Maybe I've just spent too much time with the GMAT, but I find these much easier to digest with the underlining in place, so...
Ralph Ellison and Amiri Baraka both argued that music was perhaps the ultimate expression of Afro-American culture,
that it was the one vector of African culture that there was no possibility to eradicate.
(A) that it was the one vector of African culture that there was no possibility to eradicate
(B) the one vector of African culture that could not be eradicated
(C) for it was the one vector of African culture, and that it was impossible to eradicate
(D) a vector of African culture that there was no possibility to eradicate
(E) as being the one vector that could not be eradicated from African culture
Let's approach this the
MGMAT way, working from the splits. Every answer starts differently, and it is probably not clear exactly what's at issue there, so let's look later in the answers for a split. Here's something promising:
(A) ...there was no possibility to eradicate
(B) ...could not be eradicated
(C) ... impossible to eradicate
(D) ...no possibility to eradicate
(E) ...could not be eradicated...
There was no possibility to eradicate is very awkward, especially following
that, so eliminate A and D.
From there we might eliminate each of C and E for its unique flaws, rather than looking for another split.
Among other problems, C changes the meaning of the sentence. In the original, Ellison and Baraka say one thing about music, that it the one expression that can't be eradicated. Perhaps they believe that there are many other vectors of African culture. In C, on the other hand, Ellison and Baraka say two things about music, that it is the one expression, and that it can't be eradicated.
E also changes the meaning. In the original, music is an aspect of African culture that can't be eradicated from African-American culture. In E, music couldn't be eradicated from African culture. Also, the word
being and the tense
could not are problematic, though I wouldn't be eager to start with either of those considerations.
By the way, the basic structures of all the answers A through D are fine.
In A, the subordinating conjunction+subordinate clause,
that it was the one vector of African culture that there was no possibility to eradicate follows the subordinating conjunction+subordinate clause,
that music was perhaps the ultimate expression of Afro-American culture. This is fine when the second subordinate clause explains or unpacks the first, as in
Our contract requires that you compensate me for the repairs made to your roof, that you pay for both time and materials.In B, the noun
the one vector of African culture that could not be eradicated follows the noun
the ultimate expression of Afro-American culture. This is fine when the second noun modifies, specifies, or adds information about the first. Search on
appositive for more info. D uses the same sort of structure.
In C, the word
for is used as conjunction to join two independent clauses. That's fine. When used as a conjunction,
for means something like
because.