Personality and cognition are found to be two interrelated concepts and to both have a predictive power on educational and life outcomes. With this study we aimed at evaluating the extent to which personality traits interact with cognition in acquiring cognitive competences during higher education. In a sample of university students at different stages of their career and from different fields of study, we collected Big Five traits, as a measure of personality, and Intelligent Quotient (IQ), as a proxy of cognition. A set of multiple regressions served to explore the relative contribution of IQ and personality traits on the performance on two cognitive competences tests: literacy and numeracy. Results showed that IQ highly modulated numeracy but had a moderate or no impact on literacy while, compared with IQ, personality affects literacy more. In a further explorative analysis, we observed that both the effects of personality and IQ on cognitive competences were modulated by the level of the students' career (freshmen, undergraduates, and bachelor graduates). Different traits, and particularly conscientiousness, increased or decreased their impact on achieved scores depending on the educational level, while IQ lost its effect in undergraduates suggesting that personal dispositions become more influential in advancing the academic carrier. Finally, the field of study resulted to be a predictor of numeracy, but also an important covariate altering the pattern of personality impact.