin wrote in France while he was living there --> "to research on X" is INCORRECT
(B) to research about the books James Baldwin wrote in France --> "to research about X" is INCORRECT
(C) to research into James Baldwin's books written while in France --> "to research into X" is INCORRECT
(D) to research on the books of James Baldwin, written while he lived in France --> "to research on X" is INCORRECT
(E) to research the books James Baldwin wrote while he lived in France --> "to research X" is CORRECT
There you go - option E is the only one that uses the proper idiom structure "to research X."
Don't study for the GMAT. Train for it.