Reviewing the last compile date of production programs is the most efficient way to detect unauthorized changes to production programs, as it can quickly identify any discrepancies between the expected and actual dates of program modification. The last compile date is a timestamp that indicates when a program was last compiled or translated from source code to executable code. Any changes to the source code would require a recompilation, which would update the last compile date. The IS auditor can compare the last compile date of production programs with the authorized change requests and reports to verify that only approved changes were implemented. The other options are not as efficient as option A, as they are more time-consuming, labor- intensive or error-prone. Manually comparing code in production programs to controlled copies is a method of verifying that the code in production matches the code in a secure repository or library, but it requires access to both versions of code and a tool or technique to compare them line by line. Periodically running and reviewing test data against production programs is a method of verifying that the programs produce the expected outputs and results, but it requires designing, executing and evaluating test cases for each program.
Verifying user management approval of modifications is a method of verifying that the changes to production programs were authorized and documented, but it does not ensure that the changes were implemented correctly or accurately. References: CISA Review Manual (Digital Version) , Chapter 4: Information Systems Operations and Business Resilience, Section 4.3: Change Management Practices.

In the PDCA cycle, the "Plan" phase is where targets and objectives are defined. Focusing on this phase allows the auditor to evaluate the accuracy and appropriateness of the defined targets before they are implemented and measured in subsequent phases.
References
* ISACA CISA Review Manual 27th Edition, Page 315-316 (PDCA Cycle)