We ask whether failing one or more of the state-mandated high-school exit examinations affects whether students graduate from high school. Using a new multi-dimensional regression-discontinuity approach, we examine simultaneously scores on mathematics and English language arts tests. Barely passing both examinations, as opposed to failing them, increases the probability that students graduate by 7.6 percentage points. The effects are greater for students scoring near each cutoff than for students further away from them. We explain how the multi-dimensional regression-discontinuity approach provides insights over conventional methods for making causal inferences when multiple variables assign individuals to a range of treatments.