By 1940, the pilot Jacqueline Cochran held seventeen official national

Thanks for bringing this up TorGmatGod. At the onset, I would completely agree with GMATNinja that it often becomes an exercise in futility, to try to reduce GMAT sentence correction to a straitjacket set of grammar rules.

What is however interesting, is that GMAT does drop clues in many official questions. Let's look at few of them:

An incorrect official sentence:

Many of the earliest known images of Hindu deities in India date from the time of the Kushan empire, fashioned either from the spotted sandstone of Mathura or Gandharan grey schist.

Official explanation: Placement of modifier fashioned.... suggests that the Empire (the closest noun) not the images of the deities, was fashioned out of these materials.

There are of course numerous examples in which the past participial phrase correctly modifies either the immediate preceding noun or the immediate preceding noun phrase (whichever makes sense). Couple of examples:

An officially correct sentence, where the past participial phrase correct modifies the immediate preceding noun:

Building on civilizations that preceded them in coastal Peru, the Mochica developed their own elaborate society, based on the cultivation of such crops as corn and beans, the harvesting of fish and seafood, and the exploitation of other wild and domestic resources.
- Notice that the past participial phrase based on... correctly modifies the immediate preceding noun society.

An officially correct sentence, where the past participial phrase correct modifies the immediate preceding noun-phrase:

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.
- Notice that the past participial phrase found... correctly modifies the immediate preceding noun-phrase Fossils of the arm of a sloth.

Lastly, let's look at an example, where past participial phrase seems to modify the subject of the preceding clause:

Diabetes, together with its serious complications, ranks as the nation’s third leading cause of death, surpassed only by heart disease and cancer.
- On first look, the past participial phrase surpassed.... seems to modify diabetes (subject of the preceding clause); however, if we look at it closely, surpassed.... could as well be modifying the nearest noun-phrase nation’s third leading cause of death, since in this sentence Diabetes is effectively the nation’s third leading cause of death.