A slightly complicated Question...

Hi - I am a US citizen and entered Beijing, China on an F-visa (single entry). My flight was round trip - New York to Beijing and Beijing to New York. During my stay, I would like to visit Korea. If I purchase a round trip ticket from Beijing to Seoul, and Seoul to Beijing (arriving 1 day before my Beijing to New York flight), can I take advantage of the free transit?

Also, just to confirm, all I need is to show the Customs' agent a print out of my ticket (Beijing to New York?)

Thank you,

Ray from USA