Two experiments tested the hypothesis that simple arithmetic requires working memory resources. Subjects were presented with a simple verification task (e.g. 8 + 4 = 12. True? False?) with (or without) secondary tasks. We varied the difficulty of the problems (i.e. easy vs hard problems) and the potential for inducing associative confusion (e.g. 8 4 = 12). Secondary tasks were chosen so as to overload the phonological loop and the central executive of the working memory system. We found greater disruption of performance on true problems when both the phonological loop and the central executive were overloaded, and greater disruption of performance on false problems when the central executive system was overloaded. This pattern of results is consistent with the working memory resource hypothesis and suggests that the central executive is a critical system involved in simple arithmetic. Finally, the results of the present study on both true and false problems and their implications for cognitive arithmetic theories are discussed.