Final answer:
Empire Company does not need to record an adjusting entry for paying the custodian for January office cleaning services.
Step-by-step explanation:
The situation that does not require Empire Company to record an adjusting entry at the end of January is c) At the end of January, Empire Company pays the custodian for January office cleaning services. Adjusting entries are used to record transactions that have occurred but have not yet been entered into the financial statements. In this case, the payment for January office cleaning services is a normal transaction that does not require adjustment at the end of the month.