IMO - D.

A -> should have had "...in the stride-piano tradition of Willie (The Lion) Smith and <in something..> or <that of> Duke Ellington..."

B -> again reference missing.

C -> <who> extra.

E -> again same error as A.

"both" in the sentence could have come in "...in the stride-piano tradition of <both> Willie (The Lion) Smith and Duke Ellington..."

what is the OA?

Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted in the stride-piano tradition of Willie (The Lion) Smith and Duke Ellington, yet in many ways he stood apart from the mainstream jazz repertory.

A. Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted ------> same as B
B. Thelonious Monk, the jazz pianist and composer, produced a body of work that was rooted both --------> usage of wrong idiom as the correct one is "both in x and in y or both x and y"
C. Jazz pianist and composer Thelonious Monk, who produced a body of work rooted ------> awkward
D. Jazz pianist and composer Thelonious Monk produced a body of work that was rooted
E. Jazz pianist and composer Thelonious Monk produced a body of work rooted both-----> same reasoning as A and B.

Great discussion here - and one big takeaway is that the word "both" is a pretty good signal that parallel structure is going to be necessary.

With A, we have "Monk produced a body of work BOTH rooted in X..." so we need a second clause that leads with a verb and a description, something like "and derived from Y". Since that's not there, A is incorrect.

With B, we have "Monk produced a body of work that was rooted both in X...". The verb is outside of the split for "both", so we just need "and in Y". But, again, that's not present, so we can't use "both" in this way, either.

D just avoids the use of "both" altogether, which is perfect, as the fixed portion of the sentence doesn't lend itself to use with "both" in any of the ways it appears. But the presence of "both" should tip you off - you need to have two parallel items, and if they're not there you can get rid of that choice.

IMO : D

OA is D

Good work guys...