The possibility of gaining storage space is an argument often advanced in favor of permitting question-answering systems to make occasional errors. Absolute bounds are established on the amount of memory savings that is achievable with a specified error level for certain types of question-answering systems. Question-answering systems are treated as communication channels carrying information concerning the acceptable answers to an admissible set of queries. Shannon's rate-distortion theory is used to calculate bounds on the memory required for several question-answering tasks. For data retrieval, pattern classification, and position-matching systems, it was found that only small memory gains could be materialized from error tolerance. In pair-ordering tasks, on the other hand, more significant memory savings could be accomplished if small error rates are tolerated.