A question answering (QA) system can be built using multiple QA modules that can individually serve as a QA system in and of themselves. This paper proposes a learnable, strategy-driven QA model that aims at enhancing both efficiency and effectiveness. A strategy is learned using a learning-based classification algorithm that determines the sequence of QA modules to be invoked and decides when to stop invoking additional modules. The learned strategy invokes the most suitable QA module for a given question and attempts to verify the answer by consulting other modules until the level of confidence reaches a threshold. In our experiments, our strategy learning approach obtained improvement over a simple routing approach by 10.5% in effectiveness and 27.2% in efficiency.