Hydrodynamics and jet quenching are responsible for the elliptic flow v_{2} and suppression of large transverse momentum (p_{T}) hadrons, respectively, two of the most important phenomena leading to the discovery of a strongly coupled quark-gluon plasma in high-energy heavy-ion collisions. A consistent description of the hadron suppression factor R_{AA} and v_{2}, especially at intermediate p_{T}, however, remains a challenge. We solve this long-standing R_{AA}⊗v_{2} puzzle by including quark coalescence for hadronization and final state hadron cascade in the coupled linear Boltzmann transport-hydro model that combines concurrent jet transport and hydrodynamic evolution of the bulk medium. We illustrate that quark coalescence and hadron cascade, two keys to solving the puzzle, also lead to a splitting of v_{2} for pions, kaons, and protons in the intermediate p_{T} region. We demonstrate for the first time that experimental data on R_{AA}, v_{2}, and their hadron flavor dependence from low to intermediate and high p_{T} in high-energy heavy-ion collisions can be understood within this coupled framework
