Which of the following situations qualifies for the BAQ code 'W'?

The BAQ code 'W' is specifically designated for members who are married to another service member and have dependent children. This classification recognizes the unique financial responsibilities and considerations that come with being a dual-military couple, particularly when there are dependent children involved. The presence of children in the household typically increases the family's financial needs, which BAQ aims to address through appropriate allowances.

In the context of the other options: a single service member with no dependents does not meet the criteria for this specific code, as they would not have additional financial responsibilities. Similarly, while a handicapped child over the age of 21 may influence other types of benefits or allowances, they do not fit the definition of dependent children for BAQ purposes. Lastly, having a dependent parent living with the member may qualify for other types of support, but not for the BAQ code 'W'. Therefore, option B correctly reflects the requirements necessary for qualification under the BAQ system for the mentioned code.