(a) That's correct. Whatever is given in exchange for a promise does not have to be of equivalent value. Why not? Because otherwise the requirement of consideration would too greatly restrict the freedom of parties to make enforceable agreements on their own terms.
The rule is that consideration has to be of some value. It must at least be 'real' rather than illusory. But it does not have to be 'adequate' in the sense of being equal to or even close in value to what it is given in exchange for. It can be a mere token.
This approach certainly makes the requirement of consideration something of a formality. But even so, it is an essential element of informal agreements, and one that has important consequences in contract law.