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Question 13 pts

Two brothers (A & B) are dividing common assets (a used car, a painting, a bicycle, and a camera) between themselves using the method of sealed bids . Their bids on the items are shown below.

	A	B
Used car	$5,000	$5,200
Painting	$600	$700
Bicycle	$300	$250
Camera	$100	$350

What's the value of A's fair share?

	$3,000
	$3,250

	$6,000
	$300

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Question 23 pts

Two brothers (A & B) are dividing common assets (a used car, a painting, a bicycle, and a camera) between themselves using the method of sealed bids . Their bids on the items are shown below.

	A	B
Used car	$5,000	$5,200
Painting	$600	$700
Bicycle	$300	$250
Camera	$100	$350

What's the value of B's fair share?

	$700
	$3,000

	$3,250
	$6,500

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Question 33 pts

Two brothers (A & B) are dividing common assets (a used car, a painting, a bicycle, and a camera) between themselves using the method of sealed bids . Their bids on the items are shown below.

	A	B
Used car	$5,000	$5,200
Painting	$600	$700
Bicycle	$300	$250
Camera	$100	$350

After initial settlement (i.e., each item goes to someone), figure out how much A has to pay or receive.

	Receives $700
	Receives $2,700

	Pays $300
	Pays $3,000

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Question 43 pts

Two brothers (A & B) are dividing common assets (a used car, a painting, a bicycle, and a camera) between themselves using the method of sealed bids . Their bids on the items are shown below.

	A	B
Used car	$5,000	$5,200
Painting	$600	$700
Bicycle	$300	$250
Camera	$100	$350

After initial settlement (i.e., each item goes to someone), figure out how much B has to pay or receive.

	Pays $3,000
	Pays $6,250

	Receives $3,000
	Receives $6,250

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Question 53 pts

Two brothers (A & B) are dividing common assets (a used car, a painting, a bicycle, and a camera) between themselves using the method of sealed bids . Their bids on the items are shown below.

	A	B
Used car	$5,000	$5,200
Painting	$600	$700
Bicycle	$300	$250
Camera	$100	$350

Describe the final settlement of items and money (i.e., who gets which items and how much money does each one have to pay or receive ). Which of the following is a correct statement?

	B gets used car, painting & camera and pays $2,850.
	B gets painting & camera and receives $2,850.

	A gets bicycle and receives $2,700.
	A gets bicycle and receives $2,850.

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Question 63 pts

Round 5.46 using the Huntington-Hill rounding rules. (Hint: $\sqrt{5\times6}=\sqrt{30}=5.4772$ )

	5.5
	5

	6
	4

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Question 73 pts

Round 5.48 using the Huntington-Hill rounding rules. (Hint: $\sqrt{5\times6}=\sqrt{30}=5.4772$ )

	6
	5.5

	7
	5

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Question 83 pts

Round 5.49 using the Huntington-Hill rounding rules. (Hint: $\sqrt{5\times6}=\sqrt{30}=5.4772$ )

	5.4
	5

	5.5
	6

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Question 93 pts

Three players (A, B, and C) are dividing 12 candy bars as shown below using the method of markers . The players’ bids are indicated in the figure.

$C:\Users\AD\Desktop\9.JPG$

Which item(s) goes to A?

	1, 2, 3
	5, 6, 7

	4, 5, 6, 7
	10, 11, 12

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Question 103 pts

Three players (A, B, and C) are dividing 12 candy bars as shown below using the method of markers . The players’ bids are indicated in the figure.

$C:\Users\AD\Desktop\10.JPG$ Which item(s) goes to C?

	4, 5, 6, 7
	10, 11, 12

	5, 6, 7
	1, 2, 3

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Question 113 pts

Three players (A, B, and C) are dividing 12 candy bars as shown below using the method of markers . The players’ bids are indicated in the figure.

$C:\Users\AD\Desktop\11.JPG$

Which item(s) will be left over?

	4, 8, 9
	5, 6, 7

	10, 11, 12
	4, 9, 10

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Question 123 pts

A 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 1,000 emergency blue lights. The lights will be apportioned based on the size of the student population (i.e., the larger the population, the more lights). The table below gives the size of the student population of each campus in percentage .

Campus section	Main Campus	North Campus	East Campus	West Campus	South Campus
Student population *percentage*	11.57%	7.87%	35.62%	17.98%	26.96%

If the upper quota is used, how many emergency lights should be allocated to the “East Campus”?

	354
	356

	357
	358

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Question 133 pts

Campus section	Main Campus	North Campus	East Campus	West Campus	South Campus
Student population percentage	11.57%	7.87%	35.62%	17.98%	26.96%

If the lower quota is used, how many emergency lights should be allocated to the “East Campus”?

	354
	356

	358
	357

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Question 143 pts

A small country consists of four states (A, B, C, and D, for short). The populations of the four states are shown below. We want to find the apportionment of the 100 seats in the country’s House of Representatives using Hamilton’s method.

States	A	B	C	D
Population	30,400	99,600	60,100	9,900

(Hint: 30,400+99,600+60,100+9,900=200,000)

What is the standard divisor?

	200,000
	15.2

	2,000
	100

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Question 153 pts

States	A	B	C	D
Population	30,400	99,600	60,100	9,900

(Hint: 30,400+99,600+60,100+9,900=200,000)

What is the standard quota of state A?

Hint : 30,400/2,000=15.2, 99,600/2,000=49.8, 60,100/2,000=30.05, 9,900/2,000=4.95

	200,000
	1000

	15.2
	200

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Question 163 pts

States	A	B	C	D
Population	30,400	99,600	60,100	9,900

(Hint: 30,400+99,600+60,100+9,900=200,000)

What is the final apportionment of under Hamilton’s method?

	A=15, B=49, C=30, D=5
	A=14, B=50, C=30, D=6

	A=15, B=50, C=30, D=5
	A=15, B=49, C=30, D=4

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Question 173 pts

For the graph shown below

$C:\Users\AD\Desktop\17.JPG$ which edges are adjacent to EF?

	AB
	EF

	There isn't any.
	EC, FD

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Question 183 pts

For the graph shown below

$C:\Users\AD\Desktop\17.JPG$ which vertices are adjacent to E?

	C, D
	A, C

	C, F
	D, F

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Question 193 pts

For the graph shown below

$C:\Users\AD\Desktop\17.JPG$ does the graph have at least one Euler Circuit ?

	Yes, there are several Euler circuits
	Yes, but only one Euler circuit

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Question 203 pts

For the graph shown below

$C:\Users\AD\Desktop\17.JPG$ does the graph have an Euler Path ?

	No
	Cannot tell from the given information.

Yes

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Question 213 pts

For the graph shown below

$C:\Users\AD\Desktop\17.JPG$ does the graph have at least one Hamilton Circuit ?

	No
	Cannot tell.

Yes

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Question 223 pts

For the graph shown below

$C:\Users\AD\Desktop\17.JPG$ does the graph have at least one Hamilton Path ?

	Yes
	No

Cannot tell.

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Question 233 pts

For the graph shown below

$C:\Users\AD\Desktop\17.JPG$ to Eulerize the graph, which edge(s) do you want to add?

	CD
	BD & DF

	AD & BC
	AB & CD

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Question 243 pts

For the graph shown below

$C:\Users\AD\Desktop\24.JPG$ is this a complete graph?

	Yes
	No

Cannot tell.

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Question 253 pts

For the graph shown below

$C:\Users\AD\Desktop\24.JPG$

how many Hamilton circuits starting at vertex D (and ending in vertex D) exist here?

	5
	6

	12
	3

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Question 263 pts

For the graph shown below

$C:\Users\AD\Desktop\24.JPG$

how many Hamilton paths starting at vertex D and ending at vertex B are there?

	1
	3

	2
	6

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Question 273 pts

For the graph shown below

$C:\Users\AD\Desktop\24.JPG$ to Eulerize the graph, which edge(s) do you want to add?

	AC
	AB

	Cannot Eulerize this graph.
	AD & BC

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Question 283 pts

For the weighted graph shown below, apply the “go cheap” algorithm and find the tour that's the cheapest. Start from A.

$C:\Users\AD\Desktop\28.JPG$

	ACBDEA
	ADECB

	ADECBA
	ABCDEA

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Question 293 pts

For the weighted graph shown below, apply the “go cheap” algorithm and find the cheapest cost of the resulting tour. Start from A.

$C:\Users\AD\Desktop\28.JPG$

	$190
	$122

	$140
	$90

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Question 303 pts

For the weighted graph shown below, apply the “the “cheapest-link” algorithm” and find the tour that's cheapest.

$C:\Users\AD\Desktop\28.JPG$

	AECDBA
	ADBCE

	ADBCEA
	CEBDAC

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Question 313 pts

For the weighted graph shown below, apply the “the “cheapest-link” algorithm” and find the cheapest cost of the resulting tour.

$C:\Users\AD\Desktop\28.JPG$

	$140
	$116

	$96
	$122

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Question 323 pts

Four players (A, B, C, and D) are dividing a pizza worth $20 among themselves using the lone-divider method. The divider divides it into 4 shares, s1, s2, s3, and s4. The following table shows the value of the four shares in the eyes of each player, but some of the entries are missing.

	s1	s2	s3	s4
A	$5.00	$5.00	$4.50
B		$5.00
C	$5.10	$4.90	$5.40
D	$4.80	$4.80	$5.10

What's the value that should be entered for s4 for D (i.e., that's the blank on the lower-right corner)?

	$5.20
	$5.30

	$4.90
	$5.00

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Question 332 pts

How many edges does K5 graph have?

	15
	10

	50
	5

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Question 342 pts

If KN graph has total sum of degrees of all vertices 72, what is N here?

	8
	10

	36
	9