A pre-built computer capable of mining and gaming decently? I'd say that's not possible. You'll get PCs that are able to run most current games at medium settings but it won't be viable for mining.

I used my two years old gaming rig for mining until I realised that after subtracting the electricity cost that PC makes me less money when mining 24/7 than solving some tasks and clicking some ads for an hour or two a day gets me.