Bi-magnetic core/shell nanoparticles are gaining increasing interest due to their foreseen applications. Inverse antiferromagnetic(AFM)/ferrimagnetic(FiM) core/shell nanoparticles are particularly appealing since they may overcome some of the limitations of conventional FiM/AFM systems. However, virtually no simulations exist on this type of morphology. Here we present systematic Metropolis Monte Carlo simulations of the exchange bias properties of such nanoparticles. The coercivity, H C, and loop shift, H ex, present a non-monotonic dependence with the core diameter and the shell thickness, in excellent agreement with the available experimental data. Additionally, we demonstrate novel unconventional behavior in FiM/AFM particles. Namely, while H C and H ex decrease upon increasing FiM thickness for small AFM cores (as expected), they show the opposite trend for large cores. This presents a counterintuitive FiM size dependence for large AFM cores that is attributed to the competition between core and shell contributions, which expands over a wider range of core diameters leading to non-vanishing H ex even for very large cores. Moreover, the results also hint different possible ways to enhance the experimental performance of inverse core/shell nanoparticles for diverse applications.