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This paper analyzes the test memory requirements for core-based systems-on-a-chips and identifies useless test data as one of the contributors to the total amount of test data. The useless test data comprises the padding bits necessary to compensate for the difference between the lengths of different chains in multiple scan chain designs. Although useless test data does not represent any relevant test information, it is often unavoidable, and leads to the tradeoff between the test bus width and the volume of test data in multiple scan chain-based cores. Ultimately, this tradeoff influences the test access mechanism design algorithms leading to solutions that have either short test time or low volume of test data. Therefore, in this paper, a novel test methodology is proposed which, by dividing the wrapper scan chains (WSCs) into two or more partitions, and by exploiting automated test equipment memory management features, reduces the amount of useless test data. Extensive experimental results using ISCAS'89 and ITC'02 benchmark circuits are provided to analyze the implications of the number of WSCs in the partition, and the number of partitions on the proposed methodology.