I know this is a really old thread but this is reference for anyone searching this.
I got a mid 2011 iMac i7 4GB from my University Newspaper, it was dead. I got Apple to fix it and replace the HDD and load up macOS Sierra on it.
It ran like crap. I know it ran like crap because I have a 2008 i7 12GB PC desktop I built myself, which was WAY faster.
I ran tests and checked out the System Monitor - heavy swap usage and RAM was almost maxed out. I was just browsing the internet and having Spotify Open. The iMac almost died when I booted up XCODE. It basically came to a halt when I launched the Simulator for an iPhone.
I picked up a 16GB kit and put it in myself. The thing runs night and day different. I'm using 7.09 GB right now just doing homework (Spotify/Mail/Calendar/Safari). This goes past 8GB when I run XCODE and the iOS Simulator.
No offense to anyone, but I have seen a lot of BAD advice on this on other mac forums saying it won't speed up your computer. That's so wrong. If your HDD is being used heavily as a scratch disk for temp files, you're decreasing the HDD life span and creating a bottle neck. Secondly, who seriously runs ONE application at a time? Come on now......
To anyone with a 2011 iMac with 4 or 8GB ram, definitely get a 16GB kit if you use photoshop or develop apps. I can easily see myself using this 2011 iMac indefinitely until the GPU dies or something.