  If only one family of "neutron stars" exists, their maximum mass must be
equal or larger than $2 M_\odot$ and then only in less than about $18\%$ of
cases the outcome of the merger of two neutron stars is a direct collapse to a
black hole, since the newly formed system can avoid the collapse at least until
differential rotation is present. In the so-called two-families scenario, stars
made of hadrons are stable only up to about $1.5-1.6 M_\odot$, while the most
massive compact stars are entirely made of strange quark matter. We show that
in this scenario the outcome of the merger of two neutron stars is a prompt
collapse in at least $34\%$ of the cases. It will therefore be easy to
discriminate between the two scenarios once the gravitational waves emitted at
the moment of the merger are detected.
