If an individual lives in State A, works for an investment adviser wit...

We know candidates taking the Series 63 will have to understand registration of securities professionals to this level of detail. First, the state where the individual lives is irrelevant. What matters to the State Securities Administrator is, first, where the individual maintains a place of business. That is State B in your hypothetical, so the IAR must register with the Administrator of State B. If all clients in State C are institutional clients, no registration is required there. But if the IAR serves more than 5 retail investors residing in State C, the IAR must register there, as well.

This assumes that the agent is working for a state registered investment adviser. If the agent worked for a federally covered adviser the agent would only register where he / she works.