Flory-Huggins (FH) and integral equation theories (IETs) are used to describe the equation of state and the relevant mixing properties of hard sphere binary mixtures in the limit of high size-asymmetry. The results are compared with those obtained from the heuristic equation of state of Mansoori (BMCSL) [J. Chem. Phys. 54, 1523 (1971)] and with the Flory-Huggins scheme of other authors. By choosing a physical recipe for the volume fractions of the two species in the mixture FH theory is shown to be a good approximation to the entropy and the Gibbs free energy of mixing, which shows improvement at high size-asymmetry. In addition, the results of the IETs are found to be in overall quantitative agreement with BMCSL. The implications of our study concerning colloidal systems are discussed.