titration of a weak diprotic acid (TBR Gen chem CH 5 passage 8 #75)

[whiteshadodw]

i narrowed it down to C or D, but i just didn't have the slightest clue.

TBR says that the following always holds true regardless of how much HCO3 or rather how much H2CO3 you start off with in the titration:

pH = pKa1 + pKa2

i've found this to be derived in my gen chem book, but it took almost a page of derivation. is this question too detailed for it to show up on the MCAT?

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[whiteshadodw]

i've attached the derivation for this formula for those interested.