Are there two ways to look at this? To be fair, the question talks only of a balanced V1 and does not mention a balanced "field" so I could not assume that we were field length limited.
Could we have situation where the field is not balanced but the V1 is balanced? Or is there only one definition of balanced V1 and that is when the TODA = ASDA? I thought that a balanced V1 could be manufactured and would be TODR = ASDR (ASDA). But I see that if this were the case I could still not increase my V1 to match Vmcg since this would push my ASDR possibly beyond the geometry of the stopway?
My thinking is of a lightly loaded aircraft who's TODR = ASDR (therefore balanced V1). There is no mention though of the ASDA and if I said the ASDA is sufficiently large then I could do two things: 1) reject from a higher V1 thus reducing my TODR but increasing ASDA (no longer balanced V1 but pointless) or 2) increase the weight which would increase TODR and ASDR keeping a balanced V1. I could do this up until the point that ASDA is reached. All along through this there is no mention of the TODA being equal to ASDA so this is not a balanced field. The question didn't say I could not unbalance the V1 or at least that is my interpretation.
My thinking with "A" was that I could use the option (if I had it) of pushing up my V1 which would increase my ASDR, admittedly, but would decrease my TODR. I can also see the other logic though.
My brain is fried so if this reads as utter rubbish I'll pick it up tomorrow and correct it!
