Budget gaming pc

I recently have been trying to build a gaming pc and i found these parts :

Moderboard:Gigabyte-GA-970A-DS3

Cpu:AMD-Bulldozer-FX-4100-Black-Edition-3-60Ghz-Quad-Core

Ram:Kingston-HyperX-8GB-DDR3-1600MHz-Desktop-Memory

HDD:Western-Digital-Caviar-Blue-500GB-7200rpm-SATA-6Gb/s-16MB-3-5-inch-Hard-Drive

PSU:550W-Powercool-High-Efficiency

GPU:ati 7770 Gigabyte GHZ edition

Case:Sharkoon Vaya Case ATX

Are these parts competible together? and is this build good enough to play battlefield 3 on medium setting 1920x1080 ?

Thank you

what is your budget

 

550-600$

 

here you go this is a great build for the money http://pcpartpicker.com/ca/p/z1Km

Where are you from? Canada and the US have different prices, so it's best to know.

I live in europe malta