Deck 4: The Mathematics of Apportionment: Making the Rounds

Question 1

The Faculty Senate at your university has been delegated the duty of apportioning the 500 university owned laptops to five different programs (Engineering, Social Sciences, Nursing, Arts and Sciences, and Business). The laptops are going to be apportioned to each program based on the number of Astudents enrolled in the program. The table below shows the enrollment numbers for each program.

Answer 1

Engineering: 49; Social Sciences: 96; Nursing: 34; Arts and Sciences: 251; Business: 70

Question 2

A local department store has budgeted for 100 eight-hour retail shifts to be staffed every week. The number of shifts staffed on a single day of the week is apportioned based on the total number of
shoppers who visit the store during the day. The following table shows the average daily number of
shoppers over a two month period.

What is the standard divisor for this apportionment problem?
Based on the scenario above , how many eight-hour retail shifts should be staffed on Friday if
Hamilton's Method is used to do the apportionment?

Answer 2

19

Question 3

A newly formed Midwestern state is made up of four counties (A, B, C and D) . The state legislature has a total of 200 seats which need to be apportioned out to each of the counties based on their respective populations. The table below gives the current population of each of the counties.

Use Hamilton's Method to apportion the 200 seats.

Answer 3

A state is apportioned fewer seats than its lower quota.

Question 4

A kindly old grandmother is going to distribute 50 one dollar bills to her four grandchildren, Jenn, Emily, Lisa and Allison, based on how many minutes of housework they've completed over the past week. The table below gives the number of minutes each child spent doing housework during the week.
Based on the scenario above , find a modified divisor which would allow the 50 one dollar bills to be apportioned using Webster's Method.

Question 5

A local movie theatre has budgeted for 50 six-hour concession shifts to be staffed every week. The number of shifts staffed on a single day of the week is apportioned based on the total number of moviegoers who visit the theatre during the day. The following table shows the average daily number of moviegoers over a two month period.

Based on the scenario above, how many six-hour concession shifts should be staffed on Saturday if Hamilton's Method is used to do the apportionment?

Question 6

A local movie theatre has budgeted for 50 six-hour concession shifts to be staffed every week. The number of shifts staffed on a single day of the week is apportioned based on the total number of moviegoers who visit the theatre during the day. The following table shows the average daily number of moviegoers over a two month period.

Based on the scenario above, what is the standard quota for Wednesday?

Question 7

A local movie theatre has budgeted for 50 six-hour concession shifts to be staffed every week. The number of shifts staffed on a single day of the week is apportioned based on the total number of moviegoers who visit the theatre during the day. The following table shows the average daily number of moviegoers over a two month period.

What is the standard divisor for this apportionment problem?

Question 8

Clearly explain what it means for the New State paradox to occur.

Question 9

A small country consists of four states, Awesomeland, Bodaciousville, Cooltown, and Dudesburgh. The total population of the country is 400,000 people. The table below gives the standard quota for each state.

Based on the scenario above , find the population of Awesomeland.

Question 10

A kindly old grandmother is going to distribute 225 pieces of candy to her four grandchildren, Alex,Beth, Carl and Dave, based on how many minutes of housework they’ve completed over the past week.
The table below gives the number of minutes each child spent doing housework during the past week.

Based on the scenario above , find a modified divisor which would allow the 225 pieces of candy to be apportioned using Webster's Method.

Question 11

The small country of Fowler, consisting of four states Kudrle, Hedges, Murray, and Kowalowski, needs to apportion all of the seats in its newly created Parliament. One seat in the Parliament is proportional to 44,000 people from a state's population. The table below gives the standard quotas for each of the states.

Question 12

A kindly old grandmother is going to distribute 225 pieces of candy to her four grandchildren, Alex, Beth, Carl and Dave, based on how many minutes of housework they've completed over the past week. The table below gives the number of minutes each child spent doing housework during the past week.

Use Adam's Method to apportion the 225 pieces of candy.

Question 13

The small country of Fowler, consisting of four states Kudrle, Hedges, Murray, and Kowalowski, needs to apportion all of the seats in its newly created Parliament. One seat in the Parliament is proportional to 44,000 people from a state's population. The table below gives the standard quotas for each of the states.
Based on the scenario from problem 9, what is the population of Hedges?

Question 14

A local department store has budgeted for 100 eight-hour retail shifts to be staffed every week. The
number of shifts staffed on a single day of the week is apportioned based on the total number of
shoppers who visit the store during the day. The following table shows the average daily number of
shoppers over a two month period.

What is the standard divisor for this apportionment problem?

Question 15

The Faculty Senate at your university has been delegated the duty of apportioning the 500 university owned laptops to five different programs (Engineering, Social Sciences, Nursing, Arts and Sciences, and Business). The laptops are going to be apportioned to each program based on the number of Astudents enrolled in the program. The table below shows the enrollment numbers for each program.
Based on the scenario above, find a modified divisor which would allow the 500 laptops to be apportioned using Adam's Method.

Question 16

A kindly old grandmother is going to distribute 50 one dollar bills to her four grandchildren, Jenn, Emily, Lisa and Allison, based on how many minutes of housework they've completed over the past week. The table below gives the number of minutes each child spent doing housework during the week.

Question 17

A small country consists of four states, Awesomeland, Bodaciousville, Cooltown, and Dudesburgh. The total population of the country is 400,000 people. The table below gives the standard quota for each state.

How many seats are being apportioned?

Question 18

A local department store has budgeted for 100 eight-hour retail shifts to be staffed every week. The number of shifts staffed on a single day of the week is apportioned based on the total number of
shoppers who visit the store during the day. The following table shows the average daily number of
shoppers over a two month period.

What is the standard divisor for this apportionment problem?
Based on the scenario above , what is the standard quota for Saturday?

Question 19

A small country consists of four states, Awesomeland, Bodaciousville, Cooltown, and Dudesburgh. The total population of the country is 400,000 people. The table below gives the standard quota for each state.

Based on the scenario above, how many seats would be apportioned to Bodaciousville using the Huntington-Hill Method.

Question 20

A newly formed Midwestern state is made up of four counties (A, B, C and D). The state legislature
has a total of 200 seats which need to be apportioned out to each of the counties based on their respective populations. The table below gives the current population of each of the counties.

Use Hamilton’s Method to apportion the 200 seats.
Based on the scenario above, find a modified divisor which would allow the 200 seats to be apportioned using Jefferson's Method.

Question 21

The small country of Fowler, consisting of four states, Kudrle, Hedges, Murray, and Kowalowski, needs to apportion all of the seats in its newly created Parliament. One seat in the Parliament is proportional to 44,000 people from a state's population. The table below gives the standard quotas for each of the states.

Based on the scenario above, which modified divisor would be appropriate if the Huntington-Hill Method was used to apportion the seats in Parliament?

A) 199.9
B) 200.0
C) 200.1
D) 200.2
E) None of the above.

Question 22

A local city is made up of four wards ( Ward 1, Ward 2, Ward 3, and Ward 4). Through a Federal grant, the city has received 200 brand new bicycles to promote alternative means of transportioan. The bicycles will be apportioned based on the population of each ward. The table below shows the population of each of the wards.

Use Adam's Method to apportion the 200 bicycles.

A) Ward 1: 34; Ward 2: 58 ; Ward 3: 91; Ward 4: 17
B) Ward 1: 34; Ward 2: 57 ; Ward 3: 92; Ward 4: 17
C) Ward 1: 33; Ward 2: 57 ; Ward 3: 92; Ward 4: 18
D) Ward 1: 33; Ward 2: 58 ; Ward 3: 91; Ward 4: 18
E) None of the above.

Question 23

A new zoo is being built in the town. The zoo will be partitioned into six different habitats (Polar, Tropical, Temperate, Savanna, Desert, and Tide Pools). Donors have given enough money to purchase 48 interactive touch-screen educational tools. These touch-screens will be apportioned to the different habitats based on the number of different species on display. The table below gives the number of species on display in each habitat.

Based on the scenario above, how many interactive touch-screen educational tools would be installed in the Tropical habitat if Hamilton's Method was used to do the apportioning?

A) 12
B) 13
C) 14
D) 15
E) None of the above.

Question 24

Your college campus is broken into five sections (Main Campus, North Campus, East Campus, West Campus, and South Campus). The board of trustees has recently approved the installation of 70 emergency blue lights. The lights will be apportioned based the area of each section (i.e. the larger the section, the more lights). The table below gives the area, in acres, of each section of campus.
Based on the scenario above, what is the standard quota for East Campus?

A) 5.4
B) 8.9
C) 12.6
D) 18.5
E) None of the above.

Question 25

A local city is made up of four wards ( Ward 1, Ward 2, Ward 3, and Ward 4). Through a Federal grant, the city has received 200 brand new bicycles to promote alternative means of transportioan. The bicycles will be apportioned based on the population of each ward. The table below shows the population of each of the wards.

Based on the scenario above, find a modified divisor which would allow the 200 bicycles to be apportioned using Webster's Method.

A) 72.9
B) 73
C) 73.1
D) All of the above.
E) None of the above.

Question 26

A newly formed Southern state is made up of four counties (A, B, C , and D ). The state legislature has a total of 50 seats which need to be apportioned out to each of the counties based on their respective populations. The table below gives the current population of each of the counties.

Use Hamilton's Method to apportion the 50 seats.

A) A: 9 ; B: 15 ; C: 12 ; D: 14
B) A: 9 ; B: 15 ; C: 13 ; D: 13
C) A: 9 ; B: 16 ; C: 12 ; D: 13
D) A: 10 ; B: 16 ; C: 12 ; D: 12
E) None of the above

Question 27

Your college campus is broken into five sections (Main Campus, North Campus, East Campus, West Campus, and South Campus). The board of trustees has recently approved the installation of 70 emergency blue lights. The lights will be apportioned based the area of each section (i.e. the larger the section, the more lights). The table below gives the area, in acres, of each section of campus.
What is the standard divisor for this apportionment problem?

A) 20
B) 30
C) 40
D) 50
E) None of the above.

Question 28

A new zoo is being built in the town. The zoo will be partitioned into six different habitats (Polar, Tropical, Temperate, Savanna, Desert, and Tide Pools). Donors have given enough money to purchase 48 interactive touch-screen educational tools. These touch-screens will be apportioned to the different habitats based on the number of different species on display. The table below gives the number of species on display in each habitat.

Based on the scenario above, what is the standard quota for Savanna?

A) 1.2
B) 5.0
C) 8.7
D) 9.6
E) None of the above.

Question 29

Four friends (Joe, Tom, Miah, and Brownie) are lost on a tropical island. Luckily the friends find a stash of 75 coconuts. The coconuts will be apportioned based on the weight of each person (i.e. the heavier person is, the more he gets). The table below shows the weight of each of the four friends.

Based on the scenario above , which modified divisor would be appropriate if Webster's Method was used to apportion the coconuts?

A) 9.5
B) 10
C) 10.5
D) 11
E) None of the above.

Question 30

Your college campus is broken into five sections (Main Campus, North Campus, East Campus, West Campus, and South Campus). The board of trustees has recently approved the installation of 70 emergency blue lights. The lights will be apportioned based the area of each section (i.e. the larger the section, the more lights). The table below gives the area, in acres, of each section of campus.
Based on the scenario above , which apportionment results in a violation of the Quota Rule?

A) Main Campus: 17 ; North Campus: 22; East Campus: 12; West Campus: 13 ; South Campus: 6
B) Main Campus: 18 ; North Campus: 21 ; East Campus: 12; West Campus: 14 ; South Campus: 5
C) Main Campus: 16; North Campus: 22; East Campus: 13; West Campus: 14; South Campus: 5
D) Main Campus: 18 ; North Campus: 23; East Campus: 13; West Campus: 12; South Campus: 4
E) All of the above.

Question 31

Four friends (Joe, Tom, Miah, and Brownie) are lost on a tropical island. Luckily the friends find a stash of 75 coconuts. The coconuts will be apportioned based on the weight of each person (i.e. the heavier person is, the more he gets). The table below shows the weight of each of the four friends.

Use Jefferson's Method to apportion the 75 coconuts.

A) Joe: 22 ; Tom: 17 ; Miah: 16 ; Brownie: 20
B) Joe: 21 ; Tom: 18 ; Miah: 16 ; Brownie: 20
C) Joe: 22 ; Tom: 17 ; Miah: 15 ; Brownie: 21
D) Joe: 21 ; Tom: 18 ; Miah: 15 ; Brownie: 21
E) None of the above

Question 32

A newly formed University is made up of five schools (Art, Business, Engineering, Nursing, and Sciences). The board of trustees is given the task of apportioning the 50 faculty members based on the respective enrollment levels of each of the schools. The table below gives the projected enrollment for each of the schools.

Based on the scenario above , which modified divisor would be appropriate if the apportionment was done using Jefferson's Method?

A) 43
B) 44
C) 45
D) 46
E) None of the above.

Question 33

The small country of Fowler, consisting of four states, Kudrle, Hedges, Murray, and Kowalowski, needs to apportion all of the seats in its newly created Parliament. One seat in the Parliament is proportional to 44,000 people from a state's population. The table below gives the standard quotas for each of the states.

How many seats are there in the Parliament?

A) 200
B) 400
C) 500
D) 25000
E) None of the above.

Question 34

The small country of Barksdale, consisting of the four states Ichabod, Maize, Ranger, and Tala, needs to apportion all of the seats in its newly created Parliament. The table below gives the standard quotas for each of the states.

Based on the scenario above, which modified divisor would be appropriate if the Huntington-Hill Method was used to apportion the seats in Parliament?

A) 1259
B) 1260
C) 1261
D) 1262
E) All of the above.

Question 35

A new zoo is being built in the town. The zoo will be partitioned into six different habitats (Polar, Tropical, Temperate, Savanna, Desert, and Tide Pools). Donors have given enough money to purchase 48 interactive touch-screen educational tools. These touch-screens will be apportioned to the different habitats based on the number of different species on display. The table below gives the number of species on display in each habitat.

Based on the scenario above, the apportionment given below Polar: 2; Tropical: 16; Temperate: 7; Savanna: 9; Desert: 5; Tide Pools: 11

A) violates the quota rule.
B) is an example of the Alabama paradox.
C) is an example of the new state's paradox.
D) is an example of the population paradox.
E) None of the above.

Question 36

Your college campus is broken into five sections (Main Campus, North Campus, East Campus, West Campus, and South Campus). The board of trustees has recently approved the installation of 70 emergency blue lights. The lights will be apportioned based the area of each section (i.e. the larger the section, the more lights). The table below gives the area, in acres, of each section of campus.
Based on the scenario above, how many Emergency Blue Lights would be installed on South Campus if Hamilton's Method was used to do the apportioning?

A) 3
B) 4
C) 5
D) 6
E) None of the above.

Question 37

A new zoo is being built in the town. The zoo will be partitioned into six different habitats (Polar, Tropical, Temperate, Savanna, Desert, and Tide Pools). Donors have given enough money to purchase 48 interactive touch-screen educational tools. These touch-screens will be apportioned to the different habitats based on the number of different species on display. The table below gives the number of species on display in each habitat.

What is the standard divisor for this apportionment problem?

A) 25
B) 30
C) 35
D) 40
E) None of the above.

Question 38

A newly formed University is made up of five schools (Art, Business, Engineering, Nursing, and Sciences). The board of trustees is given the task of apportioning the 50 faculty members based on the respective enrollment levels of each of the schools. The table below gives the projected enrollment for each of the schools.

Use Hamilton's Method to apportion the 50 faculty members.

A) Art: 17 ; Business: 5 ; Engineering: 9 ; Nursing: 7 ; Sciences: 12
B) Art: 18 ; Business: 5 ; Engineering: 8 ; Nursing: 8 ; Sciences: 12
C) Art: 17 ; Business: 4 ; Engineering: 9; Nursing: 8; Sciences: 12
D) Art: 18 ; Business: 4 ; Engineering: 9 ; Nursing: 7 ; Sciences: 12
E) None of the above

Question 39

The small country of Barksdale, consisting of the four states Ichabod, Maize, Ranger, and Tala, needs to apportion all of the seats in its newly created Parliament. The table below gives the standard quotas for each of the states.

If the population of Ichabod is 22,932, then what is the total population of Barksdale?

A) 129780
B) 135240
C) 139610
D) 152140
E) None of the above.

Question 40

A newly formed Southern state is made up of four counties (A, B, C , and D ). The state legislature has a total of 50 seats which need to be apportioned out to each of the counties based on their respective populations. The table below gives the current population of each of the counties.

Based on the scenario above, which modified divisor would be appropriate to use if the apportioning was done using Adam's Method?

A) 790
B) 800
C) 810
D) 820
E) None of the above.