From the last years of the Lula government until now Brazil has been going through a revolution in the federal system of higher education. One of several universities created to include more people from public schools, as well as indigenous and Afro-descendants, is the Federal University of the ABC (UFABC), in the metropolitan region of Sao Paulo. Fifty per cent of vacancies are reserved for admittance through the system of quotas. The objective of this paper is to investigate whether students who were admitted based on their racial and socio-economic situation have a similar level of academic achievement than their colleagues who have not participated in quotas to join the university, and what lessons should be considered for future selections of students in the federal system of higher education in Brazil. In addition to the conceptual part, the approach adopted in this research complements the descriptive with the causal statistics, where the first deals with variables like skin color, gender, income and learning difficulties, and the second tries to explain the success in academic studies. Both approaches focus on the differences among students who entered the university through socioeconomic and racial quotas, since the aim is to understand whether there are differences between the two types of students. The conclusion was that in the beginning the quota students presented a lower level of academic achievement in relation to non-quota students, but this difference is reduced over the years, even if not end on equal ground. However, the simple fact that there is a reduction of academic inequality between the two groups is already a success of educational policies concerning inequality reduction, and they should be improved continuously.