Hello Everyone!
Let's tackle this question, one issue at a time, and narrow it down to the right option quickly! To start, here is the original question with any major differences between the options highlighted in orange:
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
(B) Thelonious Monk, the jazz pianist and composer, produced a body of work that was rooted both
(C) Jazz pianist and composer Thelonious Monk, who produced a body of work rooted
(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
After a quick glance over our options, a couple things stand out that we can focus on:
1. How they begin: Thelonious Monk... / Jazz pianist and composer Thelonious Monk...
2. both rooted / that was both rooted / rooted / that was rooted / rooted both
Let's start with #2 on our list because it deals with a pretty simple concept: to use the word "both" or not to use it! Whenever you see the word "both" in a sentence, make sure that it follows this format in some way:
both X and Y
It's also important to make sure X and Y are both parallel items, which is the key here to ruling out some confusing and just plain wrong answers. Let's focus on finding the X and Y in each sentence, and rule out any that aren't parallel. (I added the remainder of the sentence to help you see more clearly.)
(A) 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. --> NOT PARALLEL
(B) Thelonious Monk, the jazz pianist and composer, produced a body of work that was rooted both 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. --> NOT PARALLEL
(C) Jazz pianist and composer Thelonious Monk, who produced a body of work 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. --> OK (doesn't use the word "both" at all)
(D) Jazz pianist and composer Thelonious Monk produced a body of work that was 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. --> OK (doesn't use the word "both" at all)
(E) Jazz pianist and composer Thelonious Monk produced a body of work rooted both 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. --> NOT PARALLEL
We can eliminate options A, B, & E because they use the idiom "both X and Y," but the X and Y items aren't parallel. They all have X as "in the stride-piano tradition" and Y as "Duke Elllington," which are not parallel items at all!
Now that we have it narrowed down to only 2 options, let's take a closer look at #1 on our list: how to begin. To make problems easier to spot, I've included the rest of the sentence again:
(C) Jazz pianist and composer Thelonious Monk, who produced a body of work 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.
This option is INCORRECT because it's missing a verb! By starting the next phrase with "...,who produced...," we've turned it into a non-essential clause or modifier! This means we have a SUBJECT + MODIFIER + SUBORDINATE CLAUSE, which isn't enough to make it a complete sentence.
(D) Jazz pianist and composer Thelonious Monk produced a body of work that was 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.
This is CORRECT! It eliminated the use of "both," making it clear that the stride-piano tradition belongs to Willie Smith and Duke Ellington, which makes sense. It also puts the adjectives (jazz pianist and composer) next to the subject, Thelonious Monk, which also works. Oh, and it's a complete sentence with a clear subject (Thelonious Monk) and verb (produced).
There you have it - option D is the correct choice!
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