Dual-process theories and the intuitive rules theory are influential in the domain of cognitive psychology and of the psychology of mathematics education respectively. We discuss similarities between these frameworks that have developed largely separately. We examine quantitative reasoning with geometrical concepts, a paradigmatic task in the intuitive rules research tradition, from a typical dual-process perspective. First, in two experiments we validate that intuitive responses result from processes exhibiting two main heuristic processing characteristics as posited in the dual-process framework: fastness and effortlessness. Moreover, we discuss the reaction time (RT) findings with regard to the currently central debate in the dual-process literature about how heuristic and analytic processes interact. A position concerning this topic is currently lacking in the intuitive rules theory. We discuss how our RT findings contribute to the theorizing in the current dual-process literature.