(b) That's wrong. Perhaps surprisingly, there is probably sufficient consideration in these circumstances. It is true that B is already legally bound to pay $5,000 to C and that he is therefore not promising to do something that he is not already bound to do. But it is important that initially B owes that obligation only to C, not to A. When B makes a promise to A that he (B) will pay C what he owes her, B is making himself liable directly to A if he fails to pay C. A therefore obtains a legal right to sue B for damages if B fails to pay C.
Therefore, the promise to perform an obligation owed to a third party in return for a counter-promise (the $100 payment in this case) is sufficient consideration to make a legally binding agreement between A and B.