When are molar and molal concentrations the same?

Question

What would have to be true about any solvent for one of its dilute solutions to have essentially the same molar and molal concentrations?
This question is driving me wild the possible answers are the following. I doubt it has anything to do with the solutes miscibility with water, it's polarity, or it's molar mass being similar to water. Any ideas?

It must be miscible with water.
The volume cannot change appreciably as solute is added.
It cannot be volatile.
The density must be very close to 1 g/mL.
It must be polar.
Its molar mass must be close to the molar mass of water.

Answer 1

First of all, judging from your options your solvent is defined (water)
Let's imagine you have 1 M and 1m.

1 M means 1 mole solute per 1 L solution
1 m means 1 mole sollute per 1 kg solvent.

The two will be equal when 1 kg of solvent corresponds to 1 L of solution.
The density of pure water is approximately 1 g/mL. If adding the solute doesn't change the volume much, then you will have
1mL solution equals ~1mL solvent which equals ~1 g solvent (since d~1g/mL). So 1000 mL solution correspond to ~ 1 kg solvent and M is close enough to m.

Note that for any other solvent with d<>1 g/mL this would not be true. E.g. if you had d=2 g/mL
then 1 L of solution would be ~1 L solvent and that would be ~2 kg solvent, meaning that 1 M would be approximately 0.5 m.

So you need 2 conditions to be satisfied at the same time:
a)the volume must not change much when solute is dissolved
b)the density of the solvent (NOT of the solution) must be approximately 1 g/mL

Answer 2

The volume can not change when solute is added.

If it does, but Molarity and Molality will change.

Answer 3

The volume cannot change is the correct answer.