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A question-answering (QA) system answers queries from a given set about data sets drawn from a given ensemble. Shannon's rate-distortion function provides the minimum amount of memory that a QA system must employ in order to achieve an average distortion less than (the distortion can, for example, be the average proportion of erroneous answers produced by the system). The ability of a system to convert an amount of distortion into a saving in memory is measured by the ratio . A system will be called elastic if this ratio goes to zero as , the size of the data set ensemble, tends to infinity. The asymptotic bounds to are derived, giving rise to elasticity conditions which involve only general system parameters.