Some universities, often the most prestigious in a higher education system, select qualified applicants solely on the basis of their measured academic or cognitive abilities. The universities' assumption is that these cognitive abilities are an accurate and complete measure of the applicants' capacity to benefit from university study. This study assesses the extent to which the cognitive measures used are partially the result of other, non-cognitive factors unrelated to future academic performance. Sole reliance on cognitive measures skews university admission in favour of those of higher socioeconomic status. Data for the study were collected by the University of Chile's Department of Evaluation, Measurement and Educational Registration (DEMRE) from 190,000 applicants seeking admission to Chile's 39 selective universities in 2019. The analysis identifies the direct and indirect effects of variables measuring applicants' cognitive and non-cognitive attributes. Logistic regression models were constructed to estimate the differential effect of the two types of factors on admission. The results indicate that non-cognitive factors have an indirect effect on admission through their effect on cognitive scores. Access to selective universities in Chile is partially influenced by students' prior social, cultural, and economic conditions. As a consequence, university education is distributed partially on the basis of social origin and not just ability. The admission process should be changed to reduce discrimination against applicants based on their social origin.