MAGOOSH OFFICIAL SOLUTION:
A question about presidential hopeful Walter Mondale.
Split #1: position of the word "only." What should "only" modify? The quantity notable for its low number is the number of electoral votes, only 13. The word "only" should come at the end of the underlined section, immediately before this number. The choices (B) & (E) have "only winning" and "only won," as if winning were an activity less acceptable than something else. These are incorrect.
Beyond this split, the answers are different enough that each needs its own analysis.
(A) The double contrast in this one is awkward: [clause] though [clause] but [clause]. The events in the sentence do not warrant two major changes in logical direction such as this, so this choice is incorrect.
(B) In some ways, this is the opposite of (A) in that there's no logical contrast at all, as if all the facts of the sentence belong harmoniously together with no problem. This problem and the placement of the word "only" make this choice wrong.
(C) This choice is logically and grammatically correct. It is clear and direct. This is a promising choice.
(D) In the first half of this sentence, everything before the last comma, this sentence commits the famous missing verb mistake. The sentence has a long absolute phrase, then the noun "Walter Mondale," then a participial modifier, but this noun has no bonafide verb before the word "but" starts the second independent clause. This is incorrect.
(E) This choice commits the mistake of false parallelism, simply putting every verb willy-nilly into parallel regardless of their logical relationships. It also misplaces the word "only." This is incorrect.
The only possible answer is (C).