Final answer:
A veteran's service is considered broken when discharged for more than 24 hours, constituting a break in service that may affect benefits and the calculation of service length.
Step-by-step explanation:
The service of a veteran is considered broken when they are discharged for more than 24 hours. Specifically, the correct answer to the student's question is A) 24 hours. If a veteran is discharged and then re-enlists or is called back to active duty after a period exceeding 24 hours, it is typically seen as a break in service. This interruption can have an impact on benefits and length of service calculations. It's important to note that different agencies and veterans' programs may have specific definitions for what constitutes a break in service.