SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Test Review Ch 4 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 1) According to the 2000 U. S. Census, 6.753% of the U.S. population lived in the state of New York. Rounded to two decimal places, what was New York's standard quota in 2000? (Use the fact that the House of Representatives has 435 seats.) 1) A small country consists of four states. The population of State A is 67,200, the population of State B is 78,300, the population of State C is 73,800, and the population of State D is 80,700. The total number of seats in the legislature is ) The standard divisor is 2) 3) The standard quota for State C is 3) 4) Under Hamilton's method, the apportionments to each state are 4) 5) Under Jefferson's method, the apportionments to each state are 5) 6) Under Adams' method the apportionments to each state are 6) 7) Under Webster's method the apportionments to each state are 7) 8) Under the Huntington-Hill method the apportionments to each state are 8) A small country consists of four states. The population of State A is 44,800, the population of State B is 52,200, the population of State C is 49,200, and the population of State D is 53,800. The total number of seats in the legislature is ) The standard quota for State C is 9) 10) The standard quota for State B is 10) 1

2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the figure below to answer the following question(s). 11) Which graph has an Euler circuit? A) Graph 4 B) Graph 2 C)Graph 3 11) 12) Which graphs are disconnected? A) Graph 2 and Graph 3 B) Graph 1 and Graph 4 C)Graph 2 only D) Graph 3 only 12) 13) Which graph has 3 components? A) Graph 4 B) Graph 3 C)Graph 2 13) 14) In which graph is it true that every edge is a bridge? A) Graph 4 B) Graph 1 C)Graph 2 D) Graph 3 14) 15) Which graph describes the following situation: 3 boys and 3 girls go to a dance and every boy dances with every girl. A) Graph 2 B) Graph 3 C)Graph 4 15) 2

16) Which graph describes the following situation: A country is made of two states each having three major cities. A) Graph 3 B) Graph 1 C)Graph 4 D) Graph 2 16) 17) Which graph has no circuits?

3 16) Which graph describes the following situation: A country is made of two states each having three major cities. A) Graph 3 B) Graph 1 C)Graph 4 D) Graph 2 16) 17) Which graph has no circuits? A) Graph 1 B) Graph 3 C)Graph 4 D) Graph 2 17) 18) In which graph does each vertex have the same degree? A) Graph 3 B) Graph 4 C)Graph 2 18) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. An undercover police officer is assigned the job of once a night walking each of the 48 blocks of a certain section of town described by the street grid shown below. The walk starts and ends at A. The officer wants to minimize the total number of blocks he has to walk each night. 19) How many vertices of odd degree are there in the graph representing this problem? 19) 20) An optimal eulerization of the graph representing this problem can be obtained by adding 20) 21) Suppose that it takes the officer 5 minutes to walk a block. In an optimal trip, the officer will cover the entire neighborhood in 21) 3

4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the figure below to answer the following question(s). 22) Which of the graphs has an Euler circuit? A) Graph 3 only B) Graph 2 only C)Graphs 1 and 3 only 22) 23) Which of the graphs has an Euler path but no Euler circuit? A) Graphs 1 and 2 B) Graph 1 only C)Graph 3 only D) Graph 2 only 23) 24) Which of the following statements is true? A) Graph 3 is an eulerization of Graph 2. B) Graphs 2 and 3 are both eulerizations of Graph 1. C)Graph 3 is an eulerization of Graph 1. D) Graph 2 is an eulerization of Graph 1. 24) 4

5 Answer Key Testname: TEST REVIEW CH 4 1) ID: EMM ) ID: EMM ) ID: EMM ) State A: 22 seats; State B: 26 seats; State C: 25 seats; State D: 27 seats. ID: EMM ) State A: 22 seats; State B: 26 seats; State C: 25 seats; State D: 27 seats. ID: EMM ) State A: 22 seats; State B: 26 seats; State C: 25 seats; State D: 27 seats. ID: EMM ) State A: 22 seats; State B: 26 seats; State C: 25 seats; State D: 27 seats. ID: EMM ) State A: 22 seats; State B: 26 seats; State C: 25 seats; State D: 27 seats. ID: EMM ) ID: EMM ) ID: EMM ) E ID: EMM ) A ID: EMM ) B ID: EMM ) A ID: EMM ) D ID: EMM ) C ID: EMM

6 Answer Key Testname: TEST REVIEW CH 4 17) C ID: EMM ) D ID: EMM ) 20 ID: EMM ) 12 edges. ID: EMM ) 5 hours. ID: EMM ) B ID: EMM ) B ID: EMM ) D ID: EMM

Section Graphs, Paths, and Circuits. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section Graphs, Paths, and Circuits. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 14.1 Graphs, Paths, and Circuits INB Table of Contents Date Topic Page # January 27, 2014 Test #1 14 January 27, 2014 Test # 1 Corrections 15 January 27, 2014 Section 14.1 Examples 16 January 27,