Our numerical simulations show that axisymmetric, torsional, magnetoelastic oscillations of magnetars with a superfluid core can explain the whole range of observed quasiperiodic oscillations (QPOs) in the giant flares of soft gamma-ray repeaters. There exist constant phase QPOs at f is < or approximately equal to 150 Hz and resonantly excited high-frequency QPOs (f>500 Hz), in good agreement with observations. The range of magnetic field strengths required to match the observed QPO frequencies agrees with that from spin-down estimates. These results suggest that there is at least one superfluid species in magnetar cores.