An extensive series of Monte Carlo (MC) simulations were performed in order to explore the validity of simple primitive models of electrolyte solutions and in particular the effect of ion size asymmetry on the bulk thermodynamic properties of real salt solutions. Ionic activity and osmotic coefficients were calculated for 1:1, 2:1, and 3:1 electrolytes by using the unrestricted primitive model (UPM); i.e., ions are considered as charged hard spheres of different sizes dissolved in a dielectric continuum. Mean ionic activity and osmotic coefficients calculated by the MC simulations were fitted simultaneously to the experimental data by adjusting only the cation radius while keeping the anion radius fixed at its crystallographic value. Ionic radii were further optimized by systematically varying the cation and anion radii at a fixed sum of ionic radii. The success of this approach is found to be highly salt specific. For example, experimental data (mean ionic activity and osmotic coefficients) of salts which are usually considered as dissociated such as HCl, HBr, LiCl, LiBr, LiClO(4), and KOH were successfully fitted up to 1.9, 2.5, 1.9, 3, 2.5, and 4.5 M concentrations, respectively. In the case of partially dissociated salts such as NaCl, the successful fits were only obtained in a more restricted concentration range. Consistent sets of the best fitted cation radii were obtained for acids, alkali, and alkaline earth halides. A list of recommended ionic radii is also provided. The reliability of the optimized ionic radii was further tested in simulations of the osmotic coefficients of LiCl-NaCl-KCl salt mixtures. A very good agreement between the simulated and experimental data was obtained up to ionic strength of 4.5 M.