Sentence Correction

sagarock wrote:And my other doubts are whether we have to check the sentence when ing modifier modifying nouni.e it is acting as adjective.for ex-
1.rising inventories,if not accompanied by sales,can lead to...
2.declining values of houses have brought ...
3.growing plants lot of attention from the gardener.

rising inventories,if not accompanied by sales,can lead to.

2.declining values of houses have brought ...

3.growing plants attract lot of attention from the gardener

The state has proposed new rules that would set minimum staffing levels for nurses, rules intended to ensure that at least one nurse is assigned for every four patients put through triage in a hospital emergency room.

A. rules intended to ensure that at least one nurse is assigned for every four patients put through triage in a hospital emergency room
B. rules with the intent of ensuring one nurse at least to be assigned for every four patients to be put through triage in a hospital emergency room
C. rules intending to ensure at least one nurse is assigned for every four patients in a hospital emergency room put through triage
D. with the intent of ensuring that at least one nurse should be assigned for every four patients in a hospital emergency room that are put through triage
E. and this is intended to ensure one nurse at least to be assigned for every four patients put through triage in a hospital emergency room

Because she knew many of the leaders of colonial America and the American Revolution personally, Mercy Otis Warren was continually at or near the center of political events from 1765 to 1789, a vantage point combining with her talent for writing to make her one of the most valuable historians of the era

(A) a vantage point combining with her talent for writing to make

(B) a vantage point, when combined with her talent for writing, that made

(C) a vantage point that combined with her talent for writing, and it made

(D) and this vantage point, which combined with her talent for writing to make

(E) and this vantage point, combined with her talent for writing, made

sagarock wrote: 1.Each year companies in the United State could save as much as $58 billion in employee illness prevention and gain as much as $200 billion through improving performance of workers if they simply provided .
here improving is acting as gerund,i guess which makes sentence absurd.also modifier 'in employee illness'is wrong.

ex-ANIMAL-HIDE SHIELDS with wooden frames were essential items of military equipment, PROTECTING warriors against enemy arrows and spears.
here protecting is modifying Ahs .why Ahs were essential because they protect from arrows and spears.

2. Though called a sea, the landlocked Caspian is actually the largest lake on Earth, covering
why landlocked caspian is largest because it covers....

3.The greatest road system built in the Americas prior to the arrival of Christopher Columbus, the Incan highway was over 2,500 miles long, extending from
northern Ecuador through Peru to Southern Chile.
how the incan highway was over 2500 miles ? extending also modify the incan highway

4.Fossils of the arm of a sloth, found in Puerto Rico in 1991, have been dated at 34 million years old, making the sloth the earliest known mammal on...
here making does indirectly modify fossils

Fossils of the arm of a sloth, found in Puerto Rico in 1991, have been dated at 34 million years old, making the sloth the earliest known mammal on..
is fossils dating responsible for making the sloth.......?

There is one more question in which ing is wrongly used.And this question is giving me very hard time.i want your take on it.
Emily Dickinson's letters to Susan Huntington Dickinson were written over a period beginning a few years before Susan's marriage to Emily's brother and ending shortly before Emily's death in 1886, outnumbering her letters to anyone else.
IMO here ing is wrong because outnumbering happens long time after letters were written.what iam missing?

Fossils of the arm of a sloth, found in Puerto Rico in 1991, have been dated at 34 million years old, making the sloth the earliest known mammal on the Greater Antilles islands

Emily Dickinson's letters to Susan Huntington Dickinson were written over a period beginning a few years before Susan's marriage to Emily's brother and ending shortly before Emily's death in 1886, outnumbering her letters to anyone else

1.Is it important in gmat to know the subtle difference between verb ing and gerund?

2.Is there any official question testing this difference?

Rising inventories, when unaccompanied correspondingly by increases in sales, can lead to production cutbacks that would hamper economic growth.

(A) when unaccompanied correspondingly by increases in sales, can lead
(B) when not accompanied by corresponding increases in sales, possibly leads
(C) when they were unaccompanied by corresponding sales increases, can lead
(D) if not accompanied by correspondingly increased sales, possibly leads
(E) if not accompanied by corresponding increases in sales, can lead

3.If so, than what is the surest method to find the difference?

3.If so, than what is the surest method to find the difference?