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(A) exist at the core of nearly all galaxies and the mass of each black hole is proportional to
(A) doesn’t seem all that bad. It certainly sounds fine, but there’s a problem with the parallelism and meaning.
Before we get into that, consider the following:
- I believe that Santa Claus is real and that the Knicks will win the 2018 NBA title. → We have two parallel phrases (subordinate clauses, if you like jargon) that begin with “that.” And that’s great: it’s super-clear that these are two things that I believe.
- I believe that Santa Claus is real and the Knicks will win the 2018 NBA title. → Now the parallelism is different. Without “that”, we just have two parallel, independent clauses: “I believe that Santa Claus is real” and “the Knicks will win the NBA title.” That changes the meaning: now, the sentence doesn’t connect “I believe” with “the Knicks will win the NBA title.” And it seems that the latter clause is a fact, rather than something I BELIEVE is true.
We have a similar situation in (A). On both sides of the “and”, we have full, independent clauses:
- “Scientists have recently found evidence that black holes exist at the core of nearly all galaxies…”
- ”…the mass of each black hole is proportional to its host galaxy.”
Here’s the problem: the second independent clause is just a completely separate statement. The second clause (“the mass of each black hole is proportional…”) seems to be a separate fact; without “that” in front of that clause, it’s not clear that scientists have found evidence to support the statement. The statement is just a separate thing.
There’s also a comparison problem with (A). We have “the mass of each black hole is proportional to its host galaxy”, which is illogical: the mass of each black hole might be proportional to
the mass of its host galaxy, but it’s weird to suggest that the mass is somehow proportional to the galaxy itself.
So we have a couple of (admittedly somewhat subtle) reasons to eliminate (A).
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(B) exist at the core of nearly all galaxies and that the mass of each black hole is proportional to that of
Now the parallelism is better: “Scientists have found evidence
that black holes… probably exist… and
that the mass of each black hole is proportional…” Cool: now it’s clear that scientists have found evidence for these two things.
The other thing that should jump out at you is the phrase “that of.” “That” is a singular pronoun in this situation (more on “that” in
this article), and it clearly refers back to “mass” in (B). And that’s great: “…the mass of each black hole is proportional to
the mass of its host galaxy.”
So we can keep (B).
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(C) exist at the core of nearly all galaxies, and that the mass of each black hole is proportional to
(C) is identical to (B), except that the phrase “that of” is missing. And as we mentioned in the explanation for (A), that’s a problem: literally, (C) says that “the mass of each black hole is proportional to its host galaxy”, and that’s not quite right: the mass of the black hole is proportional to the
mass of the host galaxy – not to the galaxy itself.
So (C) is out.
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(D) exists at the core of nearly all galaxies, and that the mass of each black hole is proportional to that of
(D) is identical to (B), except for one little problem: “Scientists have found evidence that black holes…
exists…” That’s a wonderfully clear subject-verb error, and we can eliminate (D).
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(E) exists at the core of nearly all galaxies and the mass of each black hole is proportional to that of
(E) has exactly the same subject-verb error as (D): “Scientists have found evidence that black holes…
exists…” Plus, the parallelism is a problem, because “and” isn’t followed with “that” – see the explanation for (A) for more on this issue.
So (E) is out, and (B) is our answer.