If a Change in Nozzle Design Increases a Given Rocket $\sqrt{2}$

If a change in nozzle design increases a given rocket engine's exhaust speed by a factor of two, by what factor does this increase or decrease the amount of propellant needed to get its payload to a specific final velocity? (Assume the payload and engine mass is small compared to that of the fuel, and choose the closest answer.)

A) 4
B) 2
C) $\sqrt{2}$
D) 1
E) $1 / 2$
F) $1 / 4$