Let me try this, though i feel its not the best GMAT question...
The nurses went on strike to protest their being overworked.
(A) their being overworked
Here, their is the personal pronoun which referes to the gerund "Being" or the gerundial phrase " Being Overworked"
Thus, the sentence follows the correct form.
(B) themselves being overworked
A reflexive pronoun -themselves is used only when the direct or indirect object of a verb is the same as the subject of the same verb; which is not the case over here.
(C) themselves as overworked
as is used before a clause, prepositional phrase, or adverb
(D) their overworking
Though this sounds awkward, i went for it in the first place... overworking is used as a noun here. However, i discarded it only because it sounds awkward..
(E) overworking themselves
Changes meaning
However i want to say that i wudnt have gone for A if the answer wudnt have been there beneath the spoiler.
Anyone has a better expanation
Raunek