  We consider the q-Painlev\'e III equation arising from the birational
representation of the affine Weyl group of type $(A_2 + A_1)^{(1)}$. We study
the reduction of the q-Painlev\'e III equation to the q-Painlev\'e II equation
from the viewpoint of affine Weyl group symmetry. In particular, the mechanism
of apparent inconsistency between the hypergeometric solutions to both
equations is clarified by using factorization of difference operators and the
$\tau$ functions.

Exactly Solvable and Integrable Systems