Math 17 Midterm Exam
Summer 2016
Name __________________________________
1. You and your extended family are planning a big summer trip so everyone can vacation together.
After months of debate, the choices have been narrowed down to four: San Francisco, Orlando, Boston,
and New York City. Everyone in the family ranks the choices and the preference schedule for the results
is given below:
1st
2nd
3rd
4th
11
SF
O
B
NYC
9
NYC
SF
B
O
8
B
NYC
O
SF
5
O
B
SF
NYC
4
B
O
NYC
SF
__________a. How many votes are needed for a vacation destination to have a majority of the votes?
__________b. Use the Plurality Method to determine the top vacation destination.
__________c. If the Borda Count Method was used to determine the top vacation destination, how
many points would SF earn?
__________d. Who would win in a (head-to-head) Pairwise Comparison between Orlando and Boston?
__________e. Which vacation destination would be the top choice if Plurality with Elimination is used
to determine the winner?
2. Consider the weighted voting system [q: 8, 4, 3, 2, 1].
__________a. What is the largest possible value for q?
__________b. What is the smallest possible value for q?
3. Consider the weighted voting system [20: 12, 9, 6, 5] and the Banzhof Power Index.
__________a. Is the coalition {P1, P2, P4} a winning coalition?
__________b. List the critical player(s), if any, in the coalition {P1, P3, P4}.
__________c. List the critical player(s), if any, in the coalition {P2, P3, P4}.
__________4. Your salary increases from $12.00 dollars/hour to $14.88! What is the percent of
increase for your raise?
__________5. The stock for KSBW, Inc. debuts at $50. The next day the stock has increased 8%, then
decreased 2%, then increased 4%. What is the overall percent of increase or decrease in the stock over
this time?
__________6. You invest $3000 in a CD paying simple interest of 4% APR. What is the value of the CD
after 3 years?
7. You invest $4000 in an account for 6 years. Calculate the maturity value of the investment if the
interest rate is
_______________a. 4% compounded annually
_______________b. 4% compounded quarterly
8. A bus company has 14 buses to use during rush hour and wants to assign buses to each route on the
number of passengers riding on each of the routes. The number of passengers for each route is given in
the table below:
Route
Number of Passengers
A
85
B
92
C
76
D
43
E
54
Total
350
__________a. What is the standard divisor for this problem?
__________b. What is the standard quota for route C?
c. Apportion the 14 buses using Hamilton’s Method.
A _____
B _____
C _____
D _____
E _____
9. Four artists are dividing a large, open room into 4 smaller studios using the Lone Divider Method.
The bids for each of the choosers are given below:
Charles {1, 4}
Cindy {4}
Callie {1, 2}
What is one way the studio could be divided?
Charles ______
Cindy ______
Callie ______
Donald (Divider) ______
10. Kevin and Jack are dividing a $20 vanilla and strawberry cake using the Divider/Chooser Method.
Kevin is the divider and likes vanilla four times more than he likes strawberry.
__________a. What is the value of the vanilla cake to Kevin?
__________b. What is the value of the strawberry cake to Kevin?
c. Show a possible fair cut of the cake in Kevin’s eyes.
Vanilla
S’berry
11. Jill and Lill have been roommates for ages but now they are both moving to other cities. While
roommates, they purchased a canoe and kayak together and they’ve decided to allocate the two items
using the method of Sealed Bids. Their bids are given below:
Canoe
Kayak
Jill
500
300
Lill
450
350
__________a. Who will get the canoe?
__________b. Who will get the kayak?
__________c. What is a fair share for Jill?
__________d. What is a fair share for Lill?
e. What is the final allocation of the items, include any money paid or received by Jill and Lill?
Jill ___________________________________
Lill ___________________________________