First lets confirm, V1 must be increased to reach Vmcg!
Information given is that it is a balanced field calculation, so we can't assume it is an unlimited runway, it means V stop/go is a predetermined point/speed for this specific runway.
In the case that V1 is LESS than Vmcg, conditions will be that it is an unbalanced field, that's the whole point of of having the definition Balanced field, it is to make calculations easier, to determine the MAXIMUM speed, that you can reach, and still decide to stop or to continue!
The conditions you are mentioning would make it an unbalanced field.
TODR = ASDR = BALANCED FIELD
I agree that conditions would be that V1 could be increased, ASDR will increase, TODR will decrease, Field required would be Increased - however that would make it an unbalanced field!
Answer A describes an unbalanced field take off!
If you are not field limited, your V1 will increase with mass.
But if you discover that you are field limited, and can't reach your required V1 what would you do?
Reduce mass, this will let you accelerate faster, reach the speed you require earlier, also a lighter aircraft will be able to stop faster, less inertia when braking!
So reducing mass gives you the chance to increase your V1 within the limits, this is one alternative.