  Different theoretical approaches for the thermodynamic properties and the
equation of state for multicomponent mixtures of nonadditive hard spheres in
$d$ dimensions are presented in a unified way. These include the theory by
Hamad, our previous formulation, the original MIX1 theory, a recently proposed
modified MIX1 theory, as well as a nonlinear extension of the MIX1 theory
proposed in this paper. Explicit expressions for the compressibility factor,
Helmholtz free energy, and second, third, and fourth virial coefficients are
provided. A comparison is carried out with recent Monte Carlo data for the
virial coefficients of asymmetric mixtures and with available simulation data
for the compressibility factor, the critical consolute point, and the
liquid-liquid coexistence curves. The merits and limitations of each theory are
pointed out.
