Cognition emerges from the coordination of computations in multiple brain areas. However, elucidating these coordinated computations within and across brain regions is challenging because intra- and inter-areal connectivity are typically unknown. Testable hypotheses about these interactions are also generally unavailable. To study coordinated computation, we trained multi-area recurrent neural networks (RNNs) to discriminate the dominant color of a checker-board and output decision variables reflecting a direction decision, a task previously used to investigate decision-related dynamics in dorsal premotor cortex (PMd) of monkeys. We found that multi-area RNNs, as opposed to single RNNs, reproduced the decision-related dynamics observed in PMd during this task. The RNN solved this task by a novel mechanism in which RNN dynamics integrated color information on an axis subsequently readout by an orthogonal direction axis. Direction information was selectively propagated through preferential alignment with the inter-areal connections, while the color information was filtered. These results suggest that cortex uses modular computation to generate minimal but sufficient representations of task information, selectively filtering unnecessary information between areas. Finally, we leverage multi-area RNNs to produce experimentally testable hypotheses for computations that occur within and across multiple brain areas, enabling new insights into distributed computation in neural systems.