Ahh...to be 16 again! I shot a nice muley buck when I was 16, and the mount is still on my wall. I shot it with a Rem model 600 in .243, and a year later I sold that rifle for the action because I'd shot too many rounds through it and wore out the barrel. I used the money towards a Rem 700 in .270 that fall, and used it on a spike buck that year.
The .270 Win actually shoots a .277 diameter bullet, so it's technically bigger than .275.
I'll be hunting bear in early/mid October this year, and I have a mule deer hunt in eastern Arizona that starts Nov 6th. I'll be using my 7mm rem mag loaded with 145 grain Speer Grand Slam bullets. It's the same load I've been loading for it for many years. I bought that rifle in about 1989, so I've been using it for ~20 years, and it's killed a bunch of stuff for me.
Here it is with an antelope, about a month after my wife and I were married.