Part of the proposed increase in state education spending

[JbhB682]

Tax revenues are a record high in Country X, since the election of the third party candidate

'Since' is a tricky word: it can be both an adverb (meaning much the same as 'because') or a preposition (with a meaning similar to 'after'). In the example you cited, you don't need to use a comma, so that doesn't relate to Ron's rule.

Reading through the posts above, Ron is really just talking about the phrase starting 'with...'. Here it certainly is a modifier, and here's a simpler example:
The students had a huge party at the end of the semester, with many of them dancing late into the night.

Take a look at SC 740 and SC 782 from OG 2018 for more examples like this.

Hi Sage - have a followup on this

In your example,
i. the red is a prepositional phrase playing the role of an adverb ..what is it modifying --- is it modifying "Had" ? Seems like the red is modifying a noun i.e. party, describing what went on during the party

How can the red be an adverb in that case

ii. Can you confirm the red is different than a COMMA + VERB'ing, adverbial modifier ?

[Sage Pearce-Higgins]

The red part is an adverbial modifier: it's giving information about the fact that the students had a party at the end of the semester. It's important to note that it's not an adverb. Adverbial modifiers can give information about the action or the whole clause.

I can't think of simple rule to say how a 'comma with' modifier differs from a 'comma -ing' modifier. I suppose that they're used in different contexts: a 'comma -ing' modifier has a subject that could also be seen as doing the action described in the modifier, whereas the 'comma with' modifier has a different subject.

I can see that you're investing a lot of time in your GMAT studies. I would encourage you to think practically about directing your studies towards improving your score rather than trying to "nail" every possible topic. Unless, of course, you're thinking of becoming a GMAT instructor.