Interesting question.
The Directors met with the entire accounting department but were not able to resolve many of the issues presented; clearly, they needed to be reorganized
A.The Directors met with the entire accounting department but were not able to resolve many of the issues presented; clearly,
they needed to be reorganized
"they" makes "the Directors" reorganized, changes the meaning of the sentence and makes it illogical.B.The Directors met with the entire accounting department but were not able to resolve
their many issues; clearly,
they needed to be reorganized
Awkward & the problem of "they" same as AC.The entire accounting department met with the Directors but
were not able to resolve many of the issues presented; clearly,
they needed to be reorganized
Well, "were" here is wrong, should be used singular first. The second problem is that "they" here should be singular too.D.The entire accounting department met with the Directors but was not able to resolve many of the issues presented; clearly,
they needed to be reorganized
Again,"they" here is wrong.E.The Directors met with the entire accounting department but were not able to resolve many of the issues presented;clearly,the department needed to be reorganized
Correct.BTW, I'm not sure whether if changes the word in C & D by singular, the option would be correct. Still needs discussion.