When reporting from memory, people may often be asked unanswerable questions--questions for which the correct answer has never been encoded. These unanswerable questions should be met with an "I don't know" response. Previous research has shown that a manipulation commonly used to enhance memory at retrieval--context reinstatement--reduces appropriate "do not know" responding to unanswerable questions. Here we investigated whether this reduction is due to increased belief that a given question is answerable, or solely to increased confidence in specific responses for questions already believed to be answerable. In two experiments, we show that context reinstatement reduces "do not know" responding even when a "do not remember" option is available to express beliefs that particular questions are answerable. These results indicate that improved access to contextual information at retrieval creates an erroneous belief that unanswerable questions are in fact answerable.