Use the following preference schedule to answer questions #1 - #4. Number of Voters st choice 2 nd Choice 3 rd choice 4 th choice

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1 M130 Sample Final Exam Name TA Name Calculators are allowed, but cell phones or palm pilots are NOT acceptable. Mark Version A on your scantron. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Clearly mark your answers on the scantron form. Use the following preference schedule to answer questions #1 - #4. Number of Voters st choice 2 nd Choice 3 rd choice 4 th choice A B C D D C B A D B C A C A B D 1) Under the extended plurality method who comes in 3 rd? A) A- 71 first place votes: first B) B- 0 first place votes: last C) C-63 first place votes: second D) D-37 first place votes: third 2) Which candidate wins the election under the Borda count method? A) A : 4*71+1*22+1*15+3*63= 510 points: first B) B : 3*71+2*22+3*15+2*63 = 428 points C) C : 2*71+3*22+2*15+4*63 = 490 points D) D : 1*71+4*22+4*15+1*63 = 282 points 3) The candidate that comes in 2 nd place using the recursive Borda count method is A) A gone, since A wins the election B) B : 3*71+1*22+2*15+2*63 = 391 points- wins, gets second place overall C) C : 2*71+2*22+1*15+3*63 = 390 points D) D : 1*71+3*22+3*15+1*63 = 245 points 4) Which candidate has a majority? Total votes = = 171; 171/2 = 85.5; Majority = 86 A) A- 71 first place votes: too small B) B- 0 first place votes: too small C) C-63 first place votes: too small D) D-37 first place votes: too small E) No candidate has a majority. 5) You have $550 to invest. If you put it in the Smart Fund there is a 27% chance that it will increase in value by $80 within a year, but there is a 73% chance that it will decrease in value by $100. What is your expected gain or loss from an investment in the Smart Fund? A) $51.40 gain B) $51.40 loss 80 (0.27) + (-100)(0.73) = -51.4, or $51.40 loss C) $21.60 gain D) $21.60 loss

2 Refer to the weighted voting system[ 51 : 39,21,18,17 ] and the Banzhaf definition of power to answer questions #6 - #8. 6) The winning coalitions for the weighted voting system are (votes must be greater than or equal to quota of 51) A) { 39,21,18,17 }, { 39,21,18 }, { 39,21,17 }, { 39,18,17 }, { 21,18,17 }, { 39,21 }, { 39,18},{ 39,17} B) { 39,21,18,17 }, { 39,21,18 }, { 39,21,17 }, { 39,18,17 }, { 21,18,17 } C) { 39,21,18,17 }, { 39,21,18 }, { 39,21,17 }, { 39,18,17 }, { 21,18,17 }, { 39,21 }, { 39,18},{ 39,17},{ 21,18 }, { 21,17 }, { 18,17} D) { 39,21,18,17 }, { 39,21,18 }, { 39,21,17 }, { 39,18,17 }, { 21,18,17 }, { 39,21 }, { 39,18},{ 39,17},{ 21,18 }, { 21,17 } 7) Which player(s) are critical in the coalition{ 21,18,17 }? (If they left, they would cause the coalition to lose) A) None of the players are critical. B) All of the players are critical. C) Only players 21 and 18 are critical. D) 21 is the only critical player. 8) What is the Banzhaf power distribution? ( underlined critical players in # ;21-2;18-2;18-2 total is 12) A) ,,, ,0,0, ,,, B) 0 C) Refer to the weighted voting system [ : 9,6,5] D) ,,, E) None of the above 13 and the Shapley-Shubik definition of power to answer questions #9 - #11. 9) What are the sequential coalitions for this system? (must all be same size- list all combinations of 9,6,5) A) 9,6,5, 9,6, 9, 5 B) 9,6,5, 9,6, 9,5, 6, 5 C) 9,6,5, 9,5,6, 6,9,5, 6,5,9, 5,9,6, 5,6, 9 D) 9,6,5, 6,9,5, 5,9, 6 10) Which player is pivotal in the sequential coalition 5,6, 9? (start at left, 5 is not enough, 5+6 is not enough, but is) A) 9- pivotal 4 times: <6,9,5>, <6,5,9>, <5,9,6>, <5,6,9> B) 6- pivotal once: <9,6,5> C) 5- pivotal once: <9,5,6> D) There is no pivotal player. 11) What is the Shapley-Shubik power distribution for the weighted voting system? (total pivotal times: 6) A) 2 1 1,, ,0, 1 1 1,, B) 0 C) D) 3 2 1,, E) None of the above 12) Rorbat is investing money to make a movie. He puts $560 in a savings account. After one year he has $590. What is the annual yield for this account? =30 net gain. 30/560 = rounds to 5.36% A) 5.6% B) 4% C) 0.30% D) 5.36%

3 Use the following to answer questions #13 - #15 A 1 C 1 13) Which of the following is NOT a fair share for player C? (see blue boxes for C s fair share possibilities) A) B) C) D) 14) What does player B receive under the Method of Markers? (see red boxes for final fair shares) A) B) C) D) 15) What are all the leftover items under the Method of Markers? A) B) C) D) There are no items left over. B 1 Use the following to answer questions #16 - #18 Marcia retires from her job, leaving 3 items to be divided among her co-workers. They decide to divide the items up using the method of sealed bids. Their bids on each item are as follows: Mad Max Sarah Connor James T. Kirk Spirograph $20 $6 $13 Millenium Falcon model $1,500 $2,200 $5,000 Atari 2600 $400 $293 $150 Fair shares: $640 $833 $ ) What is Sarah Connor s fair share? (6+2, )/3 = 24999/3 = 833 A) $2,499 B) $833 C) $1,575 D) $742 17) Who gets the Atari 2600? A) Mad Max- has the highest bid B) Sarah Connor C) James T. Kirk D) No one gets the Atari ) After the final allocation, how much will James T. Kirk have to pay in? (Kirk pays estate =3279, and then the A) $1,721 estate pays 833 to Sara Connor, and 220 to Mad Max. B) $3,279 This means a surplus of =2226, which is C) $5,000 split 3 ways. 2226/3=742. Kirk pays =2537) D) $2,537 A 2 B 2 C 2

4 Use the following to answer questions #19 - #22. There are 40 seats available in the Toy Doll House of Commons. The Cabbage Patch Kids have a population of 134. The Garbage Pal Kids have a population of 115. The Barbies have a population of ) What is the standard divisor? ( )/40=450/40=11.25 A) 450 B) 40 C) D) ) Which of the following is the best interpretation of the standard divisor? A) The number of dolls each seat represents B) How many seats each doll gets C) The total number of dolls D) The total number of seats 21) What are the standard quotas for the Cabbage Patch Kids, Garbage Pal Kids, and Barbies respectively? A) 12, 11, 17 B) 11, 10, 17 C) 12, 10, 18 D) 11.91, 10.2, (divide the population by the standard divisor) 22) Under Hamilton s Method, what is the final apportionment? A) 12, 11, 17 B) 12, 10, 18 (allocate 2 surplus seats to highest fractions: and become 12 and 18) C) 11, 10, 19 D) 13, 10, 17 23) Which of the following illustrates an Euler circuit for the graph below? A) C, D, E, A, B, F, D, C B) C, D, E, A, B, C C) C, D, E, A, B, F, D, B, C (start and stop at same vertex, travel each edge exactly once) D) No Euler circuit possible. 24) In the graph below, once the minimum number of deadheads are added, how many edges are in the Euler circuit? A) 19 B) 18 C) 17 D) 16

5 Use the graph below to answer questions #25 - #27. 25) The cheapest link algorithm yields a Hamilton circuit of weight = 29 A) 32 B) 28 C) 29 D) 25 26) The nearest neighbor algorithm from vertex D yields the following Hamilton circuit A) A, B, C, D, E, A B) A, C, D, E, B, A C) A, D, E, B, C, A (this is the same circuit as D, A, C, B, E, D) D) A, D, C, B, E, A 27) How many Hamilton circuits are possible in the graph including mirror images? (n-1)! In this case, (5-1)! = 4!=1*2*3*4=24 A) 120 B) 10 C) 24 D) 5 Use the graph to answer questions #28 - #29. EXTRA COPY OF GRAPH: 28) Using Kruskal s algorithm, what is the weight of the minimum spanning tree? =37 A) 36 B) 37 C) 38 D) 39 29) How many edges are in the minimum spanning tree? (n-1) A) 9 B) 10 C) 11 D) 12 30) Find the 38 th Fibonacci number if the 36 th and 37 th Fibonacci numbers are: ,930, ,157,817 = 39,088,169 A) 38 B) 9,227,465 C) 39,088,169 D) Cannot be determined. F = 14,930, 36 and = 24,157, F.

6 Use the following digraph to answer questions #31- #35 31) What tasks must be completed before task E? A) A, B, C only B) A, B only C) C only D) There are no tasks that need to be completed before task E. 32) The decreasing time algorithm generates the priority list (list tasks in order of decreasing completion time) A) F, B, A, E, C, D B) D, C, E, A, B, F C) A, B, C, D, E, F D) A, B, C, E, F, D 33) The length of the critical path is A) 19 B) 22 C) 17 D) 16 34) The critical path algorithm generates the priority list (list tasks in order of decreasing critical time) A) F, E, D, C, B, A B) A, B, C, D, E, F C) D, F, E, B, C, A D) A, C, B, E, F, D 35) Schedule the tasks on two processors using the priority list A, B, C, D, E, F.

7 Use the following to answer questions #36- #40 At Ice Cream Palace they have a sundae bar. The options are as follows: Ice Cream: chocolate, vanilla, strawberry, butter pecan Sauce: hot fudge, caramel, strawberry sauce, pineapple sauce Topping: rainbow sprinkles, whipped cream, none Nuts: walnuts, almonds, none 36) How many different sundaes are possible? 4*4*3*3 = 192 A) 48 B) 144 C) 14 D) 96 37) How many sundaes have strawberry ice cream and pineapple sauce? 1*3*1*3 = 9 A) 9 B) 12 C) 2 D) 6 38) What is the probability that someone will order a sundae with almonds? 4*3*4*1/144 = A) 48 B) 0.33 C) 0.25 D) ) The odds that Thundercat will win the next race are 4 to 9. What is the probability that Thundercat will win? A) 0.44 B) 2.25 C) /(4+9) = 4/13 = D) ) There is a 3 in 10 chance that Miss Fancy Buttons will win the last race. What are the odds that Miss Fancy Buttons will win? A) 3 to 10 B) 10 to 3 C) 3 to 7 (3 chances she can win, 7 chances she won t win) D) 7 to 3 Use the following data to answer questions #41 - #42: 78, 82, 85, 87, 90, 92, 99, 102, 103, 108, 110, ) What is the mean of the data? A) B) 92 C) 99 D) (total/how many: 1148/12 = ) 42) What is the median of the data? A) B) 92 C) 95.5 (middle numbers are 92 and 99: (92+99)/(2) = 95.5) D) 99

8 Use the following normal distribution to answer questions #43 - #44. Consider the normal distribution of coral snake length: Mean length: 64 cm Standard deviation length: 2 cm 43) What percentage of coral snakes are between 58 cm and 66 cm in length? A) 83.85% (2.35% % + 34% + 34%) B) 49.85% C) 15.85% D) 50% 44) What percentage of coral snakes are longer than 66 cm? A) 83.85% B) 49.85% C) 15.85% D) 16% (13.4% % %) 45) Identify the Min, Median, and Q 3 using the box plot. A) Min = 0, Median = 20, and Q 3 = 40 B) Min = 20, Median = 70, and Q 3 = 80 C) Min = 40, Median = 70, and Q 3 = 80 D) Min = 70, Median = 80, and Q 3 = 90 Min Q 1 M Q 3 Max 46) Suppose you purchase 50 crickets to start a colony to feed your tarantula. Chompy s Pet Supply tells you that you should expect your colony to increase by about 5 new crickets each month. Which of the following answers are the correct recursive and explicit formulas describing your cricket population? A) = P ; = 5 + N 50 B) = N P ; = 50 + N 5 C) = P ; = 5 + N 50 N D) = N + 5 (Start value, or P 0, is 50, common difference, or d, is 5) = + N ; P ) You are trying to book your band, Measure Zero, at Plank s Constant Bar. The manager says you will receive $100 base pay, and an additional $2 for every person who pays at the door. The contract summarizes the information with the following formula: = N 2. How many people have to pay to see you before you make $200? A) 25 people B) 30 people C) 45 people D) 50 people 200 = N * 2 solve for N: = 100, then divide by 2, get 50 48) Walt purchases a stereo/cd player for $35. He marks the price up by 50% for retail sale. However, after two months he marks the price down 25%. What is the price to the customer? A) $43.75 B) $52.50 C) $ (1+0.50)(1-0.25) D) $65.63