Scientists have recently found evidence that black holes—regions of space in which matter is so concentrated and the pull of gravity so powerful that nothing, not even light, can emerge from them—probably exist at the core of nearly all galaxies and the mass of each black hole is proportional to its host galaxy.


(A) exist at the core of nearly all galaxies and the mass of each black hole is proportional to-> why do we compare "mass of each black hole" to " black hole's host galaxy". Let compare mass to mass.

(B) exist at the core of nearly all galaxies and that the mass of each black hole is proportional to that of-> It is better. Parallelism is maintained too.

(C) exist at the core of nearly all galaxies, and that the mass of each black hole is proportional to-> Same as A.

(D) exists at the core of nearly all galaxies, and that the mass of each black hole is proportional to that of-> Subject verb agreement issue. we need "exist", because we are talking about "black holes" (plural).

(E) exists at the core of nearly all galaxies and the mass of each black hole is proportional to that of-> Subject verb agreement issue. we need "exist", because we are talking about "black holes" (plural).

So, I think B.

Clear B.

Scientists have recently found evidence that black holes—regions of space in which matter is so concentrated and the pull of gravity so powerful that nothing, not even light, can emerge from them—probably exist at the core of nearly all galaxies and the mass of each black hole is proportional to its host galaxy.


(A) exist at the core of nearly all galaxies and the mass of each black hole is proportional to

The key noun in the sentence is the plural ‘black holes’ so the verb that corresponds to black holes must be plural. What is that verb? ‘exist’ (ignore all of the content that comes in between the hyphens).

Now, ‘exist’ is correct, but the issue remaining is that the sentence conveys this idea that the mass of each black hole is proportional to its galaxy. The real intent here is to say that the mass of the black hole is proportional to the mass of its galaxy.

Out.

(B) exist at the core of nearly all galaxies and that the mass of each black hole is proportional to that of

Correct. The demonstrative pronoun ‘that of’ makes it clear that the mass of the black hole is proportional to the mass of its galaxy.

(C) exist at the core of nearly all galaxies, and that the mass of each black hole is proportional to

Same issue as A)

(D) exists at the core of nearly all galaxies, and that the mass of each black hole is proportional to that of

‘exists’ is singular’. OUT.

(E) exists at the core of nearly all galaxies and the mass of each black hole is proportional to that of

‘exists’ is singular. OUT.
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I might be missing here something but aren't the answers:
A
E
out, not only because of subtle meaning issues but also because we are dealing here with run-on sentences. As mentioned by previous users, what comes after "and" in both cases are independent clauses, so connecting them (disregarding the meaning issues) we require a comma followed by a coordinate conjunction. Thus, we can get rid of A and D.
I am not 100% sure if we can assume the reverse to be also true (I would greatly appreciate some opinions on that), that once we use a comma followed by a coordinate conjunction what follows must be an independent clause (it seems to be implied by the answer offered by GMAT). But if that would be the case, we could also get rid of:
C
D
leaving B as the only viable option without tedious interpretation of the subtle meaning.

We may have addressed your questions here and here. Those posts also have a couple follow-up questions and answers, so you might want to check those out too.

If nothing in the thread helps, let us know!
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Jack386
Short answer: no and no.

A comma is not required when we use a conjunction to join two independent clauses. It's very common, and some sentences might fare poorly without it, but we don't absolutely have to have it. For instance, I might say "I'm cold and I want to go home." There's just not enough complexity to warrant a comma.

On the flip side, we definitely don't have to have an independent clause after every instance of comma + and. The simplest example is a list, where we might end a sentence with something like ", and monkeys." However, we might see a comma in almost any places where it clarifies the meaning or structure, and we commonly see commas used to set off modifiers. So if I have two nouns or phrases joined with AND, and then I want to add a modifier in between them, I will end up with "comma + and" without an independent clause after.

He voted for Bill X, angering his supporters, and Bill Y, alarming his enemies.

We can also use comma + and to set off a modifier at the end of a sentence:

She wears a heavy jacket every day, and not just in the winter.
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GMATNinja DmitryFarber

Thank you for the replies, links and explanations were indeed quite helpful. Of course a list seems to be an exception in this matter.
So it seems like a GMAT SC question could still be correct even if a comma would be missing between two independent clauses. However, these cases seem to be rather the exception than the rule.

>>> Apart from the grammar rules around optional "that", where it acts like a conjuction ; obligatory "that", acting like an introductory clause ; subjunctive "that", acting for indicating something to be done by a another person.

(expert's explanation): We have the *repetition of a structuring word* such as "that" which often helps us to see the intended meaning and structure. Scientists have found evidence of two things:
- THAT black holes exist
and
- THAT the mass is proportional.
*********

Scientists have recently found evidence that black holes..... its host galaxy.

(A) exist at the core of nearly all galaxies and the mass of each black hole is proportional to
Black Holes, subject = P
exist, verb = P
S=V

Parallelisim: Scientist have found 2 things: "that" black holes exist and "...." mass of each..."
that to create a parallel structure is missing here.

the mass OF each black hole, subject = S
is, verb= S
S=V

its, possessive pronoun, S= (the black hole's) host galaxy, but it is actually for the mass of the black hole, not black hole in general.

(B) exist at the core of nearly all galaxies and that the mass of each black hole is proportional to that of
Black Holes, subject = P
exist, verb = P
S=V

// structure is taken care of.

that of its, is pointing towards, the mass of (its) black holes galaxy.

(C) exist at the core of nearly all galaxies, and that the mass of each black hole is proportional to
Black Holes, subject = P
exist, verb = P
S=V

// structure: ok

to its galaxy: require a that of, to point towards the mass of the black hole | error

(D) exists at the core of nearly all galaxies, and that the mass of each black hole is proportional to that of
Black Holes, subject = P
exists, verb = S
S≠V

(E) exists at the core of nearly all galaxies and the mass of each black hole is proportional to that of
Black Holes, subject = P
exists, verb = S
S≠V

// and "that of" is taken care in D&E.