The predictions of the pair radial distribution function (RDF) at contact value, compressibility factor, and chemical potentials for binary and ternary hard-sphere mixtures obtained with the Barrio-Solana, the Santos et al., and the generalized Lebowitz mixing rules are compared using the Carnahan-Starling, Kolafa, and Khoshkbarchi-Vera one-component hard-sphere EOS. An expression for the pair RDF at contact value for Barrio-Solana mixing rule and the expressions for the chemical potentials in multicomponent hard-sphere fluids are derived. As a general rule, the equations of state obtained based on the generalized Lebowitz mixing rule predict better the pair RDF at contact value simulated data. The compressibility factor and the chemical potentials simulation results are generally better predicted by either the Santos et al. or the Barrio-Solana mixing rule, depending on the packing fraction, the composition, and the diameter ratio values. For a binary hard-sphere fluid with large diameter ratio, sigma (2)/sigma (1) = 20, in the high-density region and at low mole fractions of the larger component, the Barrio-Solana mixing rule predicts the compressibility factor simulation results considerably more accurately than the other mixing rules studied here.