There are definitely other ways to derive all this but with a quick glance you don't really need to do any computation involving intervals. The key is either th

There are definitely other ways to derive all this but with a quick glance you don't really need to do any computation involving intervals. The key is either the second to last flat, a half step up from the last sharp, C, or F. To me this is much simpler than seeing 3 sharps and going, C->G->D->A. It's definitely good to know the latter but definitely not necessary for ascertaining the key.