think and consider carefully before you sign it. dun sign the offer letter if you do not wan the job.
if everything is stated on the offer letter and you sign for it, you should take the responsibility as well.
its fair.

i bet company C will tell you in the end:- if you can't wait then please go for the other offer and let go off this.
i believe company C also have a lot of candidate to choose as u r not the only one. y should they pick u in a rush while they might be candidates which are better than you. unless you r really good that they must have you.