Although neutron stars are only the size of an average city, they are

A it is.

A. they are so dense that they. Correct. Makes complete sense. Follows the structure "So...that"
B. they are of such density, they - Incorrect. 'that' is required after the comma
C. so dense are they as. Incorrect. wrong use of voice (passive not required)
D. such is their denseness, they. Incorrect. 'such' is redundant.
E. there is so much density that they. Incorrect. wrong referent for 'there'

Official Explanation

Answer A - (A) properly uses "so dense that" to introduce a clause that shows the result of their denseness. (B) incorrectly replaces the word "that" with a comma. Because (C) has no word after as there is no subject to the verb contain.
(E) is ambiguous about how the density is related to the sentence. (A) remains the best statement of this idea.

I chose the correct answer but what do you mean when you say such is redundant?

stars===> they
so eliminate D and E
B and C do not make sense in comparison with A beside they are not grammatically correct.

The original sentence does not seem to contain any errors. The plural pronoun "they" is appropriate, as it refers to the plural "neutron stars." The phrase "so dense that" properly introduces a clause that describes the result of the stars' great density. Proceed to analyze the answer choices, but expect to choose (A).

A quick scan of the choices does not reveal any obvious patterns. Since no error was noticed in the initial analysis of the sentence, don't spend much time here. Move on for a quick look to make sure nothing was missed.

(B) replaces "so dense" with the wordier "of such density." It also incorrectly replaces the word "that" with a comma, creating a run-on sentence. To see this, imagine one writing, It was a small room. The bed didn't fit. To emphasize the small size of the room, one could write, It was such a small room. The bed didn't fit. Then, in order to emphasize the connection between the two thoughts - to convey that it was the smallness of the room that prevented the bed from fitting - the sentences can be combined with that: It was such a small room that the bed didn't fit. But without "that," the result is two sentences improperly combined (i.e., a run-on sentence): It was such a small room, the bed didn't fit. This is what (B) does, so it must be eliminated.

(C) creates the nonsensical "so dense are they as typically contain" Eliminate (C).

(D) replaces the active "they are so dense" with the passive "such is their denseness." Also, like (B), this choice incorrectly replaces the word "that" with a comma, creating a run-on sentence.

(E) changes the meaning of the sentence because it is ambiguous about how the density is related to everything else. "There is so much density" does not indicate what is dense. Get rid of (E).

As expected, (A) is correct.

Although neutron stars are only the size of an average city, they are so dense that they typically contain at least 40 percent more mass than the earth's sun.

A. they are so dense that they - has no error. Hence, (A) is the right answer choice.
B. they are of such density, they - does not have the ''such...that'' structure
C. so dense are they as - does not have the ''so...that'' structure
D. such is their denseness, they - In addition to the awkwardness that (D) introduces, (D) does not contain ''such...that'' structure.
E. there is so much density that they - does not clearly describe 'who' or 'what' has the property ''so much density''