  We present definitive detection statistics for 12.2 GHz methanol masers
towards a complete sample of 6.7 GHz methanol masers detected in the Methanol
Multibeam survey south of declination -20 degrees. In total, we detect 250 12.2
GHz methanol masers towards 580 6.7 GHz methanol masers. This equates to a
detection rate of 43.1%, which is lower than that of previous significant
searches of comparable sensitivity. Both the velocity ranges and the flux
densities of the target 6.7 GHz sources surpass that of their 12.2 GHz
companion in almost all cases. 80 % of the detected 12.2 GHz methanol maser
peaks are coincident in velocity with the 6.7 GHz maser peak. Our data support
an evolutionary scenario whereby the 12.2 GHz sources are associated with a
somewhat later evolutionary stage than the 6.7 GHz sources devoid of this
transition. Furthermore, we find that the 6.7 GHz and 12.2 GHz methanol sources
increase in luminosity as they evolve. In addition to this, evidence for an
increase in velocity range with evolution is presented. This implies that it is
not only the luminosity, but also the volume of gas conducive to the different
maser transitions, that increases as the sources evolve. Comparison with
GLIMPSE mid-infrared sources has revealed a coincidence rate between the
locations of the 6.7 GHz methanol masers and GLIMPSE point sources similar to
that achieved in previous studies. Overall, the properties of the GLIMPSE
sources with and without 12.2 GHz counterparts are similar. There is a higher
12.2 GHz detection rate towards those 6.7 GHz methanol masers that are
coincident with extended green objects.
