Inverted soft/hard, in contrast to conventional hard/soft, bi-magnetic core/shell nanoparticles of MnxFe3-xO4/FexMn3-xO4 with two different core sizes (7.5 and 11.5 nm) and fixed shell thickness (similar to 0.6 nm) have been synthesized. The structural characterization suggests that the particles have an interface with a graded composition. The magnetic characterization confirms the inverted soft/hard structure and evidences a strong exchange coupling between the core and the shell. Moreover, larger soft core sizes exhibit smaller coercivities and loop shifts, but larger blocking temperatures, as expected from spring-magnet or graded anisotropy structures. The results indicate that, similar to thin film systems, the magnetic properties of soft/hard core/shell nanoparticles can be fine tuned to match specific applications.