Black colleges problem. idiom? wordy?

Castor.kim wrote:A consortium of historically Black colleges in the United States, capitalizing on such schools’ traditionally rich relationships with African nations, integrates African concerns into an international business study.

a.capitalizing on such schools’ traditionally rich relationships with African nations
b.while capitalizing on the traditionally rich relationships of such schools and African nations
c.through capitalizing on such schools’ and African nations’ traditionally rich relationships
d.which capitalize on the traditionally rich relationships of such schools and African nations
e.in capitalizing on such schools’ and African nations’ traditionally rich relatio

in B must be schools' relationships with African nations or relationships between such schools and African nations. Another error is -ing form gives evidence for how it integrates.
in C such schools' and African nation's relationships means relationships of every one of them, not interrelationship.
in my thought..
a. school's traditionally.. looks wordy
b. relationship of.. looks non-sense and distort the meaning..
c. school's and african nations' ... looks wordy, but its parallel..
d. relationship of .. like b
e. like c.. looks wordy..

any way, gmat want to decide the most efficient one..
I choose "c"

but OA is [spoiler]"A"[/spoiler]

please explain about your opinion..