On your exam you wrote: “since there is no resistance given, all 120vac will go through the circuit.”
Perhaps it’s just not stated well, but the first part of that statement does not lead to the second.
With this question, if you recognize the configuration of the loads, you don’t need to know the resistance of each load to know how much voltage gets dropped across each load. You just need to know the basics of voltage and voltage drop in series and parallel circuits.
You do correctly see how the detector switch being closed affects the main.