The use of participle phrase

I took this sentence from here:

https://www.fortunecity.com/bally/durrus ... mch21.html

The comma is present

More examples from OG10 (getting more and more confused):

1) The root systems of most flowering perennials either become too crowded, resulting in loss of vigor, or spread too far outward, producing a bare center (verb phrase (resulting ...) modify the action of the first clause).

2) The Parthenon was a church from 1204 until 1456, when Athens was taken by General Mohammed the Conqueror, the Turkish sultan, establishing a mosque in the building and using the Acropolis as a fortress (establishing and using modify Athens, thus producing an absurd statement).

3) The concept of the grand jury dates from the twelfth -century, when Henry II of England ordered panels of common citizens, preparing lists of suspected criminals in their communities. (preparing . . . communities functions as a participial phrase modifying citizens ).

4) In 1791 Robert Carter III, one of the wealthiest plantation owners in Virginia, stunned his family, friends, and neighbors by filing a deed of emancipation, setting free the more than 500 slaves who were legally considered his property.

5) By a vote of 9 to 0, the Supreme Court awarded the Central Intelligence Agency broad discretionary powers enabling it to withhold from the public the identities of its sources of intelligence information (enabling ... clearly modifies powers).

6) Five fledgling sea eagles left their nests in western Scotland this summer, bringing to 34 the number of wild birds successfully raised since transplants from Norway began in 1975 (The "-ing" (present participle) form introduces action that is simultaneous with the action of the main clause; i.e., bringing indicates that the number of wild birds became 34 when the sea eagles left their nests).

I still cannot understand the logic which determines what subject/object/phrase/clause should participle phrase modify???

Explanations by MGMAT staff:

a) Our car was repaired by a mechanic, working as quickly as possible. (the second part modifies mechanic)

This isn't a good sentence, because (1) it's in the passive voice for no good reason and (2) the phrase could be taken as modifying 'car' (in fact in exactly the same way you posit in your next example).
Better: Working as quickly as possible, a mechanic repaired our car. This fixes both of the aforementioned problems.

b) Maria went to sleep, hoping to please her mother. (hoping modifies Maria)

This is OK, yes, but it's better to place the modifier next to the subject: Maria, hoping to please her mother, went to sleep.

Maria went to sleep, awakening to scary dreams, relieved when it was morning (awakening modifies Maria)

This is not OK. When you use a participial phrase like this, the implication is that the participial phrase is either an explanation of the first clause (see Maria), is concurrent with it, or is a consequence of it.
Concurrent: James settled into his chair, taking off his shoes in anticipation of a long day of desk work.
Consequence: The blizzard dumped 2 feet of snow on Providence, paralyzing the city's businesses for several days.
Your sentence isn't any of these; it requires transitions that show clearly that Maria awakened AFTER going to sleep. Its current wording implies that Maria awakened AS she was going to sleep, which makes no sense.

c) Among lower- paid workers, union members are less likely than non union members to be enrolled in lower- end insurance plans that impose stricter limits on medical services and require doctors to see more patients, spending less time with each. ("spending less with each" modifies "require doctors to see more patients")

This one isn't so hot either. I wouldn't call it unambiguously wrong, but a strict interpretation of the wording would gather that 'spending less time with each' refers to insurance plans, not doctors.
If this one is rewritten as '...require doctors to see more patients and (thus to) spend less time with each,' the problem disappears, although the participial phrase also disappears! The use of AND makes it unambiguous that it's the doctors who 'spend less time with each.' (The words in parentheses are optional, depending on the writer's intended emphasis.)

d) The cameras of the Voyager II spacecraft detected six small, previously unseen moons circling Uranus, doubling to twelve the number of satellites now known as orbiting. (the second part modifies the first part).

D is ok.

Good extract on the issue:

Another common error is that students tend to overlook the fact that the two actions have to be in a cause-and-effect relationship or a before-and-after sequential relationship.

Having considerate and loving parents, Mary loves sports and outdoor activities.

Some students tend to think that the function of participle clauses is to incorporate more than one action in a sentence. They fail to realize that the two actions have to have some relationship, as illustrated in the following:

Cause-and-effect relationship: Having considerate parents, she could do whatever she wants.

Sequential relationship: Having locked the door, I went to sleep.

Making sense of participle phrases

Participle phrases are often used in English, and you’ll need to understand their use for all four parts of the International English Language Testing System (Ielts). This is a confusing area of grammar for many learners of English. Learning how to use participle phrases is made more difficult because few course books have a full and clear summary of how they’re formed and used.

Participle form

A participle is a word that's formed from a verb. It has two main forms: the present (or active) participle, and the past (or passive) participle.

To form the present participle, add "ing" to the base verb. For example, the present participle from the verb "to bore" is "boring."

Past participles usually have the same ending as past tense verbs (e.g., bored). However, with irregular verbs the past participle form carries a different ending than the past tense (e.g., gave/given and was/been).

Participle phrases

Participles are mainly used as part of a verb form (e.g., "the audience was bored by the movie") or as an adjective (e.g., "the bored audience").

Unlike normal adjectives, however, participles can also take on direct objects and form participle phrases (e.g., "Needing cash, Tong went to the ATM"). "Needing" is a present participle, and "cash" is its direct object. The words "needing cash" form a participle phrase. This phrase is a shorter way of saying the adverbial clause of reason, "because he needed cash."

As participle phrases leave out nouns, pronouns, auxiliary verbs and conjunctions, they focus on the action that is happening. They're often used in writing to reduce wordiness by replacing longer adverbial or relative clauses. These phrases also help your writing flow by eliminating choppy or repetitive sentence structures.

Reduced adverbial clauses

If the subjects of an adverbial clause and the main (or independent) clause in a sentence are the same, the adverbial clause may be reduced to a participle phrase with the same meaning.

This is often done with adverbial clauses showing time and reason relationships, but some other types of adverbial clause (condition and contrast) can also be reduced. There are four main situations:

1. Same time

When the action in the adverbial clause happens at the same time as the action in the main clause, you can use a participle phrase for one of the actions.
"As Tong was laying his head on the pillow, he could hear someone crying"
can be reduced to
"Laying his head on the pillow, Tong could hear someone crying."
You can see that the subject of the adverbial clause (Tong) is left out and made the subject of the main clause, replacing "he." The time conjunction "as" and the auxiliary verb "was" are also deleted. The present (or active) participle "laying" is left behind.
You follow the same process when the verb in the adverbial clause is in the passive voice.
"When a newspaper photograph is seen close up, it looks like masses of dots."
becomes
"(When) seen close up, a newspaper photograph looks like masses of dots."
This time, the conjunction "when" can be kept or deleted, depending on your preference. The past (or passive) participle "seen" is used.

2. After

If one action happens immediately after another action, you use the participle phrase for the first action.
"After Tong got up, he went to see if his son was alright."
may be shortened to
"(After) getting up, Tong went to see if his son was alright."
The conjunction "after" can be left in or out. The present (active) participle "getting" is used.

3. During

If one action happens in the middle of a longer action, use a participle phrase for the longer action.
"While Tong was walking towards his son's room, he saw a woman crying in the hotel corridor"
becomes
"(While) walking towards his son's room, Tong saw a woman crying in the hotel corridor."
"While" can be left in or removed, as you prefer.

4. Before

When the action in the adverbial clause happens before the action in the main clause, you have two ways of making the time relationship clear. Firstly, you may use the conjunction "after" with the present (active) participle or the past (passive) participle.
"After Tong had hit a hole in one in the golf tournament, he celebrated with the club members"
can be shortened to
"After hitting a hole in one in the golf tournament, Tong celebrated with the club members."
Always keep the conjunction "after" because it makes the time relationship clear. Alternatively, you can use the active perfect participle form (having + past participle) or the passive perfect participle form (having been + past participle). As the example is using the active voice, it would be reduced to:
"Having hit a hole in one in the golf tournament, Tong celebrated with his club members."
There's no need to use "after" with a perfect participle as both would be showing the same time relationship.

The battle with participals continues!!! Here, I provide additional explanation kindly provided by MGMAT staff:

c) Among lower- paid workers, union members are less likely than non union members to be enrolled in lower- end insurance plans that impose stricter limits on medical services and require doctors to see more patients, spending less time with each. ("spending less with each" modifies "require doctors to see more patients")

About the insurance plans: There's an ambiguity. The phrase in question doesn't clearly refer to just one thing. Here is the essence of the problem, presented in a symbolic form:
"X required Y to do Z, making W happen."
There are two interpretations of this sentence:
(1) the fact that W happened was a proximate result of X's requiring Y to do Z;
(2) the fact that W happened was a proximate result of Y's doing Z. These are nontrivially different, although the difference is pretty philosophical at times.
Here are examples illustrating both possibilities:
(1) The government required citizens to pay for diplomats' lavish banquets, creating active resentment. --> Here, the clearly intended meaning is that the government creates the active resentment. This is generally considered a good sentence, because government is the MAIN SUBJECT OF THE PRECEDING CLAUSE (in the same way that 'health insurance plans' is the head of the subordinate clause in the example).
(2) The government required citizens to pay for diplomats' lavish banquets, depleting savings accounts and IRAs in the process. --> Here, common sense makes it clear that the citizens are depleting savings accounts and IRAs. This is still a bad sentence, though, because the 'default' subject based on solely grammatical considerations is the government (which is absurd).

1. a) Our car was repaired by a mechanic, working as quickly as possible. (the second part modifies mechanic)

*the second part modifies the whole clause.

2. b) Maria went to sleep, hoping to please her mother. (hoping modifies Maria)

*"hoping to please her mother" modifies the preceding clause.

3. Maria went to sleep, awakening to scary dreams, relieved when it was morning (awakening modifies Maria)

*its not a complete one.

c) Among lower- paid workers, union members are less likely than non union members to be enrolled in lower- end insurance plans that impose stricter limits on medical services and require doctors to see more patients, spending less time with each. ("spending less with each" modifies "require doctors to see more patients")

*"spending less with each" modifies " the lower-end plans require doctors to see more patients"

d) The cameras of the Voyager II spacecraft detected six small, previously unseen moons circling Uranus, doubling to twelve the number of satellites now known as orbiting. (the second part modifies the first part).

* ok.

c) Among lower- paid workers, union members are less likely than non union members to be enrolled in lower- end insurance plans that impose stricter limits on medical services and require doctors to see more patients, spending less time with each. ("spending less with each" modifies "require doctors to see more patients")

*"spending less with each" modifies " the lower-end plans require doctors to see more patients"

"spending less with each" - Doesn't it modify doctor?

For me no. If "spending less with each" were to modify doctors, it would be put immidiately behind the doctor as under:

C) Among lower- paid workers, union members are less likely than non union members to be enrolled in lower- end insurance plans that impose stricter limits on medical services and require doctors, spending less time with each, to see more patients.

But who is doing the "spending"?

To me, doctors are doing the spending less time with the patients.

How does one say that "lower plans" is spending less time?

That is a good point.

I have read many times that you have to analyze the sentence from a gramatical point of view, so although it is obvious that the doctors are doing the "spending less time" (and not the "lower plans"), it is actually obvious from a meaning point of view; and it seems that that is not the analysis that GMAT wants.

Thoughts on that?

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