Hi sirluke90,
The flash point depends not only on the vapour pressure, but also on the lowest vapour concentration that makes the air mix flammable. Logically enough, since a non-flammable compound like trichlorofluoromethane may be very volatile, but the mix won't catch fire.
Admitting that 5% and 3% are by volume, and that atmospheric pressure is nearly 1 bar (it's not exactly) for simpler figures, at +20°C equilibrium compound A has 10% volume concentration in air, or 2× its LFL, while B has 30% or 10× its LFL. You might expect that at some lower temperature hence vapour pressure, A is below its closed-cup flash point and B above.
Though, the question is over-simplified and formally unanswerable, because we ignore how the vapour pressures of A and B vary with the temperature. This differs among the compounds. The vapour pressure of B could drop more steeply at cold, so that some temperature exists where A is above its flash point and B is below its flash point.
If your examiner wrote the question, find some delicate way to formulate the objection, like "we suppose that the vapour pressures of A and B vary similarly with the temperature".