IMac – Sourcing a replacement graphics card for an iMac

No you are correct there are no upgrade options available for the 21.5" iMacs (Mid-2011). Yes, you are stuck with what comes in each of the two 21.5" models available. Your eyes are not deceiving you on the iMac Specs, what you see is what you get no exceptions.

You graphics card options are:

1. Buy the 21.5-inch: 2.5GHz model and get the AMD Radeon HD 6750M with 512MB
2. Buy the 21.5-inch: 2.7GHz model and get the AMD Radeon HD 6770M with 512MB

According to MacWorld's article / review "21.5- and 27-inch iMacs (Mid 2011)"

So in reality you have two options, and its all in which machine you buy. If all you want is a graphics boot, your going to have to pay the premium to upgrade all the other components too, unfortunately there is no way around it, other than letting apple know you want options, give them some feedback stating so.

It's quite likely that this issue is caused by hardware (a failing GPU, most likely) but there's a possibility that it's caused by software.

To figure out where the problem lies, boot your computer into a clean install (either Mac OSX/Linux/Windows on a bootable drive, or use your "install Mac OS" install disk/partition). If you experience any kind of problems while using a clean install of any OS, you know the problem is hardware.

You should run a backup as soon as possible, then replace your GPU (Guide) (or take it for a repair). Only attempt to repair it yourself if you completely understand the instructions, if you're unsure, a self-repair may cause more damage

If there are no problems while using a clean OS, the easiest way to fix the problem would be to reinstall Mac OSX; remember to backup your files first so you don't lose anything.