Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Malia buys a chocolate-strawberry-vanilla cake in Figure(i) for $14.00 . She cuts the cake into six 60° wedges as shown in Figure
(ii). Malia likes chocolate twice as much as vanilla and likes vanilla twice as much as strawberry.
1) What is the value of piece 1 to Malia?
A) $4.00
B) $3.00
C) $2.00
D) $1.00
E) none of these
2) What is the value of piece 3 to Malia?
A) $2.00
B) $1.00
C) $3.00
D) $4.00
E) none of these
3) What is the value of piece 5 to Malia?
A) $4.00
B) $2.00
C) $1.00
D) $3.00
E) none of these
4) What is the value of piece 2 to Malia?
A) $1.00
B) $2.00
C) $1.50
D) $2.50
E) none of these
5) What is the value of piece 4 to Malia?
A) $1.00
B) $2.50
C) $1.50
D) $2.00
E) none of these
6) What is the value of piece 6 to Malia?
A) $2.00
B) $2.50
C) $1.00
D) $1.50
E) none of these
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Ned buys a chocolate-strawberry-vanilla cake in Figure (i) for $14.00. He cuts the cake into six 60° wedges as shown in Figure (ii).
Ned values strawberry six times as much as chocolate. He does not value vanilla cake at all.
7) How much does Ned value piece 3?
A) $4.00
B) $8.00
C) $12.00
D) $6.00
E) none of these
8) How much does Ned value piece 2?
A) $3.00
B) $2.00
C) $4.00
D) $5.00
E) none of these
9) How much does Ned value piece 4?
A) $3.50
B) $2.00
C) $2.50
D) $3.00
E) none of these
10) How much does Ned value piece 6?
A) $2.50
B) $1.00
C) $0.50
D) $2.00
E) none of these
11) How much does Ned value piece 5?
A) $2.50
B) $1.00
C) $1.50
D) $2.00
E) none of these
2
Angela and Ben want to divide fairly the chocolate-strawberry cake shown below. The total cost of the cake was $6.00. Angela
values strawberry three times as much as she values chocolate, while Ben values chocolate twice as much as he values
strawberry.
12) In Ben's eyes, the piece shown below is worth
A) $4.50.
B) $5.00.
C) $4.00.
D) $4.75.
E) none of these
13) In Angela's eyes, the piece shown below is worth
A) $2.25.
B) $3.75.
C) $5.00.
D) $4.50.
E) none of these
14) In Ben's eyes, the piece shown below is worth
A) $2.50.
B) $3.50.
C) $3.00.
D) $4.00.
E) none of these
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15) In Angela's eyes, the piece shown below is worth
A) $3.50.
B) $2.25.
C) $3.75.
D) $3.00.
E) none of these
16) Which of the following is a fair division of the cake?
****** EACH PLAYER GETS AT LEAST HALF OF THE VALUE
A) Angela gets the piece shown below, Ben gets the remaining piece.
B) Angela gets the chocolate half, Ben gets the strawberry half.
C) Angela gets the piece shown below, Ben gets the remaining piece.
D) Angela gets the strawberry half, Ben gets the chocolate half.
E) none of these
Three players (Ady, Brenden, and Cara) are sharing a pie. Suppose that the pie is divided into three slices (
following table gives the value of each slice in the eyes of each of the players.
,
, and
). The
17) Which of the three slices are fair shares to Ady?
A)
,
B)
C)
D)
18) Find a fair division of cake using
A) Ady:
;
Brenden:
;
Cara:
B) Ady:
;
Brenden:
;
Cara:
C) Ady:
;
Brenden:
;
Cara:
D) Ady:
;
Brenden:
;
Cara:
E) Ady:
;
Brenden:
;
Cara:
,
,
E)
, and
as fair shares.
4
Four players (Alli, Blake, Corey, and Devin) are sharing a cake.
Suppose that the cake is divided into four slices
,
,
, and
.
19) To Devin,
is worth $2.70,
is worth $3.90,
which of the four slices are fair shares to Devin.
A)
B)
have equal value, and the entire cake is worth $14.00. Determine
and
,
, and
C)
and
D)
and
E)
and
,
, and
20) To Blake,
and
have equal value,
is worth as much as
and
is worth $14.00. Determine which of the four slices are fair shares to Blake.
A)
and
B)
C)
D)
and
E)
combined, and
is worth $2.40. The entire cake
and
Alan, Boris, Cali, and Doris are dividing a cake among themselves. The cake is divided into four slices
21) To Boris, the entire cake is worth $18.00 and the value of
$1.00 less than
is $4.00. Boris values
,
twice as much as
,
, and
. He values
.
as
. What are fair shares to Boris?
A) { }
B) { ,
,
C) { ,
}
}
D) { }
E) none of these
Solve the problem.
22) Amy's little brother Jimmy has eaten 40% of a chocolate cake. Amy, Brad, and Cecilia wish to equally divide the remainder of the
cake. What percentage of the original cake would be considered a fair share to each?
A) 10%
B) 33 %
C) 20%
D) 60%
E) none of these
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23) Alan, Brianna, Claire, and Doug wish to equally divide a half chocolate, half vanilla cake. Each player values chocolate three
times as much as they value vanilla. What fraction of the chocolate half of the cake would be considered a fair share to each?
A)
B)
C)
D)
E) none of these
24) Consider a fair division problem involving five players. The phrase "a player receives a fair share" describes the fact that
A) the player receives a share that, in that player's own opinion, has a value that is exactly equal to 20% of the total.
B) the player receives a share that is at least as valuable as that of any other player.
C) the player receives a share that, in that player's own opinion, has a value that is equal to 20% or more of the total.
D) the player receives a share that, in every player's opinion, has a value that is equal to 20% or more of the total.
E) none of these
25) An estate consisting of a car, a boat, a house, and a collection of rare books must be divided fairly among five heirs. This type of
problem is called
A) the method of sealed bids.
B) a mixed fair division problem.
C) a discrete fair division problem.
D) a continuous fair division problem.
E) none of these
26) Which of the following is a discrete fair division problem?
A) Dividing a tropical island.
B) Dividing an antique car collection.
C) Dividing a cheese pizza.
D) Dividing a gallon of ice cream.
E) none of these
27) Which of the following is a continuous fair division problem?
A) Dividing the family jewels.
B) Dividing an art collection.
C) Dividing a house plus all the furniture in it.
D) Dividing a cream pie.
E) none of these
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1) C
2) B
3) A
4) C
5) B
6) E
7) D
8) A
9) A
10) C
11) B
12) B
13) B
14) B
15) B
16) D
17) A
18) A
19) E
20) C
21) C
22) C
23) A
24) C
25) C
26) B
27) D
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