the mass of the column of water above an object will have an effect on the pressure felt by that object
That is totally right, but the effect of the mass of the water column is represented by (density x gravity x depth), not by total mass of water in the tank.
I agree with you that this question is irritating though, mostly because it's easy to overthink it, if you want to call it that, and assume that since they gave you so much info about the size of the tank and all, that by knowing total mass of it's contents, you can then figure out depth. Obviously twice as much mass means the water is twice as deep, given a constant sized tank.
You could argue though that this is just depth to the bottom of the tank. There's no specifics about how long the balloon strings are, and thus you really don't know the EXACT depth of the balloon when it's tied down. This gives me reason to suspect maybe water mass IS the useless info.
So I guess this is one of those problems where it pays to consider all the answers, and make sure you eliminate all the worst ones, leaving this slightly iffy one as the best answer.
I agree with Movax's explanation of # of molecules, and rubber's thermal conductivity. Both of those are arguably useful for figuring out temperature change of the air. "Variation with depth in the speed of the balloon" is a complicated phrase for sure, and would definitely be the other possibly good answer, at least to me. Movax's explanation seems logical, balloons that accelerated faster probably started at a higher temperature.
Wish I had a better answer for you, especially since you specifically asked me to throw in my two cents, but this is definitely a question I'd debate too, if all these explanations weren't already offered.
