This study analyzed the relative importance of different cognitive abilities for solving complex mathematical word problems (CWPs)--a demanding task of high relevance for diverse fields and contexts. We investigated the effects of spatial, verbal, numerical, and general reasoning abilities as well as gender on CWP performance among N = 1282 first-year university engineering students. Generalized linear mixed models unveiled significant unique effects of spatial ability, [beta] = 0.284, verbal ability, [beta] = 0.342, numerical ability, [beta] = 0.164, general reasoning, [beta] = 0.248, and an overall gender effect in favor of male students, [beta] = 0.285. Analyses revealed negligible to small gender effects in verbal and general reasoning ability. Despite a gender effect in spatial ability, d = 0.48, and numerical ability, d = 0.30--both in favor of male students--further analyses showed that effects of all measured cognitive abilities on CWP solving were comparable for both women and men. Our results underpin that CWP solving requires a broad facet of cognitive abilities besides mere mathematical competencies. Since gender differences in CWP solving were not fully explained by differences in the four measured cognitive abilities, gender-specific attitudes, beliefs, and emotions could be considered possible affective moderators of CWP performance.