The role of hydrophobicity of phenylalanine-glycine nucleoporins (FG-Nups) in determining the transport of receptor-bound cargo across the nuclear pore complex (NPC) is investigated using Langevin dynamics simulations. A coarse-grained, minimal model of the NPC, comprising a cylindrical pore and hydrophobic-hydrophilic random copolymers for FG-Nups was employed. Karyopherin-bound receptor-cargo complexes (Kaps) were modeled as rigid, coarse-grained spheres without (inert) and with (patchy) FG-binding hydrophobic domains. With a sequence-agnostic description of FG-Nups and the absence of any anisotropies associated with either NPC or cargo, the model described tracer transport only as a function of FG-Nup hydrophobicity, f. The simulations showed the emergence of two important features of cargo transport, namely, NPC selectivity and specificity. NPC selectivity to patchy tracers emerged due to hydrophobic Kap-FG interactions and despite the sequence-agnostic description of FG-Nups. Furthermore, NPC selectivity was observed only in a specific range of FG-hydrophobic fraction, 0.05 ≤ f ≤ 0.20, resulting in specificity of NPC transport with respect to f. Significantly, this range corresponded to the number fraction of FG-repeats observed in both S. cerevisiae and H. sapiens NPCs. This established the central role of the FG-hydrophobic fraction in determining NPC transport, and provided a biophysical basis for conservation of the FG-Nup hydrophobic fraction across evolutionarily distant NPCs. Specificity in NPC transport emerged from the formation of a hydrogel-like network inside the pore with a characteristic mesh size dependent on f. This network rejected cargo for f > 0.2 based on size exclusion, which resulted in enhanced translocation probability for 0.05 ≤ f ≤ 0.20. Extended brush configurations outside the pore resulted in entropic repulsion and exclusion of inert cargo in this range. Thus, our minimal NPC model exhibited a hybrid cargo translocation mechanism, with aspects of both virtual gate and selective-phase models, in this range of FG-hydrophobic fraction.