We study the phase transition from dense baryonic matter to dense quark matter within the large-Nc limit. By using simple constant speed of sound equations of state for the two phases, we derive the scaling with Nc of the critical quark chemical potential mu_crit for this phase transition. While quark matter is strongly suppressed at large Nc, the phase transition at a large but finite density could nevertheless be important to determine the maximum mass of compact stars. In particular, in the range 3<Nc<5.5 the quark phase would take place in compact stars and would lead to the formation of an unstable branch of hybrid stars. As a consequence, the maximum mass is restricted to the range 2.1M_sun<Mmax<3Msun. For larger value of Nc, the phase transition would occur at densities too high to be reached in the core of compact stars. However, the very requirement that it occurs (although at a very large density) translates into interesting constraints on the stiffness of the baryonic phase: its speed of sound must exceed 1/3.