QA systems have been making steady advances in the challenging elementary science exam domain. In this work, we develop an explanation-based analysis of knowledge and inference requirements, which supports a fine-grained characterization of the challenges. In particular, we model the requirements based on appropriate sources of evidence to be used for the QA task. We create requirements by first identifying suitable sentences in a knowledge base that support the correct answer, then use these to build explanations, filling in any necessary missing information. These explanations are used to create a fine-grained categorization of the requirements. Using these requirements, we compare a retrieval and an inference solver on 212 questions. The analysis validates the gains of the inference solver, demonstrating that it answers more questions requiring complex inference, while also providing insights into the relative strengths of the solvers and knowledge sources. We release the annotated questions and explanations as a resource with broad utility for science exam QA, including determining knowledge base construction targets, as well as supporting information aggregation in automated inference.