Concerning the entrance mechanism of graduate schools in Taiwan, the conflict of examination dates has been a crucial issue over the years. In particular, top, middle, and lower universities cluster their examinations during February, March, and April, respectively. In this paper, we developed a model to explain this phenomenon of diverging dates. The model shows that when the examination exhibits measurement error, i.e., the best (worst) student may not have the highest (lowest) testing scores, the phenomenon is an equilibrium among universities competing for better students. Specifically, when the measurement error increases, a top university will have an earlier examination to decrease the error and raise the probability of enrolling best students.