I think your reasoning is solid and you have a correct approach.

I think the question was wanting you to use the expression at constant pressure 
$$V \propto T$$

This would give you the same answer because the ideal gas law 
$$PV = nRT$$
can be rearranged to give
$$V = {nR\over P}T$$
which at constant pressure gives
$$V = const.~T$$
which is equivalent to 
$$V \propto T$$