72 hour and and 24 hour direct visa question

We arrive by plane from US to Beijing, spend one night then fly to Mongolia; Is 72 transit ok for this? On return, we take the train from Ulan Bator to Beijing and fly from Beijing back to US the next day (actually 26 hours after train is scheduled to arrive). Can we use 72 or 24 direct transit for this return? We are US citizens.