Final answer:
Agile methodologies, paired with object-oriented programming, are primary resources to boost software development efficiency. Debugging tools are helpful but not as impactful in overall productivity as Agile approaches. Software developers commonly work in the quaternary, knowledge-based sector.
Step-by-step explanation:
Two prominent resources that significantly enhance software development efficiency and productivity are object-oriented software development and Agile methodologies. While object-oriented programming focuses on creating software organized around objects rather than functions, Agile is a methodology that promotes continuous iteration of development and testing throughout the software development lifecycle of the project. In contrast, debugging tools are essential but they do not have as broad an impact on overall productivity and efficiency as Agile methodologies do.
As for the sector of the economy where software developers are most likely to be working, it is the quaternary sector. This sector is knowledge-based and includes services such as information technology, research and development, and other areas that involve intellectual services rather than the production of goods or basic services.