Do all tickets need to be connected??

I am flying to Beijing from Anchorage, AK, USA on April 22nd, with a roundtrip return on May 3. However, I have another separate airline ticket to fly to Singapore on April 25th., and will return to Beijing for my flight back to the States May 2/3. Will I qualify for 72 hour visa the first time, and 24 hour visa the second time??