VOTING - Winston-Salem/Forsyth County Schools



Multiple Choice Practice Problems CHAPTER 4 - APPORTIONMENT:

For questions 1 - 4: 4 states and 50 seats. The population of each state is provided.

|State |A |B |C |D |

|Population |3194 |9066 |4548 |8192 |

1) The standard divisor is

A) 250 B) 500

C) 5000 D) 25000

E) None of above

2) The standard quota (two decimal) for State A is

A) 6.39 B) 7.14

C) 12.78 D) 63.88

E) None of above

3) Which modified divisor works for Adam’s method?

A) 500 B) 505

C) 510 D) 515

E) None of the Above

4) Who gets the surplus in Hamilton’s method?

A) State A B) State B

C) State C D) State D

E) None of the Above

5) Under a certain apportionment method, state X has a standard quota of 48.9 and receives 47 seats in the final apportionment. This is called

A) an upper quota violation B) the Alabama paradox. C) the population paradox.

D) the new states paradox. E) a lower quota violation.

6) State Y received 100 seats under a certain apportionment method. 1 more seat was added to the legislature and then under the same apportionment method Y received 99 seats. This is called

A) an upper quota violation B) the Alabama paradox. C) the population paradox.

D) the new states paradox. E) a lower quota violation.

For questions 7 - 8: A small airline operates 5 flights (NY, BOS, DC, PHI, ATL) to major cities on the east coast. There are only 20 airplanes that the airline owns. The airplanes are apportioned among the flights on the basis of average profit per flight.

7) Which of the following best represents the key terms of an apportionment

(States; Populations; Seats) to the word problem?

A) Flights; Average Profit; Airplanes

B) Airplanes; Flights; Average Profit

C) Flights; Airplanes; Average Profit

D) Average Profit; Flights; Airplanes

E) Airplanes; Average Profit; Flights;

8) Which of following will the standard divisor represent?

A) Flights per Airplane

B) Airplanes per Flight

C) Airplanes per Average Profit

D) Flights per Average Profit

E) Average Profit per Airplane

Multiple Choice Practice Problems CHAPTER 4 - APPORTIONMENT:

For questions 1 - 4: 4 states and 50 seats. The population of each state is provided.

|State |A |B |C |D |

|Population |3194 |9066 |4548 |8192 |

1) The standard divisor is

A) 250 B) 500

C) 5000 D) 25000

E) None of above

2) The standard quota (two decimal) for State A is

A) 6.39 B) 7.14

C) 12.78 D) 63.88

E) None of above

3) Which modified divisor works for Adam’s method?

A) 500 B) 505

C) 510 D) 515

E) None of the Above

4) Who gets the surplus in Hamilton’s method?

A) State A B) State B

C) State C D) State D

E) None of the Above

5) Under a certain apportionment method, state X has a standard quota of 48.9 and receives 47 seats in the final apportionment. This is called

A) an upper quota violation B) the Alabama paradox. C) the population paradox.

D) the new states paradox. E) a lower quota violation.

6) State Y received 100 seats under a certain apportionment method. 1 more seat was added to the legislature and then under the same apportionment method Y received 99 seats. This is called

A) an upper quota violation B) the Alabama paradox. C) the population paradox.

D) the new states paradox. E) a lower quota violation.

For questions 7 - 8: A small airline operates 5 flights (NY, BOS, DC, PHI, ATL) to major cities on the east coast. There are only 20 airplanes that the airline owns. The airplanes are apportioned among the flights on the basis of average profit per flight.

7) Which of the following best represents the key terms of an apportionment

(States; Populations; Seats) to the word problem?

A) Flights; Average Profit; Airplanes

B) Airplanes; Flights; Average Profit

C) Flights; Airplanes; Average Profit

D) Average Profit; Flights; Airplanes

E) Airplanes; Average Profit; Flights;

8) Which of following will the standard divisor represent?

A) Flights per Airplane

B) Airplanes per Flight

C) Airplanes per Average Profit

D) Flights per Average Profit

E) Average Profit per Airplane

Multiple Choice Practice Problems CHAPTER 5 - EULER CIRCUITS:

For questions #1 - 3 refer to Figure #1.

1) Which of the following is NOT a circuit in the graph?

A) C, C B) A, B, F, E, A

C) B, D, C, B D) F, D, C, C, B, E, F

E) None of the Above

2) Which of the following is NOT a path in the graph?

A) F, E, B, A, E, F, D B) F, B, C, C, D

C) F, E, A, B, F, D D) F, D, E, A, B, F, C, D

E) None of the Above

3) Which one of the following statements is NOT true about this graph?

A) There is a circuit starting and ending at E.

B) There are multiple edges.

C) It is a connected graph.

D) A loop exists.

E) None of the above.

For questions # 4 – 6 refer to the four graphs in Figure #2.

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|Graph #1 |Graph #2 |Graph #3 |Graph #4 |

FIGURE #2

4) Which graph(s) have an Euler Circuit?

A) Graph #1 B) Graph #2 C) Graph #3 D) Graph #4 E) Graph #2 + #3

5) Which graph(s) have components?

A) Graph #1 B) Graph #2 C) Graph #3 D) Graph #4 E) None

6) Which graph(s) have an Euler Path?

A) Graph #1 B) Graph #2 C) Graph #4 D) Graph #1 + #4 E) Graph #2 + #4

For #7 - 9: Use Figure #3

7) Which of the following is a bridge in the graph?

A) AB B) AF C) DG D) CG E) DD

8) Which of the following is not a multiple edge?

A) AB B) CG C) GD D) CE E) NONE

9) Which is not the correct degree statement?

A) A = 3 B) C = 2 C) D = 4 D) F = 3 E) G = 6

Multiple Choice Practice Problems CHAPTER 5 - EULER CIRCUITS:

For questions #1 - 3 refer to Figure #1.

1) Which of the following is NOT a circuit in the graph?

A) C, C B) A, B, F, E, A

C) B, D, C, B D) F, D, C, C, B, E, F

E) None of the Above

2) Which of the following is NOT a path in the graph?

A) F, E, B, A, E, F, D B) F, B, C, C, D

C) F, E, A, B, F, D D) F, D, E, A, B, F, C, D

E) None of the Above

3) Which one of the following statements is NOT true about this graph?

A) There is a circuit starting and ending at E.

B) There are multiple edges.

C) It is a connected graph.

D) A loop exists.

E) None of the above.

For questions # 4 – 6 refer to the four graphs in Figure #2.

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|Graph #1 |Graph #2 |Graph #3 |Graph #4 |

FIGURE #2

4) Which graph(s) have an Euler Circuit?

A) Graph #1 B) Graph #2 C) Graph #3 D) Graph #4 E) Graph #2 + #3

5) Which graph(s) have components?

A) Graph #1 B) Graph #2 C) Graph #3 D) Graph #4 E) None

6) Which graph(s) have an Euler Path?

A) Graph #1 B) Graph #2 C) Graph #4 D) Graph #1 + #4 E) Graph #2 + #4

For #7 - 9: Use Figure #3

7) Which of the following is a bridge in the graph?

A) AB B) AF C) DG D) CG E) DD

8) Which of the following is not a multiple edge?

A) AB B) CG C) GD D) CE E) NONE

9) Which is not the correct degree statement?

A) A = 3 B) C = 2 C) D = 4 D) F = 3 E) G = 6

Multiple Choice Practice Problems CHAPTER 6 - HAMILTON CIRCUITS:

1) The number of edges in K25 is

A) 24 B) 25 C) 276 D) 300 E) 325

2) The number of Hamilton Circuits in K16 is

A) 15 B) 120 C) 15! D) 16! E) 17!

3) If a complete graph has degree 8 for each vertex, then how many edges are in the graph?

A) 36 B) 8! C) 9! D) 8 E) 9

4) A complete graph has 465 edges. How many vertices does the graph have?

A) 29 B) 30 C) 31 D) 107,880 E) 108,345

5) A complete graph has 40,320 distinct Hamilton’s circuits. How many vertices are there?

A) 6 B) 7 C) 8 D) 9 E) 10

6) The graph in Figure #1 …

A) has no Hamilton circuit.

B) has a single Hamilton circuit (and its mirror-image circuit).

C) has multiple Hamilton circuits, none contain the edge BD.

D) has multiple Hamilton circuits, all contain the edge BE.

E) none of the above

For questions 7 - 9 refer figure #2:

7) The Nearest Neighbor Algorithm applied to the graph finds the solution:

A) D, C, A, B, E, D

B) D, E, A, B, C, D

C) D, A, B, E, C, D

D) D, B, E, C, A, D

E) none of the above

8) The Cheapest Link Algorithm applied to the graph finds the solution:

A) D, C, A, B, E, D

B) D, E, A, B, C, D

C) D, A, B, E, C, D

D) D, B, E, C, A, D

E) none of the above

9) How many different Hamilton circuits would we have to find to use the Brute Force Algorithm starting at D?

A) 4

B) 5

C) 10

D) 24

E) 12

Multiple Choice Practice Problems CHAPTER 6 - HAMILTON CIRCUITS:

1) The number of edges in K25 is

A) 24 B) 25 C) 276 D) 300 E) 325

2) The number of Hamilton Circuits in K16 is

A) 15 B) 120 C) 15! D) 16! E) 17!

3) If a complete graph has degree 8 for each vertex, then how many edges are in the graph?

A) 36 B) 8! C) 9! D) 8 E) 9

4) A complete graph has 465 edges. How many vertices does the graph have?

A) 29 B) 30 C) 31 D) 107,880 E) 108,345

5) A complete graph has 40,320 distinct Hamilton’s circuits. How many vertices are there?

A) 6 B) 7 C) 8 D) 9 E) 10

6) The graph in Figure #1 …

A) has no Hamilton circuit.

B) has a single Hamilton circuit (and its mirror-image circuit).

C) has multiple Hamilton circuits, none contain the edge BD.

D) has multiple Hamilton circuits, all contain the edge BE.

E) none of the above

For questions 7 - 9 refer figure #2:

7) The Nearest Neighbor Algorithm applied to the graph finds the solution:

A) D, C, A, B, E, D

B) D, E, A, B, C, D

C) D, A, B, E, C, D

D) D, B, E, C, A, D

E) none of the above

8) The Cheapest Link Algorithm applied to the graph finds the solution:

A) D, C, A, B, E, D

B) D, E, A, B, C, D

C) D, A, B, E, C, D

D) D, B, E, C, A, D

E) none of the above

9) How many different Hamilton circuits would we have to find to use the Brute Force Algorithm starting at D?

A) 4

B) 5

C) 10

D) 24

E) 12

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FIGURE #1

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