Here we analyze gray matter indices before and after completing a challenging adaptive cognitive training program based on the n-back task. The considered gray matter indices were cortical thickness (CT) and cortical surface area (CSA). Twenty-eight young women (age range 17-22 years) completed 24 training sessions over the course of 3 months (12 weeks, 24 sessions), showing expected performance improvements. CT and CSA values for the training group were compared with those of a matched control group. Statistical analyses were computed using a ROI framework defined by brain areas distinguished by their genetic underpinning. The interaction between group and time was analyzed. Middle temporal, ventral frontal, inferior parietal cortices, and pars opercularis were the regions where the training group showed conservation of gray matter with respect to the control group. These regions support working memory, resistance to interference, and inhibition. Furthermore, an interaction with baseline intelligence differences showed that the expected decreasing trend at the biological level for individuals showing relatively low intelligence levels at baseline was attenuated by the completed training.