IMO E...
A and D can be ruled out : reason that and because are redundant phrases
C is wrong because we already have a that before..
B is incorrect here...

Hence, E

One reason that the student was ahead of her classmates was because of having taken summer school through the local college.

(A) because of having taken summer school - 'reason' and 'because' redundant
(B) her having taken summer school - 'having' is almost always wrong in GMAT
(C) that she had taken summer school - awkward
(D) because she took summer school - 'reason' and 'because' redundant
(E) she had taken summer school - CORRECT

isn't in E a run-on sentence?
we have the reason was -> she had taken
2 subjects, 2 verbs - not properly connected
I would rather go with C, as in C the SV is in the subordinate clause...

your second sentence is correct, because it is inside a which dependent clause.
in E though - we do not have such.

I personally like (C) better than (E).

In the version created using choice (C), we have:

The reason (noun) was (verb) that she ... (noun clause)

So, a noun "was" a noun clause. A noun clause makes perfect sense as the subject complement.

In the version created using choice (E) we have:

The reason (noun) was (verb) she had taken ... (independent clause)

To me this version is not as clearly correct as the version created via the use of (C), and, in any case, there is no reason to consider the version created via the use of (E) superior to the version created via the use of (C).
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