You can't answer which method is appropriate, as you aren't given enough information. You can't assume the expansion is reversible because it's isothermal; it can be either reversible or irreversible, and you aren't told which (unless there's a part of the question you haven't quoted - "basically this"?).

If it is expanding against a constant external pressure, it is irreversible and the work is -P_{ext}ΔV, as your friends used.

If it is reversible, that means the external pressure is always equal to the internal pressure, and the work is the integral of -PdV, so you get your result. You don't need to know n and T; you know nRT = PV = 400 kPa*m^{3}.