You can check the meter reading by yourself for both water and electricity, compare it with the paper that kahramaa gave to you when you applied. check if there are discrepancies regarding the meter that was charged on your bill for the month of May 2011. Based on your story, you just moved in last quarter of the month and it's not quite possible for you to have QR305 unless you keep 2 or 3 ACs on 24/7.
I agree with King29, i also pay 350 to 400 esp during summer, for a 3 bedroom flat.
We hope you resolve the problem soon.