Federal government financing is an essential key in the survival of the interstate rail system.
The correct idiomatic structure for essential is 'essential....for...'
A. an essential key in
(A) uses the wrong idiomatic structure. Hence, (A) is incorrect.
B. an essential key for
I was confused between B and C. I picked C based on intuition, without truly understanding why B is wrong. After going through a similar comment, I realized that there's a redundancy error in (B).
essential itself means 'key'. So, there's no need to restate 'key' as is done in this option. Hence, eliminate (B)
C. essential for
Uses the right idiomatic structure. Hence, (C) is the correct answer.
D. essential in
Wrong idiomatic structure in (D). Hence, eliminate (D).
E. essential
if you plug back E in the underlined portion, the sentence you get will be:
Federal government financing is essential the survival of the interstate rail system.
By reading this sentence alone, you might get a sense of something that's missing here. Additionally, it does not have the right idiomatic structure. Hence, Eliminate (E)