Transverse momentum (p(T)) spectra of pions, kaons, and protons up to p(T) = 20 GeV/c have been measured in Pb-Pb collisions at root s(NN) = 2.76 TeV using the ALICE detector for six different centrality classes covering 0%-80%. The proton-to-pion and the kaon-to-pion ratios both show a distinct peak at p(T) approximate to 3 GeV/c in central Pb-Pb collisions that decreases for more peripheral collisions. For p(T) > 10 GeV/c, the nuclear modification factor is found to be the same for all three particle species in each centrality interval within systematic uncertainties of 10%-20%. This suggests there is no direct interplay between the energy loss in the medium and the particle species composition in the hard core of the quenched jet. For p(T) < 10 GeV/c, the data provide important constraints for models aimed at describing the transition from soft to hard physics.