We explore with Monte Carlo simulations the NMR finding that solutes in special nematic liquid crystal mixtures 'feel' zero average electric field gradient F-ZZ. The simulations involve solute-solvent mixtures of 1000 identical Gay-Berne ellipsoidal particles with added electric quadrupoles of varying strengths placed at particle centres. As long as all quadrupoles are sufficiently small, F-ZZ calculated at the particle centres is equal for all particles. For larger quadrupole moments, interactions among quadrupoles alter the interparticle distribution and subsequently F-ZZ depends on both solvent and solute quadrupoles; in general, the quadrupolar interactions produce a negative contribution to energy.