  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 (QGP) 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
$R_{AA}\otimes v_2$ 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.
