First difference in all answer choices is use of Due to or because of.
We know that due to is used when we have to show something is caused by a particular thing.
In the original sentence a reason is provided hence due to options are out of the race.
(A) Because a surfeit of undergraduate students has sent class sizes soaring,
seems fine(B) Because of soaring class sizes, which is due to a surfeit of undergraduate students,
Which is modifying to class sizes, irrelevant
(C) Because class sizes have been sent soaring, which resulted from a surfeit of undergraduate students,
which is modifying to soaring in addition to this present perfect and simple past making this sentence unnecessary wordy
(D) Due to soaring class sizes from a surfeit of undergraduate students,
As discussed, it is out
(E) Due to a surfeit of undergraduate students, with the result that class sizes have been sent soaring,
Same as D
Hence A seems to be our answer
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