The study compares the potential effects of a university admission exam model based on program-specific knowledge and an alternative model relying on general study aptitude (GSA) in the context of a strongly stratified educational system with considerable excess of demand over supply of university education. Using results of the "Sonda Maturant 1998" survey, we show that in the specific context of the Czech Republic, displaying the above characteristics in the given period, an admission exam model based on general study aptitude tests may improve the access of talented individuals with lower socioeconomic status to university education. Our simulations show that with the GSA model (provided the model assumptions are met), the relative chances of an applicant with a university-educated father would be only by one-fourth higher than the relative chances of a student with a less educated father, as compared to the more than a one-third difference in case of the model emphasizing program-specific knowledge. The odds ratio for the GSA model is by 28% points lower for mother's education.