Sorry. I edited my previously reply and added the links to how to check AHT as well as the startup tone indicators. Just for clarification, is this a mid-2012 model? Anything after that wouldn't have memory modules, but would be soldered to the logic board without any way to expand.
It does a quick memory test during power on, and if it detects an error it goes quickly to the beeps. If one module is good but it doesn't sense (such as not seated) the other module at all it will just ignore it. I think it should also give a different tone if it doesn't sense any memory installed.
One of the things you might try temporarily is to test your machine one at a time with a single memory module inserted. If the sockets are fine, it should be able to operate properly on a single, good module. It could also be a bad socket, and that's kind of harder to fix, but not impossible. Under warranty, Apple would have replaced the entire logic board for a bad socket. Or maybe the rare case that both the memory and socket are bad.
I'd suggest trying "module 1" in the top socket. If it works, then try it in the bottom socket. If it works in both sockets you know that the other module is bad. If module 1 doesn't work in the top socket, I'd see if "module 2" works in the top socket. There are a several logical permutations to determine if the memory or the socket is bad. It's more likely that the memory is bad than the socket is bad.
