  The quantumness of a generic state is the resource of many applications in
quantum information theory and it is interesting to survey the measures which
are able to detect its trace in the properties of the state. In this work we
study the quantum discord and fully entangled fraction of two classes of
bipartite states and compare their behaviors. These classes are complements to
the $d\otimes d$ Werner and isotropic states, in the sense that each class
possesses the same purification as the corresponding complemental class of
states. Our results show that maximally entangled mixed states are also
maximally discordant states, leading to a generalization of the well-known fact
that all maximally entangled pure states have also maximum quantum discord.
Moreover, it is shown that the separability-entanglement boundary of a Werner
or isotropic state is manifested as an inflection point in the diagram of
quantum discord of the corresponding complemental state.
