What you are asking is really impossible to answer on the surface. Game engines differ, some are quite miserable and extremely hard on a cpu. This'll lead to bottleneck on any gpu. Some games are easy on the cpu but your choice of 4k on the resolution makes it hard on the gpu. Then there's your choices of settings, do you insist on ultra or are happy at medium etc.
Example. My i7-3770K/970 has no issues with the mods I run in skyrim, but it generally sees 6 thread usage. I get a solid 60fps. On my i5-3570k/660ti if I run the exact same mods, I'm looking at 40fps average, not because of the gpu, but because the cpu is tanked. The i7 shows 55/65% usage, the i5 shows 95/55% usage. That being cpu/gpu usage on 1080p/60Hz.
So can a r3...