Both positive presentation management (PPM) and intelligence are considered as factors influencing the variability of personality self-descriptions. The relationship between PPM and intelligence and the personality differentiation by intelligence hypothesis were examined in a large sample (N=20,183) of job applicants administered the Standard Progressive Matrices and the NEO-PI-R. A composite of 10 NEO-PI-R items served as a PPM marker. Contrary to expectations, PPM and intelligence were not related. Only the variance in openness scores was slightly and linearly associated with IQ, and the variance for neuroticism and extraversion scores was somewhat higher in the IQ range beyond 115. However, congruence and Structural Equation Modelling analyses comparing personality structures for different IQ samples underscored the structural invariance of the NEO-PI-R. It is concluded that the NEO-PI-R keeps its structural properties for individuals across the IQ distribution in selection assessment.