In a fair-division procedure, participants may receive different amounts.

A) True B) False

3.

Which of the following fair-division procedures is not envy free?

A)

Adjusted winner procedure

C)

Last-diminisher method

B)

Knaster inheritance procedure

D)

Divide-and-choose

4.

Tom and Sandy must make a fair division of three objects left by their Great Aunt Sally. They have assigned points to the objects as shown below. Using the adjusted winner procedure, who gets the car?

Object

Tom's points

Sandy's points

Painting

40

30

Jewelry

10

50

Car

50

20

A) Tom B) Sandy

5.

Tom and Sandy must make a fair division of three objects left by their Great Aunt Sally. They have assigned points to the objects as shown below. Using the adjusted winner procedure, what does Tom end up with?

Object

Tom's points

Sandy's points

Painting

40

30

Jewelry

10

50

Car

50

20

A)

Car and painting

C)

Painting and 1/5 car

B)

Car only

D)

Car and 3/7 painting

6.

Tom and Sandy must make a fair division of three objects left by their Great Aunt Sally. They have assigned points to the objects as shown below. Using the adjusted winner procedure, how many points of value does Tom feel he ends with?

Object

Tom's points

Sandy's points

Painting

40

30

Jewelry

10

50

Car

50

20

A) 67.14 B) 90 C) 50 D) 50.43

7.

Chris and Terry must make a fair division of a stereo, television, and microwave. They place point values on the objects as shown below. Using the adjusted winner procedure, what does Terry receive?

Object

Chris's points

Terry's points

Stereo

25

45

Television

60

35

Microwave

15

20

A)

Stereo and 1/4 of microwave

C)

Stereo and 6/7 of microwave

B)

Microwave and 6/7 of television

D)

Stereo and microwave

8.

Chris and Terry must make a fair division of a stereo, television, and microwave. They place point values on the objects as shown below. Using the adjusted winner procedure, what point value does Chris feel he receives in the end?

Object

Chris's points

Terry's points

Stereo

25

45

Television

60

35

Microwave

15

20

A) 60 B) 62.14 C) 50 D) 37.86

9.

Andi and Toni must make fair division of a car, house, and boat. The point values they place on the objects are given below. Using the adjusted winner procedure, what does Andi end with?

Object

Andi's points

Toni's points

Car

35

45

House

40

30

Boat

25

25

A)

House and boat

C)

House and 2/7 of car

B)

House and 2/5 of boat

D)

House and 3/5 of boat

10.

Andi and Toni must make fair division of a car, house, and boat. The point values they place on the objects are given below. Using the adjusted winner procedure, what point value does Andi end with?

Object

Andi's points

Toni's points

Car

35

45

House

40

30

Boat

25

25

A) 65 B) 55 C) 50 D) 60

11.

At the end of the lease on their apartment, Toni and Terry decide to rent separate places and so must make a fair division of the property they purchased together. The items to be divided and the point values each person places on them are given below. If Toni and Terry use the adjusted winner procedure to divide the property, who gets the microwave?

Item

Toni

Terry

CD player

15

20

Sofa

30

25

Microwave

20

25

TV

35

30

A) Toni B) Terry

12.

At the end of the lease on their apartment, Toni and Terry decide to rent separate places and so must make a fair division of the property they purchased together. The items to be divided and the point values each person places on them are given below. If Toni and Terry use the adjusted winner procedure to divide the property, what will Terry end with?

Item

Toni

Terry

CD player

15

20

Sofa

30

25

Microwave

20

25

TV

35

30

A)

CD, microwave, and TV

C)

CD and microwave only

B)

CD, microwave, and 1/6 TV

D)

CD, microwave, and 4/13 TV

13.

At the end of the lease on their apartment, Toni and Terry decide to rent separate places and so must make a fair division of the property they purchased together. The items to be divided and the point values each person places on them are given below. If Toni and Terry use the adjusted winner procedure to divide the property, how many points of value will each person think they end up with?

Item

Toni

Terry

CD player

15

20

Sofa

30

25

Microwave

20

25

TV

35

30

A) 45 B) 50 C) 54.23 D) 56.5

14.

Jack and Jill went up the hill and found an antique water pail. Jack and Jill must now make a fair division of the pail using the Knaster inheritance procedure. Jack bids $80 for the value of the pail and Jill bids $65. What is the outcome of the fair division?

A)

Jack gets the pail and pays Jill $36.25.

C)

Jack gets the pail and pays Jill $32.50.

B)

Jack gets the pail and pays Jill $40.

D)

Jack gets the pail and Jill gets $65.

15.

Jack and Jill went up the hill and found an antique water pail. Jack and Jill must now make a fair division of the pail using the Knaster inheritance procedure. Jack bids $80 for the value of the pail and Jill bids $65. How much value does Jill think she ends with?

A) $36.25 B) $32.50 C) $40 D) $43.75

16.

Jack and Jill went up the hill and found an antique water pail. Jack and Jill must now make a fair division of the pail using the Knaster inheritance procedure. Jack bids $80 for the value of the pail and Jill bids $65. How much value does Jack believe he ends with?

A) $36.25 B) $32.50 C) $40 D) $43.75

17.

Andi, Chris, and Kim must make a fair division of a car left to them by their father. Using the Knaster inheritance procedure, the values they bid on the car are given below. Find the results of the fair division.

Andi

Chris

Kim

Car

$2400

$3000

$2700

A)

Chris gets the car and pays $1900; Andi gets $900, and Kim gets $1000.

B)

Chris gets the car, Andi gets $800; Kim gets $900.

C)

Chris gets the car and pays $1500; Andi gets $1200, and Kim gets $1350.

D)

Chris gets the car and pays $2550; Andi gets $1200, and Kim gets $1350.

18.

Andi, Chris, and Kim must make a fair division of a car left to them by their father. Using the Knaster inheritance procedure, the values they bid on the car are given below.

Andi

Chris

Kim

Car

$2400

$3000

$2700

How much value does Chris think he ends up with?

A) $3000 B) $1300 C) $1100 D) $1000

19.

Three children must make fair division of a painting and sculpture left them by their mother. Using the Knaster inheritance procedure, the value each child places on the objects is shown below.

Object

A

B

C

Painting

$4000

$6300

$6000

Sculpture

$2300

$1800

$2400

Who gets the sculpture?

A) A B) B C) C

20.

Three children must make fair division of a painting and sculpture left them by their mother. Using the Knaster inheritance procedure, the value each child places on the objects is shown below.

Object

A

B

C

Painting

$4000

$6300

$6000

Sculpture

$2300

$1800

$2400

What does A get after the fair division?

A) $2466.67 B) $2100 C) Sculpture and $166.67 D) $3150

21.

Three children must make fair division of a painting and sculpture left them by their mother. Using the Knaster inheritance procedure, the value each child places on the objects is shown below.

Object

A

B

C

Painting

$4000

$6300

$6000

Sculpture

$2300

$1800

$2400

What does B get after the fair division?

A)

Painting and $366.67

C)

Painting and pays $3600

B)

Painting and pays $3233.34

D)

Painting and pays $2250

22.

Ashley, Brook, Chris, and Dana must make a fair division of the estate of their uncle Bob. The estate consists of a farm house, a car, and a horse. Using the Knaster inheritance procedure, the value each person places on each item is shown below. Who gets the horse?

Item

Ashley

Brook

Chris

Dana

House

$35,000

$50,000

$48,000

$42,000

Car

$3000

$2500

$2750

$2800

Horse

$6000

$5800

$6250

$5200

A) Ashley B) Brook C) Chris D) Dana

23.

Ashley, Brook, Chris, and Dana must make a fair division of the estate of their uncle Bob. The estate consists of a farm house, a car, and a horse. Using the Knaster inheritance procedure, the value each person places on each item is shown below.

Item

Ashley

Brook

Chris

Dana

House

$35,000

$50,000

$48,000

$42,000

Car

$3000

$2500

$2750

$2800

Horse

$6000

$5800

$6250

$5200

What does Ashley end the fair division with?

A)

Car and $18,000

C)

Car and $22,000

B)

Car and $8000

D)

Car and $9731.25

24.

Ashley, Brook, Chris, and Dana must make a fair division of the estate of their uncle Bob. The estate consists of a farm house, a car, and a horse. Using the Knaster inheritance procedure, the value each person places on each item is shown below.

Item

Ashley

Brook

Chris

Dana

House

$35,000

$50,000

$48,000

$42,000

Car

$3000

$2500

$2750

$2800

Horse

$6000

$5800

$6250

$5200

What value does Chris end the fair division with?

A) $9731 B) $14,250 C) $15,981.25 D) $1731.25

25.

Suppose that Andi and Terry view a cake as shown below. They agree to divide the cake using the divide-and-choose procedure. If Andi divides the cake, where will the cut be made?

A)

2 columns from the left

C)

2 1/2 columns from the left

B)

1 2/3 columns from the left

D)

2 1/3 columns from the left

26.

Suppose that Andi and Terry view a cake as shown below. They agree to divide the cake using the divide-and-choose procedure. If Andi divides the cake, which side will Terry choose?

Suppose that Andi and Terry view a cake as shown below. They agree to divide the cake using the divide-and-choose procedure. If Andi divides the cake and Terry chooses, how many units will Andi be left with?

A) 4 1/3 B) 5 C) 6 D) 7 2/3

28.

Suppose that Andi and Terry view a cake as shown below. They agree to divide the cake using the divide-and-choose procedure. If Andi divides the cake and Terry chooses, how many units of cake will Terry believe she gets?

A) 4 1/3 B) 5 C) 6 D) 7 2/3

29.

Suppose Chris and Toni each view a cake as shown below. They agree to use the divide-and-choose procedure. If Chris divides, where will the cut be made?

A)

4 columns from the left

C)

3 columns from the left

B)

3 1/2 columns from the left

D)

2 1/4 columns from the left.

30.

Suppose Chris and Toni each view a cake as shown below. They agree to use the divide-and-choose procedure. If Chris divides, which side will Toni choose?

A) Right B) Left

31.

Suppose Chris and Toni each view a cake as shown below. They agree to use the divide-and-choose procedure. If Chris divides and Toni chooses, how many units will Toni believe he gets?

A) 4 1/2 B) 6 C) 7 1/2 D) 10 1/2

32.

Suppose Chris and Toni each view a cake as shown below. They agree to use the divide-and-choose procedure. If Chris divides and Toni chooses, how much will Chris feel is left?

A) 4 1/2 B) 6 C) 7 1/2 D) 10 1/2

33.

Alex, Betty, and Chris each view a cake as shown below. They will share the cake using the last-diminisher method with the order Alex, Betty, and Chris cutting and passing off the right side of the cake. After Alex cuts the cake, he will hand the portion on the right to Betty. Where will Alex make his cut?

A)

2 columns from the right

C)

3 2/3 columns from the right

B)

3 columns from the right

D)

4 columns from the right

34.

Alex, Betty, and Chris each view a cake as shown below. They will share the cake using the last-diminisher method with the order Alex, Betty, and Chris cutting and passing off the right side of the cake. After Alex cuts the cake, he will hand the portion on the right to Betty. Will Betty trim the piece before handing it to Chris?

A) Yes B) No

35.

Alex, Betty, and Chris each view a cake as shown below. They will share the cake using the last-diminisher method with the order Alex, Betty, and Chris cutting and passing off the right side of the cake. After Alex cuts the cake, he will hand the portion on the right to Betty, who decides whether or not to trim the piece and then hands it off to Chris. Will Chris trim the piece he receives from Betty?

A) Yes B) No

36.

Alex, Betty, and Chris each view a cake as shown below. They will share the cake using the last-diminisher method with the order Alex, Betty, and Chris cutting and passing off the right side of the cake. Who will make the last cut and thus keep the first piece of cake?

A) Alex B) Betty C) Chris

37.

Dana, Kim, and Lu each view a cake as shown below. They will share the cake using the last-diminisher method with the order Dana, Kim, and Lu cutting and passing off the right side of the cake. Dana first cuts a piece off the right side of the cake and hands it to Kim. Where will Dana cut the cake?

A)

2 1/3 columns from the right

C)

1 1/2 columns from the right

B)

3 1/3 columns from the right

D)

4 columns from the right

38.

Dana, Kim, and Lu each view a cake as shown below. They will share the cake using the last-diminisher method with the order Dana, Kim, and Lu cutting and passing off the right side of the cake. Dana first cuts a piece she believes is worth 7 units off the right side of the cake and hands it to Kim. How many units will Kim think this slice is worth?

A) 7 B) 9 1/2 C) 11 2/3 D) 10 1/2

39.

Dana, Kim, and Lu each view a cake as shown below. They will share the cake using the last-diminisher method with the order Dana, Kim, and Lu cutting and passing off the right side of the cake. Dana first cuts a piece she believes is worth 7 units off the right side of the cake and hands it to Kim. Will Kim trim the slice?

A) Yes B) No

40.

Dana, Kim, and Lu each view a cake as shown below. They will share the cake using the last-diminisher method with the order Dana, Kim, and Lu cutting and passing off the right side of the cake. Who will be the last to trim and thus keep the first piece of cake?

A) Dana B) Kim C) Lu

41.

Dana, Kim, and Lu each view a cake as shown below. They will share the cake using the last-diminisher method with the order Dana, Kim, and Lu cutting and passing off the right side of the cake. How many units will Lu believe the piece handed him by Kim is worth?

A) 7 B) 3 1/2 C) 4 1/2 D) 10

42.

Dana, Chris, Kelly, and Terry each view a cake as shown below. They will divide the cake using the trimming procedure with the players ordered as listed above. Dana cuts the cake into five pieces, numbered from left to right, and hands them to Chris. Which pieces will Chris trim?

A) None B) #4 only C) #1 and #4 D) #5 only

43.

Kelly, Terry, Dana, and Chris each view a cake as shown below. They will divide the cake using the trimming procedure with the players ordered as listed above. Kelly cuts the cake into five pieces, numbered from left to right, and hands them to Terry. Which pieces will Terry trim?

A) None B) #3 only C) #2 and #3 and #4 D) #2 and #4 only

44.

Four heirs need to make a fair division of the property left in an estate. The objects and the point values assigned to them are given below. If the heirs want to use the trimming procedure, with the order Chris, Kelly, Dana, and Kim, would the house need to be sold?

Object

Chris's points

Kelly's points

Dana's points

Kim's points

House

20

15

18

20

Car

10

12

10

5

Painting

10

8

12

15

Furniture

5

10

10

5

Money

55

55

50

55

A) Yes B) No

45.

Four heirs need to make a fair division of the property left in an estate. The objects and the point values assigned to them are given below. If the heirs want to use the trimming procedure, with the order Chris, Kelly, Dana, and Kim, would the house need to be sold?

Object

Chris's points

Kelly's points

Dana's points

Kim's points

House

20

25

18

25

Car

10

12

10

5

Painting

10

8

12

15

Furniture

5

10

10

5

Money

55

45

50

50

A) Yes B) No

46.

Four heirs need to make a fair division of the property left in an estate. The objects and the point values assigned to them are given below. The heirs want to use the trimming procedure, with the order Chris, Kelly, Dana, and Kim. Chris divides the estate into the following parts: (1) house, (2) car and 10 points from money, (3) painting and 10 points from money, (4) furniture and 15 points from money, and (5) remaining 20 points from money. Which parts will Kelly trim?

Object

Chris's points

Kelly's points

Dana's points

Kim's points

House

20

15

18

25

Car

10

12

10

5

Painting

10

8

12

15

Furniture

5

10

10

5

Money

55

55

50

50

A) Part #4 only B) Parts #2, #3, and #4 C) Parts #2 and #4 D) None

47.

Tom and Huck need to paint a fence and agree to use a modification of the divide-and-choose procedure to make a fair division of the chore. The boys' views of the fence are shown below. If Tom divides, will Huck choose the piece he believes is larger or smaller in modifying the procedure?

A)

Huck chooses the part he feels is smaller.

B)

Huck chooses the part he feels is larger.

48.

Tom and Huck need to paint a fence and agree to use a modification of the divide-and-choose procedure to make a fair division of the chore. The boys' views of the fence are shown below. If Tom divides and Huck chooses, how many units of fence will Tom think each boy is painting?

A)

Tom paints 11 and Huck paints 11.

C)

Tom paints 16 and Huck paints 6.

B)

Tom paints 6 and Huck paints 16.

D)

Tom paints 12 and Huck paints 10.

49.

Tom and Huck need to paint a fence and agree to use a modification of the divide-and-choose procedure to make a fair division of the chore. The boys' views of the fence are shown below. If Tom divides and Huck chooses, how many units of fence will Huck think each boy is painting?

A)

Tom paints 11 and Huck paints 11.

C)

Tom paints 16 and Huck paints 6.

B)

Tom paints 6 and Huck paints 16.

D)

Tom paints 12 and Huck paints 10.

50.

Andi and Terry need to make a fair division of a sofa they bought when sharing an apartment. They agree that Andi is entitled to 2/3 of the sofa and Terry is entitled to 1/3 of the sofa. They agree to use a modification of the Knaster inheritance procedure to divide the sofa. Andi believes the sofa is worth $360 and Terry believes the sofa is worth $315. Using the Knaster inheritance procedure, how much will Andi pay Terry for the sofa?

Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below:

If Chris chooses first, what is Chris's first choice?

A) Botany B) Sociology C) Physiology D) Biology

53.

Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below:

If Kim chooses first, what is Chris's first choice?

A) Botany B) Sociology C) Physiology D) Biology

54.

Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below:

If Chris chooses first, what is Kim's first choice?

A) Biology B) Chemistry C) Botany D) Sociology

55.

Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below:

If Chris chooses first, when is the Ecology book chosen?

A)

It is Chris's second choice.

C)

It is Kim's second choice.

B)

It is Chris's third choice.

D)

It is Kim's third choice.

56.

Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below:

If Kim chooses first, when is the Ecology book chosen?

A)

It is Chris's second choice.

C)

It is Kim's second choice.

B)

It is Chris's third choice.

D)

It is Kim's third choice.

57.

Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below:

If Chris chooses first, when is the Chemistry book chosen?

A)

It is Chris's second choice.

C)

It is Kim's second choice.

B)

It is Chris's third choice.

D)

It is Kim's third choice.

58.

Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below:

If Kim chooses first, when is the Physiology book chosen?

A)

It is Chris's second choice.

C)

It is Kim's second choice.

B)

It is Chris's third choice.

D)

It is Kim's third choice.

59.

Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below:

If Chris chooses first, when is the Sociology book chosen?

A)

It is Chris's first choice.

C)

It is Kim's second choice.

B)

It is Chris's second choice.

D)

It is Kim's third choice.

60.

Suppose Kim and Chris want to take turns, using the bottom-up strategy, to allocate several textbooks currently held jointly. Their ranked preferences are listed below:

If Kim chooses first, when is the Sociology book chosen?

A)

It is Chris's first choice.

C)

It is Kim's second choice.

B)

It is Chris's second choice.

D)

It is Kim's third choice.

61.

David and Max purchased raffle tickets together and, to their surprise, won three prizes. Now they must make a fair division of their winnings. Using the adjusted winner procedure, what does David end up with?

Object

David's points

Max's points

Fly rod

50

45

Fly-fishing lessons

10

35

100 hand-tied flies

40

20

A)

Fly rod only

C)

Flies, 11/19 of fly rod

B)

Flies, fly rod

D)

Flies, 8/19 of fly rod

62.

Jen and Lynn must make a fair division of four objects inherited from their great aunt. Using the adjusted winner procedure, what does Lynn end up with?

Object

Jen's points

Lynn's points

Dinnerware

30

35

Silver

15

45

Jewelry

35

10

Photographs

20

10

A)

Dinnerware, silver

C)

Silver, 5/13 of dinnerware

B)

Silver, 8/13 of dinnerware

D)

Jewelry, photos

63.

David and Max purchased raffle tickets together and, to their surprise, won three prizes. Now they must make a fair division of their winnings. If David and Max use the adjusted winner procedure, how many points of value will each person think they end up with?

Object

David's points

Max's points

Fly rod

50

45

Fly-fishing lessons

10

35

100 hand-tied flies

40

20

A) 50 B) 61 C) 73 D) 100

64.

Kim and Tori must make a fair division of three objects. Using the adjusted winner procedure, what does Kim end up with?

Object

Kim's points

Tori's points

Ring

20

35

Necklace

70

45

Bracelet

10

20

A)

20/23 of the necklace

C)

The necklace and 1/2 of the ring

B)

3/23 of the necklace

D)

The ring and the bracelet

65.

Charles and Monte must make a fair division of a cabin. They use the Knaster inheritance procedure. Charles bids $65,000 for the value of the cabin and Monte bids $57,000. What is the outcome of the fair division?

A)

Charles gets the cabin and pays Monte $30,500.

B)

Charles gets the cabin and pays Monte $4,000.

C)

Charles gets the cabin and pays Monte $57,000.

D)

Charles gets the cabin and pays Monte $34,500.

66.

Charles and Monte must make a fair division of a cabin. They use the Knaster inheritance procedure. Charles bids $65,000 for the value of the cabin and Monte bids $57,000. How much value does Monte believe he ends up with?

A) $30,500 B) $4,000 C) $57,000 D) $34,500

67.

Four people must make a fair division of two classic cars. They use the Knaster inheritance procedure. Their bids are shown below:

A

B

C

D

T-Bird

60,000

90,000

50,000

50,000

Mustang

70,000

45,000

100,000

80,000

Who gets the Mustang?

A) A B) B C) C D) D

68.

Suppose Jack and Joe want to take turns, using the bottom-up strategy, to allocate a selection of cookies. Their ranked preferences are listed below: