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11.4 Exercise 9

Avg difficulty 2.5

Several apportionment methods have been used to allocate 125 seats to ten states and the results are shown in the table below. Determine which apportionments do not satisfy the quota rule and justify your answer.

State A State B State C State D State E State F State G
Standard Quota 41.26 16.00 5.77 2.64 7.82 10.47 0.21
Lower Quota 41 16 5 2 7 10 0
Upper Quota 42 17 6 3 8 11 1
Method X 43 16 5 2 7 10 1
Method Y 41 16 6 2 8 10 1
Method Z 42 16 7 3 7 9 1

OpenStax Contemporary Mathematics, 11.4 Apportionment Methods, exercise 9

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Adapted from Contemporary Mathematics © 2023 Rice University. Licensed under CC BY 4.0. Source: Contemporary Mathematics. Imported at revision fa7c1a1.