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A city has 60,000 residents, divided into three major ethnic groups (A, B and C). There are 25,000 ethnic group A residents, 20,000 ethnic group B residents, and 15,000 ethnic group C residents. Politically, the city is divided into 10 districts, each of which elects one alderman to the city council. Each district contains 6,000 residents.

The table below shows the demographics of each district. The values in the columns for the three ethnic groups are measured in thousands.

In the sortable table below, click on the column title to organize the table by that column's values.

District Group A Group B Group C
#01 4 2 0
#02 2 4 0
#03 1 3 2
#04 3 3 0
#05 2 2 2
#06 3 3 0
#07 3 0 3
#08 2 2 2
#09 4 0 2
#10 1 1 4

It has been found that in a district with a clear majority of residents in a certain group, a member of that majority group will be elected to the city council, an outcome referred to as a “guaranteed seat”. On the other hand, in a district without a clear majority, outcomes are less predictable, and aldermanic elections will be “tossups” between the groups tied for the most influence within the district.

Decide whether the following statements are true or false.



Not counting any tossup districts, Group A (the largest ethnic group in the city) has more guaranteed seats on the city council than either of the other groups.

If Group C (the smallest ethnic group in the city) won every tossup election, it would have four seats on the city council.

Since the city council has ten seats, it takes at least six votes to pass any regulations or ordinances. Group A is the only group who could elect a majority of at least six votes (and thus pass new regulations without compromise with the other groups).

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