Question 1

Find the percentage difference of 7 and 9.

Accepted Answer

A)  28.57% 
B)  2% 
C)  22.22% 
D)  43.75% 
A)  28.57% 
B)  2% 
C)  22.22% 
D)  43.75%

Question 2

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned. What would be the standard divisor? $$\begin{array} { l c } 
\text { District } & \text { Population } \
\text { Applewood } & 8280 \
\text { Boxwood } & 4600 \
\text { Central } & 5220
\end{array}$$

Accepted Answer

A)  1533 
B)  1656 
C)  1740 
D)  1810 
A)  1533 
B)  1656 
C)  1740 
D)  1810

Question 3

A small country has four states and a House of Representatives with 20 seats. Given the states, populations, and apportionment below, find the percentage difference in representative share between states A and C. $$\begin{array} { c c c } 
\text { State } & \text { Population } & \text { Apportionment } \
\text { A } & 234,000 & 5 \
\text { B } & 124,000 & 3 \
\text { C } & 346,500 & 7 \
\text { D } & 268,500 & 5
\end{array}$$

Accepted Answer

The answer of A small country has four states and...

Question 4

Use the following information to answer the Questions:
Thirty patrol cars are to be apportioned to three precincts according to the monthly crime totals, which are as follows:
$\begin{array}{cc}
\underline {\text { Precinct } }& \underline {\text { Crimes reported last month }} \
\text { I } & 94 \
\text { II } & 130 \
\text { III } & 108
\end{array}$
-Use the Hamilton's method to determine how many cars should go to each precinct.

Accepted Answer

I: 8, II:

Question 5

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned. If the county uses the d'Hondt method, what is the initial priority number for Central? $$\begin{array} { l c } 
\text { District } & \text { Population } \
\text { Applewood } & 8280 \
\text { Boxwood } & 4600 \
\text { Central } & 5220
\end{array}$$

Accepted Answer

A)  476 
B)  522 
C)  5220 
D)  5221 
A)  476 
B)  522 
C)  5220 
D)  5221

Question 6

A small county has populations in three regions as shown below. They have apportioned 15 seats on the county council and obtained the apportionment for each region shown below. Find the relative difference in representative shares between the Parkview and Hillside regions. $$\begin{array} { l c c } 
\text { Region } & \text { Population } & \text { Apportionment } \
\text { Parkview } & 43,000 & 6 \
\text { Hillside } & 32,800 & 5 \
\text { Riverdale } & 24,200 & 4
\end{array}$$

Accepted Answer

A)  9.2% 
B)  8.5% 
C)  16.7% 
D)  20.0% 
A)  9.2% 
B)  8.5% 
C)  16.7% 
D)  20.0%

Question 7

A country has three states with the populations shown below. The House of Representatives for the country is to have 15 members. Find the district population for each state if the country uses the Jefferson method of apportionment. $$\begin{array} { c c } 
\text { State } & \text { Population } \
\text { A } & 245,000 \
\text { B } & 320,000 \
\text { C } & 155,000
\end{array}$$

Accepted Answer

A 49,000
B

Question 8

Find the geometric mean of 3 and 7.

Accepted Answer

A)  4.38 
B)  5.00 
C)  4.58 
D)  3.16 
A)  4.38 
B)  5.00 
C)  4.58 
D)  3.16

Question 9

A small county has populations in three districts as shown below. They are to apportion 10 seats on the county council. Find the quota for Riverdale. $$\begin{array} { l c } 
\text { District } & \text { Population } \
\text { Parkview } & 43,000 \
\text { Hillside } & 32,800 \
\text { Riverdale } & 24,200
\end{array}$$

Accepted Answer

A)  4.13 
B)  2 
C)  4 
D)  2.42 
A)  4.13 
B)  2 
C)  4 
D)  2.42

Question 10

Use the following information to answer the Questions:
A senate of 20 faculty members represents three departments: math, statistics, and applied math. The seats are to be apportioned according to the numbers of students in each department, which are as follows: $\begin{array}{lccc}
  \text { Math} &97\
  \text { Statistics} && 83\
  \text { Applied math} &134\
\end{array}$

-In d'Hondt's method, what is applied math's priority number after the first seat is allocated?

Accepted Answer

A)  64 
B)  67 
C)  133 
D)  some other value 
A)  64 
B)  67 
C)  133 
D)  some other value

Question 11

Use the following information to answer the Questions:
Thirty patrol cars are to be apportioned to three precincts according to the monthly crime totals, which are as follows:
$\begin{array}{cc}
\underline {\text { Precinct } }& \underline {\text { Crimes reported last month }} \
\text { I } & 94 \
\text { II } & 130 \
\text { III } & 108
\end{array}$
-Use the Jefferson's method to determine how many cars should go to each precinct.

Accepted Answer

I: 8, II:

Question 12

Which method of apportionment always satisfies the quota condition?

Accepted Answer

A)  Hamilton 
B)  Hill-Huntington 
C)  Jefferson 
D)  Webster 
A)  Hamilton 
B)  Hill-Huntington 
C)  Jefferson 
D)  Webster

Question 13

A county has four districts with the populations shown below. They are to use the Hill -Huntington method of apportionment to distribute 20 seats on a county council. Find the tentative apportionment for district B. $$\begin{array} { c c } 
\text { District } & \text { Population } \
\text { A } & 87,000 \
\text { B } & 56,000 \
\text { C } & 72,000 \
\text { D } & 35,000
\end{array}$$

Accepted Answer

A)  3 
B)  4 
C)  5 
D)  6 
A)  3 
B)  4 
C)  5 
D)  6

Question 14

For a given set of populations and house sizes, different methods of apportionment may lead to different apportionments.

Accepted Answer

A) True 
 B)False

Question 15

Round the following to whole percentages using the Jefferson method: 36.3% + 11.7% + 7.9% + 5.6% + 10.4% + 28.1% = 100%

Accepted Answer

A)  37 + 12 + 8 + 5 + 10 + 28 
B)  36 + 12 + 8 + 6 + 10 + 28 
C)  37 + 12 + 8 + 6 + 11 + 29 
D)  37 + 12 + 8 + 6 + 10 + 28 
A)  37 + 12 + 8 + 5 + 10 + 28 
B)  36 + 12 + 8 + 6 + 10 + 28 
C)  37 + 12 + 8 + 6 + 11 + 29 
D)  37 + 12 + 8 + 6 + 10 + 28

Question 16

Round the following to whole percentages using the Webster method: 6.6% + 38.1% + 1.1% + 17.0% + 12.6% + 24.6% = 100%

Accepted Answer

A)  7 + 38 + 1 + 17 + 13 + 25 
B)  7 + 38 + 1 + 17 + 12 + 25 
C)  7 + 38 + 1 + 17 + 13 + 24 
D)  6 + 38 + 1 + 17 + 13 + 24 
A)  7 + 38 + 1 + 17 + 13 + 25 
B)  7 + 38 + 1 + 17 + 12 + 25 
C)  7 + 38 + 1 + 17 + 13 + 24 
D)  6 + 38 + 1 + 17 + 13 + 24

Question 17

The Hamilton method of apportionment can display the population paradox.

Accepted Answer

A) True 
 B)False

Question 18

Which pair of numbers has the highest percentage difference?

Accepted Answer

A)  5 and 6 
B)  8 and 10 
C)  13 and 16 
D)  18 and 22 
A)  5 and 6 
B)  8 and 10 
C)  13 and 16 
D)  18 and 22

Question 19

Given the cities and the populations below, use the Hamilton method of apportionment to distribute 25 seats on a regional board. $$\begin{array} { l c } 
\text { City } & \text { Population } \
\text { Greenville } & 34,569 \
\text { Riverdale } & 27,943 \
\text { Oceanside } & 21,350 \
\text { Parkview } & 16,138
\end{array}$$

Accepted Answer

Greenville

Question 20

Find the geometric mean of 5 and 6.

Accepted Answer

A)  5.5 
B)  5.48 
C)  4.69 
D)  3.32 
A)  5.5 
B)  5.48 
C)  4.69 
D)  3.32

Exam 14: Apportionment

Find the percentage difference of 7 and 9.

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned. What would be the standard divisor? District Population Applewood 8280 Boxwood 4600 Central 5220

A small country has four states and a House of Representatives with 20 seats. Given the states, populations, and apportionment below, find the percentage difference in representative share between states A and C. State Population Apportionment A 234,000 5 B 124,000 3 C 346,500 7 D 268,500 5

Use the following information to answer the Questions: Thirty patrol cars are to be apportioned to three precincts according to the monthly crime totals, which are as follows: I 94 II 130 III 108 -Use the Hamilton's method to determine how many cars should go to each precinct.

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned. If the county uses the d'Hondt method, what is the initial priority number for Central? District Population Applewood 8280 Boxwood 4600 Central 5220

A country has three states with the populations shown below. The House of Representatives for the country is to have 15 members. Find the district population for each state if the country uses the Jefferson method of apportionment. State Population A 245,000 B 320,000 C 155,000

Find the geometric mean of 3 and 7.

A small county has populations in three districts as shown below. They are to apportion 10 seats on the county council. Find the quota for Riverdale. District Population Parkview 43,000 Hillside 32,800 Riverdale 24,200

Use the following information to answer the Questions: Thirty patrol cars are to be apportioned to three precincts according to the monthly crime totals, which are as follows: I 94 II 130 III 108 -Use the Jefferson's method to determine how many cars should go to each precinct.

Which method of apportionment always satisfies the quota condition?

A county has four districts with the populations shown below. They are to use the Hill -Huntington method of apportionment to distribute 20 seats on a county council. Find the tentative apportionment for district B. District Population A 87,000 B 56,000 C 72,000 D 35,000

For a given set of populations and house sizes, different methods of apportionment may lead to different apportionments.

Round the following to whole percentages using the Jefferson method: 36.3% + 11.7% + 7.9% + 5.6% + 10.4% + 28.1% = 100%

Round the following to whole percentages using the Webster method: 6.6% + 38.1% + 1.1% + 17.0% + 12.6% + 24.6% = 100%

The Hamilton method of apportionment can display the population paradox.

Which pair of numbers has the highest percentage difference?

Given the cities and the populations below, use the Hamilton method of apportionment to distribute 25 seats on a regional board. City Population Greenville 34,569 Riverdale 27,943 Oceanside 21,350 Parkview 16,138

Find the geometric mean of 5 and 6.

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