Theoretical electrolyte conductivity and osmotic and activity coefficient relationships that work well over a large range of concentrations, up to 1 mol l(-1), are derived from a hypothetical modified linearized Poisson-Boltzmann distribution function. The distribution function is expressed in terms of modified Debye parameter kappa and normalization constant alpha. Both of these parameters are evaluated in terms of concentration and ion-size parameter, d, by the help of moment conditions. The modified Debye parameter kappa is also expressed as a function of the usual Debye parameter kappa (D). Also considered is the short-range part of the pair potential crucial to obtain at least qualitative agreement with experimental results of electrolytic solutions, and it is assumed that the short-range part of the potential is discontinuous at ion-size parameter.