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**Question 1

Amanda has agreed to pay off a $3750 loan by making 12 monthly payments. The total finance charge on her loan is $310. Use the table to find the APR to the nearest whole percent. Assume that all interest rates are annual rates.

Answer

16%

14%

13%

15%

Question 2

Decide whether the following sets are equal. {parsley, thyme, basil, oregano} and {y : y is an herb}

Answer

Yes

No

Question 3

If the given graph is Eulerian, find an Euler circuit in it. If it is not Eulerian, first Eulerize it and then find an Euler circuit.

Answer

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

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

Add edge BE; A, C, B, E, D, A, F, E, B, A

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

Question 4

Determine whether vertex “C” is even or odd.

Answer

Even

Odd

Question 5

Replace the # with either ∈ or ∉ to express a true statement. Alaska # { Oklahoma, Vermont, Colorado, New Jersey, Delaware, Kentucky}

Answer

∉

∈

Question 6

In the given voting system, the weights represent, in order, voters A, B, C, and so on. Determine the Banzhaf power index for each voter. [16 : 1, 5, 7, 9]

Answer

A has an index of 0. All others have an index of ½.

All have an index of1/2.

A has an index of1/2. All others have an index of 0.

A and B have an index of 0. C and D have an index of1/2.

Question 7

Use the brute force algorithm to find a minimum Hamilton circuit for the graph. Also, determine the total weight of the minimum Hamilton circuit.

Answer

–Minimum Hamilton circuit is W→Z→X→Y→W ; weight = 18

–Minimum Hamilton circuit is W→X→Z→Y→W ; weight = 15

–Minimum Hamilton circuit is W→X→Y→Z→W ; weight = 15

–Minimum Hamilton circuit is W→Z→Y→X→W ; weight = 15

Question 8

Melanie deposits $ 275 each month in an ordinary annuity to save for a trip to Europe. If the annuity pays a monthly rate of 0.6% how much will she be able to save in 3 years?

Answer

–$ 5210.71

–$ 2104.25

–$ 7076.08

–$ 11,013.82

Question 9

If the given graph is Eulerian, find an Euler circuit in it. If it is not Eulerian, first Eulerize it and then find an Euler circuit.

Answer

–Add edge CG; C, G, H, F, E, A, B, C, D

–Add edge EF; A, B, C, D, A, C, H, E, F, G, H, F, E, A

–A, B, C, D, A, E, F, G, H, F, E, A

–H, G, F, E, A, D, C, B, A

Question 10

Mark and Kate are establishing a fund for their son’s college education. What lump sum must they deposit in an account that gives 8% annual interest rate, compounded monthly, in order for them to have $60,000 in the fund at the end of 10 years?

Answer

–$ 29,351.41

–$ 31,607.41

–$ 27,031.41

–$ 28,331.41

Question 11

Below is a floor plan of a suite of offices. Place a door in one of the rooms so that a security guard can enter by the door marked “enter”, pass through each door and lock it behind him, and then exit by the door you have placed in the plan.

Answer

–Place door in room B.

–Place door in room D.

–Place door in room E.

–Place door in room A.

Question 12

What is 160% of 364? Round to the nearest hundredth.

Answer

–58,240.00

–58.24

–582.40

–5824.00

Question 13

Find the number of subsets of the set.

{12, 13, 14}

Answer

–3

–7

–6

–8

Question 14

The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year’s budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. Which option is selected using the plurality method?

Answer

–P

–R

–T

–S

Question 15

A committee is set up to vote yes or no on a logo design. The committee is composed of one person whose favorite color is (A)zure, five people whose favorite color is (B)lack, seven people whose favorite color is (C)herry, and nine people whose favorite color is (G)reen. At least sixteen votes are required for a decision, and the committee members will vote in blocs according to their favorite colors. List all winning coalitions, and identify those blocs that are critical to each of the winning coalitions.

Answer

–{A, C, G}, {B, C, G}, {C, G} ;

C and G are critical to all winning coalitions.

–{A, B, C, G}, {A, C, G}, {B, C, G}, {C, G} ;

C and G are critical to all winning coalitions.

–{A, B, C, G}, {A, C, G}, {B, C, G}, {C, G} ;

B, C, and G are critical to the coalition {A, B, C, G} ;

C and G are critical to all other winning coalitions.

–{A, C, G}, {B, C, G}, {C, G} ;

G is critical to all winning coalitions.

Question 16

Find the cardinal number of H ∪ A by referring to the given table.

Answer

–625

–543

–1042

–2006

Question 17

Find a directed path from “B to A.”

Answer

–“BECA”

–“BDA”

–“BEDA”

–“BDECA”

Question 18

Determine whether the graph below is connected or nonconnected.

Answer

–Connected

–Nonconnected

Question 19

Four candidates running for congress receive votes as follows:

Alberts: 53,163

Brown: 14,499

Cassimatis: 38,664

D’Amico: 33,831

Determine whether any of the listed candidates has a majority

Answer

–Yes

–No

Question 20

Find n(A) for the following set. A = { 0, 2, 4, 6, 8}

Answer

–n(A) = 4

–n(A) = 2

–n(A) = 5

–n(A) = 8

Question 21

Shade the Venn diagram to represent the set.

A’ ∩ B’

Question 22

Determine the value of the account at the end of 2 years with a principle of $2500 and an annual interest rate of 10%, compounding mothly.

Answer

–$ 24,624.33

–$ 3025.00

–$ 2541.84

–$ 3050.98

Question 23

In the following voting system: [15 : 1, 2, 3, 3, 4, 5] the weights represent, in order, voters A, B, C, and so on. Identify the dictator if there is one, and identify those voters with veto power if there are any.

Answer

–No dictator; voter F has veto power.

–Voter F is a dictator; voter F has veto power.

–Voter F is a dictator; no voters have veto power.

–No dictator; voters E and F have veto power.

Question 24

An airline is deciding which type of movie to show during a flight. The passengers are asked to rank the following four choices: (A)ction, (C)omedy, (M)usical, and (Drama). The results are summarized below. Rank the four choices using the Borda count method.

Answer

–M, D, A, C

–M, C, D, A

–A, M, D, C

–C, M, D, A

Question 25

In the voting system [12 : 1, 3, 5, 7] , the weights represent, in order, voters A, B, C, and so on. Write out all of the winning coalitions.

Answer

–{A, B, C, D}, {A, C, D}, {B, C, D}

–{A, B, C, D}, {A, C, D}, {B, C, D}, {C, D}

–{A, B, C, D}, {A, B, D}, {A, C, D}, {B, C, D}, {C, D}

–{A, C, D}, {B, C, D}, {C, D}

Question 26

Determine whether the indicated vertex is even or odd.

Answer

–Odd

–Even

Question 27

Decide whether the following sets are equivalent. {x : x is a multiple of 10 between 1 and 100, inclusive} and { 6, 12, 18, …, 60}

Answer

–Yes

–No

Question 28

Ashley bought a new computer for $ 1850. She paid a $ 120 down payment and financed the rest for one year at an interest rate of 7%. Find the monthly payment for the given amortized loan.

Answer

–$ 154.78

–$ 158.70

–$ 146.60

–$ 149.69

Question 29

In the following voting system, the weights represent, in order, voters A, B, C, and so on. Write out all of the winning coalitions. [16 : 1, 5, 7, 9]

Answer

–{A, B, C, D}, {A, C, D}

–{A, B, C, D}

–{A, B, C, D}, {A, C, D}, {B, C, D}, {C, D}

–{A, B, C, D}, {A, B, D}, {A, C, D}, {B, C, D}, {C, D}

Question 30

Ashley bought a new computer for $1250. She paid a $140 down payment and financed the rest for one year at an interest rate of 8%. Find the total interest paid on the given amortized loan.

Answer

–$ 48.69

–$ 45.60

–$ 53.78

–$ 57.70

Question 31

Determine whether the set is well defined or not.

{x : x is a tennis player who has won at Wimbledon}

Answer

–Well defined

–Not well defined

Question 32

There is a pizza delivery store located at the position marked A on the map. Assume that deliveries must be made at the following locations: C, G, L, O, B, E, and M, and then the delivery driver must return to the store. Use the nearest-neighbor algorithm to devise a delivery route that will minimize the number of blocks traveled. Assume the streets are two-way.

Answer

–ACGLOBEMA

–AEMBOLCGA

–AEBMOLCGA

–AEMBOLCA

Question 33

Find a Hamilton circuit in the graph that begins with the edge “BC”.

Answer

–BCEDAEB

–BCDAE

–BCEDAB

–BECADB

Question 34

The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year’s budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. Which option is selected using the pairwise comparison method?

Answer

–T

–R

–S

–P

Question 35

11.68 is what percent of 141? (Round to the nearest hundredth)

Answer

–0.12%

–8.28%

–1207.19%

–0.08%

Question 36

Use the Venn diagram below to find the number of elements in the region n(A ∪ B)

Answer

–21

–11

–14

–29

Question 37

Replace the # with either ∈ or ∉ to express a true statement. Nevada # {r : r is a state in the United ates}

Answer

–∈–∉

Question 38

Write a description of the shaded region using the symbols A, B, C, ∩, ∪, -, and as needed.

Answer

–A’ ∩ B’

–A ∪ B

–(A ∩ B)’

–A – B

Question 39

Let

U = {q, r, s, t, u, v, w, x, y, z}

A = {q, s, u, w, y}

B = {q, s, y, z}

C = {v, w, x, y, z}. List the elements in the set: A ∩ B’

Answer

–{t, v, x}

–{u, w}

–{q, s, t, u, v, w, x, y}

–{r, s, t, u, v, w, x, z}

Question 40

Find the cardinal number of the indicated set by referring to the given table.

H ∪ A,

given the following table:

Answer

–625

–543

–2006

–1042

Question 41

Find percent notation for 0.733

Answer

–73.3%

–733%

–0.0733%

–0.733%

Question 42

Use the formula for future value, A=P(1 + rt), to find the missing quantity.

A = $5369.00; P = $4550; t = 6 years

Answer

–r= 5%

–r = 3%

–r = 6%

–r = 4%

Question 43

Alex has saved $ 280 at the bank. He wants to accumulate $1750 for a trip to soccer camp. What percent of his goal has been reached?

Answer

–16%

–60%

–0.16%

–6%

Question 44

Choose the one alternative that best completes the statement or answers the question.

Use an alternative method to express the set. { 9, 12, 15, …, 45}

Answer

–{x : x is a multiple of 3 greater than 9 and less than 45}

–{w : w is a multiple of 3}

–{b : b is a multiple of 3 greater than or equal to 9}

–{x : x is a multiple of 3 greater or equal to 9 and less than or equal to 45}

Question 45

Determine whether the graph is connected or nonconnected.

Answer

–Nonconnected

–Connected

Question 46

Write a description of the shaded region using the symbols A, B, C, ∪, ∩, -, and as needed.

Answer

–B ∩ (A ∩ C)’

–B’ – (A ∪ B)

–A’ ∩ C’ ∩ B

–B – (A ∩ C)

Question 47

The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year’s budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. Which option is selected using the plurality-with-elimination method?

Answer

–T

–R

–S

–P

Question 48

The city council gave a questionnaire to its citizens, asking them to rank their priorities for next year’s budget. People were asked to rank the following four choices: (P)olice, (R)oads, (S)chools, and (T)rash removal. The results are summarized in the table below. Which option is selected using the Borda count method?

Answer

P

T

R

S

Question 49

You are given the future value of an annuity, A, the monthly payment, R, and the annual interest rate, r. Find the number of monthly payments, nt. Round your answer to the nearest whole number if necessary.

A = $ 7000; R = $ 250; r = 9%

Answer

30 months

32 months

34 months

26 months

Question 50

Find the value of the annuity at the end of the indicated time period. The amount, frequency of deposits, annual interest rate, and time period are given.

amount: $ 175; monthly; 8%; 7 years

Answer

$ 20,019.85

$ 20,219.96

$ 19,619.83

$ 20,319.95