Actually you may only be able to do that on a kitchen sink faucet, the ends of them screw off and you can get a hose adaptor for them at the hardware store, then you can get the garden faucet adaptor for the RO unit (most actually come with one).
Before we go there, does this apartment have washer/dryer hookups, if so then it would be really easy, you just Y off the cold water hookup and hook the RO unit to one side and waste it down the washer drain.