Sex differences on the Attention Test (AC), the Raven's Standard Progressive Matrices (SPM), and the Brazilian Cognitive Battery (BPR5), were investigated using four large samples (total N=6780), residing in the states of Minas Gerais and Sao Paulo. The majority of samples used, which were obtained from educational settings, could be considered a nonprobability sampling. Females outperformed males on the AC (by 2 IQ points), whereas males slightly outperformed females on the SPM (by 1.5 IQ points). On the BPR5, sex differences favoring males were statistically significant (on average 6.2 IQ points). The largest difference was in Mechanical Reasoning (13 IQ points), and the smallest was in Spatial Reasoning (5 IQ points). In addition, two methods were adopted for determining whether sex differences existed at the level of general intelligence. First, a "g" factor score was estimated after principal axis factoring of test scores. Men had an advantage of 3.8 IQ points (statistically significant) on the "g" score, which was reduced to 2.7 IQ points (not significant), when the "g" score was estimated without including Mechanical Reasoning. Second, a confirmatory factor analysis approach was conducted that allowed testing of mean differences at the latent variable level. Again, sex differences favoring males were found (0.23 or 3.44 IQ points). Regarding educational and SES variables, some sex differences favoring males were found in the SPM and in the BPR5. In general, our results agree with studies that identify small, but consistent cognitive sex differences in reasoning tasks. Societal implications are discussed. (Contains 5 tables and 3 figures.)