Well, let me write the correct versions, and see which one does not need a correction:
A. A screwdriver and wrench ARE necessary for this project.
B. The sisters and their
brother HAVE arrived from karate practice.
C. Both
Charlie and Arthur LOOK too tired for another game.
D. He and his team
approve of the decision I made.
- yes, no correction needed! so in this case the verb agrees with the subject.