Which of the following is the correct name for a cyclohexane with one methyl group at position 1 and a bromine at position 3?

The correct name is 1‑bromo‑3‑methylcyclohexane. When numbering a cyclohexane with two substituents, you first pick the set of locants that is lowest; here both possible sets are (1,3). Because the locant set is tied, you then assign the lowest number to the substituent that comes first alphabetically, which is bromine (B) before methyl (M). Thus bromine gets position 1 and the methyl group gets position 3, giving the name 1‑bromo‑3‑methylcyclohexane.