(b) That's right. This type of case is unusual. In all the earlier examples in this module, both contracting parties have made promises to each other. Such contracts are called 'bilateral' because both parties undertake obligations. The consideration in those examples was provided by the exchange of promises.
In the present case, A promises to pay a reward, but B does not promise to find the car. The agreement is 'unilateral' because only one party (A) makes a promise. A promises to pay $1,000 only if someone finds and returns the car to him. If B, knowing of the promised reward, finds and returns the car, does A's promise to pay the reward become legally binding? The problem is that, before B actually finds and returns the car, B does not appear to have given anything to A that can be counted as consideration for A's promise. And B will have already found and returned the car before A's promise to pay the reward becomes legally binding.
You will remember that the normal rule is that something already done prior to contracting is 'past consideration' and therefore insufficient to make the other person's promise legally binding. However, the courts treat unilateral contracts as a special case. If an act has been performed by one person in the expectation that another person's promise given in exchange for that act would become legally binding as soon as the act is done, then the act (for example, finding and returning the car) is regarded as 'executed' consideration rather than as 'past' consideration. Executed consideration is good consideration.