We offer a new theoretical angle for cognitive arithmetic, which is that evidence accumulation may play a role in problem plausibility decisions. We build upon previous studies that have considered such a hypothesis, and here formally evaluate the paradigm. We develop the finding that performance differences, due to variations in strategy use and aging effects, can indeed be reasonably explained through these accumulation-to-bound cognitive models. Results suggest that these models may be effectively used to learn more about the underlying cognitive processes. In this study, we modelled young (18-24) and older (68-82) adults' solution times in performing arithmetic verification (e.g. whether 8x5=41 is true/false). The domain-relevant factors in strategy use (problem-verification heuristics) and aging differences (older/younger adult groups) were analyzed by a response process model of the latency data, that is fit by participant and item. Lower thresholds accounted for the faster response times (RTs) for problems solved with heuristics (arithmetic rule-violation checking strategies), as opposed to problems solved by calculation approaches. A more rapid accumulation accounted for faster RTs on problems in which two arithmetic rules were violated (strategy combination) rather than one. Third, higher thresholds (i.e. preferring to have greater certainty before responding) accounted for older adults' slower speed. These findings are in support of accumulation models being relevant for more complex cognitive tasks, as well as to account for the age-related differences therein.