Yes.
Motherboard: ~200
Graphics Card: ~250
RAM: ~40
Processor: ~310
HD: ~150
Power Supply: ~100
Plus other things, such as speakers, a case, moniter, mouse and stuff.
That would be around $1,000 - $1,100
Specs?
Lol.
For a computer that would play everything on max (not talking good quality), you'd be looking at about
$40 case
$100 PSU
$70 mobo
$120 CPU
$40 RAM
$80 HDD
~$300 GPU
Of course if you were spending that much, you'd want better quality components, but it's possible.
It also entirely depends on resolution of the monitor. Even a HD6550 can run BF3 on max on a low resolution.