For decades, researchers have sought analytic methods that yield diagnostic information about test-takers while ensuring that high-stakes tests remain free of construct-irrelevant bias. This study applies a general cognitive-diagnostic-model (CDM) framework to analyze the quantitative and verbal skills (QVS) assessed by the Swedish Scholastic Aptitude Test (SweSAT). A three-step latent-class logistic-regression approach was used to investigate the relationship between test-takers' background characteristics and performance in each domain subskill. The analysis was conducted using representative data from 41,451 test-takers from the 2023 administration of the SweSAT, focusing on performance across four quantitative and four verbal subskills, and examining test characteristics. The results showed that the CDM method was appropriate for analyzing QVS, with evidence of measurement invariance across sex, age, and educational levels in the subskills. Additionally, the findings revealed distinct associations between sex, educational level, and age with performance in each QVS subskill. Implications for equitable selection in higher education are discussed.