Recently, it has been experimentally elucidated whether a V impurity in Al(n)V(+) clusters occupies an external or an internal site by studying their interaction with argon as a function of cluster size [S. M. Lang, P. Claes, S. Neukermans, and E. Janssens, J. Am. Soc. Mass Spectrom. 22, 1508 (2011)]. In the work presented here we studied, by means of density functional theoretic calculations, the structural and electronic properties of Al(n)V(+) clusters with n = 14-21 atoms, as well as the adsorption of a single Ar atom on them. For n < 17 the lowest energy structure of Al(n)V(+) is related to that of the pure Al(n+1)(+) cluster with the V atom substituting a surface Al atom. For n ≥ 17 the V impurity becomes embedded in the cluster, in agreement with the experimental results, and the clusters adopt a fcc-like structure instead of the icosahedral-like skeleton of pure Al(n+1)(+). We have studied the binding energy per atom, the second energy difference, and the V and Al atom separation energies, in comparison with those of pure Al(n+1)(+). We also studied the adsorption of atomic Ar on endohedral and exohedral V doped clusters. The optimized Ar adsorption geometries are formed with Ar on top of a surface atom (V for n < 17, and Al for n ≥ 17) without noticeable structural distortion of the host cluster. At the critical size (n = 17) of the exohedral-endohedral transition, the calculated Ar adsorption energy exhibits a drop and the Ar-cluster distance increases drastically, indicating that Ar becomes physisorbed rather than chemisorbed. All these results confirm the assumptions made by the experimentalists when interpreting their measurements.