School entrance examinations are both an incentive system to motivate students and a screening device to identify students with the most potential. To maximize incentives to acquire knowledge, exams should only reward achievement. But to identify the most able students, exams should also reward aptitude. Using a model in which schools are interested in both aptitude and achievement, we show how competition between schools leads each school to put more emphasis on aptitude tests which perform a primarily screening role, and less emphasis on achievement tests and grades which provide incentives for learning. This result is broadly consistent with the comparative reliance on aptitude tests in the United States relative to countries with more centralized education systems. We evaluate the theory through an analysis of the implicit weights on aptitude tests and grades in the admissions process of U.S. colleges. Colleges facing more competition for applicants, including public colleges with low tuition subsidies and private colleges, put more emphasis on aptitude tests.