I think that statement, When the concentration of B is doubled the rate remains the same.", implies that B is not a reagent in the
rate-determining step, which is the elementary step that has the slowest rate. And "When the concentration of A is doubled, the rate for the reaction: 2 A + B-> 2 C quadruples" implies that the stoichiometric coefficient of A is twice, according to
the Rate Law.
So the rate law is probably like ... Rate = [A]
2Find out more about the topic: try
http://en.wikipedia.org/wiki/Reaction_rateP.S. I don't speak English so my skills are poor. Hope you understand me.