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If you decompressed a single PKZIP archived file that had 9 separate files CONTAINED in the archive how would you examine the file slack for each of the 9 files 


This is  where the sum is not the AGGREGATE of the parts. A ZIP algorithm can produce different results with even  similar files.
The more broad discussion is called 'Data compression.'
http://en.wikipedia.org/wiki/Data_compression
Quote

The design of data compression schemes involves trade-offs AMONG various factors, including the degree of compression, the amount of distortion introduced (when using lossy data compression), and the COMPUTATIONAL resources required to compress and uncompress the data.[5]


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