The statement that provides the most accurate investigation of why Ethiopia and Egypt have run into conflict over resource management is:
Ethiopia’s building of a dam on the Nile could impact Egypt’s use of the Nile because they lie downriver.
This statement accurately reflects the core issue in the conflict, which centers around the management and use of the Nile River, particularly in relation to Ethiopia's Grand Ethiopian Renaissance Dam (GERD) project. The dam affects the flow of the Nile, which is crucial for Egypt’s water supply, leading to tensions between the two countries.