Academic institutions are seeking to attract the most capable and prospective students. Many research studies seek to identify factors determining a successful transition from secondary to tertiary education. One of the important issues is the predictive value of national testing/Matura examination results in relation to higher education institutions admission. The aim of our study is to quantify the odds to study at university and the results of centralised student assessments (the 10th grade and Matura) of mathematics and the Lithuanian language and literature for the period of five years (Matura examinations for the period 2014–2018), taking into account the student's gender, the location of the school attended, social support, and special needs indicators. We estimate that the Matura grade in mathematics is almost double more important when compared to the10th grade test results for odds of studying at higher education institutions. Grades of the Lithuanian language and literature obtained to be twice more import for males than females. From 2023 or 2024, we may observe the downward trend of people with tertiary educational attainment in Lithuania.