This paper studies how schooling admission tests affect economic performance in an economy where individuals are endowed with both academic and non academic abilities and both abilities matter for labor productivity. We develop a simple model with selective government held schools, where individuals signal their abilities by taking an admission test that sorts them into different schools. When abilities are poorly correlated in the population, as documented in the literature, a standard test based only on academic abilities is expected to be less efficient than a more balanced test, that considers both ability types. Contrary to this expectation, we show that this is not generally true, but depends both on the distribution of abilities in the population and on the marginal contribution of each ability type to individual productivity. It is also not generally true that the outcome of a more balanced test can be replicated by a sequential testing strategy, with government held schools testing academic abilities and firms testing non academic abilities on the sub-sample of graduates of elite schools.