How far up the years do I need to go to shift a 42T cog on the rear? I was given a 11-42T cassette and would like to see if I can make it work on my daughter's beater mountain bike. Currently it has a Shimano Deore XT M772. It is rated for 34T capacity, I can abuse it into chewing up to 37T, but 42t is certainly a bridge too far.

I guess another option is the derailleur hanger extender? How well do those work?