Extensive Monte Carlo simulations were performed for (neon + krypton) :mixtures for temperatures between 200 K and 600:K and pressures up to, 1 GPa, using Lennard-Jones potentials to describe the intermolecular interactions. The residual entropies were obtained via Widom's insertion method, as well as via an integration technique. At high pressures, the residual entropy is, to a very good approximation, a linear function of lambda(-1)(a), which is the reciprocal value of the average Monte Carlo displacement parameter that gives the acceptance ratio a for translational moves. The slope of this linear function varies linearly with the mole fraction and is related to the effective collision diameters of the molecules. As the displacement parameter is available during Monte Carlo simulations of fluids, its linearity with the residual entropy can be used to compute this properties with negligible computational effort at high densities, when particle insertion methods become unreliable.