Mod 10 vs Mod 11 checksum

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I know that the modulo checks (e.g. Mod 10 check sum) is designed to identify single data capturing errors. However, can is be used to conclusively differentiate between the account numbers from two different sources, provide that different Modulo check sum are used?

Here is my problem:

  • I have two sets of account numbers which have the same structure, both 11 digits long
  • In both structures the first 10 digits are randomly allocated
  • In both structures the 11th digit is calculated by a modulo check, in the one case using a MOD 10 calculation and in the other case using a MOD 11 calculation
  • I receive a number for processing purposes from either of the two sources but I do not know which source it is coming from

The question - Can I conclusively determine which source it is coming from by doing both the MOD 10 check and the MOD 11 check on the first 10 digits of the number and then comparing it to the 11th digit? - Another way to frame the question: If a MOD 10 check and a MOD 11 check is done on a 10 digit number, will the checksum for the MOD 10 check and the checksum for the MOD 11 check always be different?