A key goal of research in conversational systems is to train an interactive agent to help a user with a task. Human conversation, however, is notoriously incomplete, ambiguous, and full of extraneous detail. To operate effectively, the agent must not only understand what was explicitly conveyed but also be able to reason in the presence of missing or unclear information. When unable to resolve ambiguities on its own, the agent must be able to ask the user for the necessary clarifications and incorporate the response in its reasoning. Motivated by this problem we introduce QRAQ (Query, Reason, and Answer Questions), a new synthetic domain, in which a User gives an Agent a short story and asks a challenge question. These problems are designed to test the reasoning and interaction capabilities of a learning-based Agent in a setting that requires multiple conversational turns. A good Agent should ask only non-deducible, relevant questions until it has enough information to correctly answer the User's question. We use standard and improved reinforcement learning based memory-network architectures to solve QRAQ problems in the difficult setting where the reward signal only tells the Agent if its final answer to the challenge question is correct or not. To provide an upper-bound to the RL results we also train the same architectures using supervised information that tells the Agent during training which variables to query and the answer to the challenge question. We evaluate our architectures on four QRAQ dataset types, and scale the complexity for each along multiple dimensions.