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

Projective reduction of the discrete Painlev\'e system of type $(A_2+A_1)^{(1)}$