Answer selection is a core component in any question-answering systems. It aims to select correct answer sentences for a given question from a pool of candidate sentences. In recent years, many deep learning methods have been proposed and shown excellent results for this task. However, these methods typically require extensive parameter (and hyper-parameter) tuning, which gives rise to efficiency issues for large-scale datasets, and potentially makes them less portable across new datasets and domains (as re-tuning is usually required). In this paper, we propose an extremely efficient hybrid model (FastHybrid) that tackles the problem from both an accuracy and scalability point of view. FastHybrid is a light-weight model that requires little tuning and adaptation across different domains. It combines a fast deep model (which will be introduced in the method section) with an initial information retrieval model to effectively and efficiently handle answer selection. We introduce a new efficient attention mechanism in the hybrid model and demonstrate its effectiveness on several QA datasets. Experimental results show that although the hybrid uses no training data, its accuracy is often on-par with supervised deep learning techniques, while significantly reducing training and tuning costs across different domains.