Mathematical Ideas, 13th Edition Test Bank

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Decide whether the argument is an example of inductive or deductive reasoning.1)His last four at bats were strikeouts. Therefore, the next will bea strikeout.A)DeductiveB)InductiveAnswer:B2)Fresh fruit costs more in winter. This is January. Therefore these fresh strawberries will cost more.A)InductiveB)DeductiveAnswer:B3)Every coach knows his sport well. John Madden is a football coach. Therefore John Madden knows footballwell.A) DeductiveB) InductiveAnswer: A4) 31+31=62, 23+3=26, 37+11=48. Therefore, the sum of two prime numbers is even.A) InductiveB) DeductiveAnswer: A5) Practice makes perfect. I have practiced. Therefore, I'll be perfect.A) InductiveB) DeductiveAnswer: B6) All U.S. Presidents have come from the original 48 states. Therefore, no U.S. President can be from Alaska.A) DeductiveB) InductiveAnswer: B7) |-p|=p, therefore |-59|=59A) InductiveB) DeductiveAnswer: B8) If (-p)2=p2, then (-3)2=9A) InductiveB) DeductiveAnswer: BDetermine the most probable next term in the sequence.9) 4, 7, 10, 13, 16A) 18B) 22C) 20D) 19Answer: D10) 38, 31, 24, 17, 10A) 7B) 0C) 3D) 2Answer: C11) 486, 162, 54, 18, 6A) 1B) 2C) 23D) 3Answer: B1

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12)4,-20,100,-500,2500A)-4500B)-12,500C)12,500D)4500Answer:B13)32, 54 , 76, 98, 1110A) 1312B) 1311C) 1211D) 1213Answer: A14) 1, 4, 1, 4, 4, 1, 4, 4, 4, 1, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4A) 4B) 14C) 1D) 14Answer: C15) 1,-13 , 19,-127, 181A)1729B)-1243C)-1729D)1243Answer: B16) 1, 5, 2, 10, 4, 20A) 8B) 30C) 40D) 6Answer: A17) 0002, 0020, 0200, 2000, 2002A) 2000B) 2200C) 2020D) 2003Answer: C18) 8, 13, 20, 29, 40, 53A) 70B) 68C) 64D) 66Answer: BUse inductive reasoning to predict the next equation.19) 66-64+62-60=67-65+63-6176-74+72-70=77-75+73-71A) 86+84-82-80=87+85-83+81B) 86-84-82+80=87-85+83-81C) 86+84-82+80=87+85-83+81D) 86-84+82-80=87-85+83-81Answer: D20) 8×10=9×11-1910×12=11×13-23A) 12×14=13×15-25B) 12×14=13×15-27C) 12×14=13×15+25D) 12×14=15×23-27Answer: B2

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21)3×3=933×33=1089333×333=110,889A) 333×3333=11,108,889B) 3333×3333=111,889C) 3333×3333=112,889D) 3333×3333=11,108,889Answer: D22) 5×6=7×8-(5+6+7+8)6×7=8×9-(6+7+8+9)A) 7×8=9×10-(7+8+9+10)B) 7×8=9×10-(5+6+7+8+9+10)C) 8×9=10×11-(7+6+5+4)D) 8×9=10×11-(8+9+10+11)Answer: A23) (1×9)-7=2(21×9)-7=182(321×9)-7=2882A) (4321×9)-7=28,882B) (4321×9)-7=3881C) (4321×9)-7=38,882D) (432×9)-7=38,882Answer: C24) (7×1) x (2×1)=14(7×10) x (2×2)=280(7×100) x (2×3)=4200A) (7×1000) x (2×4)=63,000B) (7×1000) x (2×4)=56,000C) (7×1000) x (2×4)=5600D) (7×1000) x (2×4)=49,000Answer: B25) 37,037×3=111,11137,037×6=222,22237,037×9=333,33337,037×12=444,444A) 37,037×18=666,666B) 37,037×13=481,481C) 37,037×15=555,555D) 111,111×15=1,666,665Answer: C3

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26)13=12 1-1313+19=121-1913+19+127=12 1-12713+19+127+181=12 1-181A) 13+19+127+181+1729=121-1729B) 13+19+127+181+1162=121-1162C) 13+19+127+181+1243=131-1243D) 13+19+127+181+1243=12 1-1243Answer: D27)8(5)=10(5-1)8(5)+8(25)=10(25-1)8(5)+8(25)+8(125)=10(125-1)8(5)+8(25)+8(125)+8(625)=10(625-1)A) 8(5)+8(25)+8(125)+8(625)+8(1250)=10(1250-1)B) 8(5)+8(25)+8(125)+8(625)+8(3125)=10(3125-1)C) 8(5)+8(25)+8(125)+8(625)+8(3125)=8(3125-1)D) 8(5)+8(25)+8(125)+8(625)+8(5000)=10(5000-1)Answer: BUse the method of Gauss to find the sum.28) 1+2+3+. . .+850A) 180,625B) 361,675C) 722,500D) 361,250Answer: B29) 1+2+3+. . .+1000A) 500,000B) 500,500C) 1,002,001D) 250,000Answer: B30) 1+2+3+. . .+675A) 228,150B) 456,976C) 227,812.5D) 113,906.25Answer: A31) 2+4+6+. . .+500A) 15,625B) 62,500C) 252,004D) 62,750Answer: D32) 4+8+12+. . .+700A) 61,250B) 490,000C) 61,600D) 7656.25Answer: C4

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Find a pattern and use it to solve the problem.33)Find the next term:F,S,S,M,TA)WB)FC)TD)SAnswer:A34)Find the next term: 1, 1, 2, 3, 5, 8, 13A)15B)21C)18D)16Answer:B35)Find the next term: 2, 3, 5, 7, 11, 13A)15B)16C)19D)17Answer:D36)Find the next term:5,10,15,25A)35B)55C)30D)50Answer:A37)Find the next term: T, F, S, E, T, T, FA)TB)SC)ED)FAnswer:B38)Find the next term:25,4,21,6,15,8A)23B)0C)7D)11Answer:C39)How many line segments are used in the next figure?A)36B)27C)24D)30Answer:D40)How many triangles are in the next figure?A)36B)16C)12D)18Answer:B41)Draw the next figure in the pattern.A)B)C)D)Answer:D5

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42)Draw the next figure in the pattern.A)B)C)D)Answer:DDetermine if the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic orgeometric, give the next term in the sequence.43)4,9,14,19,24, . . .A)neitherB)arithmetic;29C)geometric;29Answer:B44)13,23,33,43,53, . . .A)neitherB)geometric;63C)arithmetic;63Answer:C45)5,10,20,40,80, . . .A)neitherB)geometric;160C)arithmetic;160Answer:B46)1701,567,189,63,21, . . .A)neitherB)geometric;7C)arithmetic;7Answer:B47)9,14,14,19,19, . . .A)arithmetic;24B)neitherC)geometric;24Answer:B48)5,8,13,20,29, . . .A)arithmetic;40B)geometric;40C)neitherAnswer:C49)10,20,30,50,80, . . .A)arithmetic;130B)neitherC)geometric;130Answer:B50)0,5,10,20,30, . . .A)arithmetic;40B)geometric;40C)neitherAnswer:C6

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Use the method of successive differences to determine the next term in the sequence.51)21,41,63,87,113, . . .A)143B)142C)141D)139Answer:C52)5,11,49,119,221, . . .A)386B)355C)387D)323Answer:B53)10,17,36,75,142,245, . . .A)392B)384C)404D)400Answer:A54)3,26,103,278,617,1208, . . .A)2139B)2161C)2183D)2151Answer:BDetermine what the next equation would be, and verify that it is indeed a true statement.55)(7×1)×(2×1)=14(7×10)×(2×2)=280(7×100)×(2×3)=4200A) (7×1000)×(2×4)=5600B) (7×1000)×(2×4)=63,000C) (7×1000)×(2×4)=56,000D) (7×1000)×(2×4)=49,000Answer: C56) 13+31=4414+41=55A) 15+51=66B) 33+33=66C) 15+51=62D) 51+15=66Answer: A57) 20-9=11200-89=1112000-789=1211A) 2000-6,789=13,211B) 200,000-6,789=13,211C) 20,000-6,789=13,211D) 20,000-6,789=193,211Answer: C58) 44×44=1936404×404=163,216A) 4004×404=16,032,016B) 4004×4004=1,617,616C) 4004×4004=1,603,202D) 4004×4004=16,032,016Answer: D7

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59)32+10=4243+21=6454+32=86A) 65+32=97B) 65+43=108C) 56+43=99D) 64+53=117Answer: B60) (1×9)-5=4(21×9)-5=84(321×9)-5=2884A) (4,321×9)-5=3883B) (4,321×9)-5=38,884C) (4,321×9)-5=28,884D) (432×9)-5=38,884Answer: B61) 8×10=9×11-1910×12=11×13-23A) 12×14=15×23-27B) 12×14=13×15-27C) 12×14=13×15+25D) 12×14=13×15-25Answer: B62) 8×9=10×11-(8+9+10+11)9×10=11×12-(9+10+11+12)A) 11×12=13×14-(11+12+13+14)B) 10×11=12×13-(8+9+10+11+12+13)C) 10×11=12×13-(10+11+12+13)D) 11×12=13×14-(10+9+8+7)Answer: C63) 32-12=2×442-22=2×652-32=2×8A) 62-4=2×16B) 62-42=2×10C) 62-42=4×5D) 72-52=2×12Answer: BUse the indicated formula to find the sum.64) Use S=n(n+1)2to find the sum of 1+2+3+. . .+700.A) 244,650B) 24,535C) 245,000D) 245,350Answer: D65) Use S=n(n+1)2to find the sum of 1+2+3+. . .+625.A) 195,000B) 194,376C) 195,312D) 195,625Answer: D8

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66)Use S=n2 to find the sum of 1+3+5+. . .+701.A) 123,200B) 122,500C) 123,202D) 123,201Answer: D67) Use S=n(n+1)2to find the sum of 10+11+12+. . .+600.A) 180,264B) 180,300C) 179,664D) 180,255Answer: D68) Use S=n2 to find the sum of 11+13+...+901.A) 202,475B) 203,376C) 181,476D) 203,401Answer: B69) Use S=n2 to find the sum of 1+3+5+. . .+499.A) 15,625B) 124,002C) 62,001D) 62,500Answer: D70) Use S=n(n+1)2to find the sum of 20+21+22+. . .+725.A) 262,985B) 262,279C) 263,004D) 262,260Answer: A71) Use S=n(n+1)2to find the sum of 1+2+3+. . .+3000.A) 4,499,999.5B) 2,249,250C) 4,501,500D) 4,498,500Answer: CUse the appropriate formula to find the indicated figurate number.72) the 6th square numberA) S6=12B) S6=36C) S6=21D) S6=49Answer: B73) the 8th hexagonal numberA) H8=120B) H8=96C) H8=40D) H8=136Answer: A74) the 5th triangular numberA) T5=30B) T5=15C) T5=10D) T5=12.5Answer: B75) the 10th octagonal numberA) O10=30B) O10=150C) O10=280D) O10=125Answer: C76) the 16th heptagonal numberA) Hp16=30.4B) Hp16=640C) Hp16=664D) Hp16=616Answer: D9

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77)the8th pentagonal numberA)P8=92B) P8=36C) P8=100D) P8=64Answer: ASHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Solve the problem using inductive reasoning.78) How many line segments are determined by joining dots on the last two circles?3 segments6 segmentssegmentssegmentsAnswer: 4+3+2+1=10 segments6+5+4+3+2+1=21 segments79) Find the number of games played in a round robin tournament for the given numbers of teams. In a roundrobin tournament every team plays every other team once.Number of teamsNumber of games played3 teams3 games4 teams6 games5 teams10 games6 teamsgames7 teamsgamesAnswer: 5+4+3+2+1=15 games6+5+4+3+2+1=21 games80) Write the next three "square" figurate numbers.Answer:42=1652=2562=3681) Write the next three "triangular" figurate numbers.Answer:10, 15, 2110

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82)How many rectangles are there in the last two figures?→1 rectangle→3 rectangles→?rectangles→?rectanglesAnswer: 6+5+4+3+2+1=21 rectangles10+9+8+7+6+5+4+3+2+1=55 rectangles83) When the numbers in the sequence of n-agonal numbers are divided by n, the sequence of remainders obtainedis a repeating sequence. Verify this for n=7 and find the repeating sequence of remainders.Answer: The pattern is 1, 0, 4, 6, 6, 4, 0, 1, 1, 0, 4, 6, 6, 4, 0, 1, . . ..84) Choose a value of n greater than 1. Find Sn and multiply it by 3. Find Tn and multiply it by 2. Subtract thesmaller number from the larger number. In other words calculate 3Sn-2Tn. Repeat this for various values of n.What kind of figurate numbers do you get?Answer: HexagonalMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Determine the indicated term in the given sequence.85) The 12th term of 1, 7, 13, . . .A) 73B) 66C) 69D) 67Answer: D86) The 9th term of 4 , 12 , 36 , . . .A) 8748B) 26,244C) 236,196D) 6561Answer: B87) The 8th term of 5 , 20 , 80 , . . .A) 16,384B) 81,920C) 1,310,720D) 327,680Answer: B88) The 16th term of 37, 67, 97 , . . .A) 457B) 6C) 397D) 487Answer: D89) The 9th term of 5.9, 5.5, 5.1, . . .A) 2.3B) 2.7C) 3.1D) 2.71Answer: B90) The 11th term of 3.47, 3.87, 4.27, . . .A) 7.47B) 8.27C) 7.87D) 9.07Answer: A11

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91)The 16th term of3.48,3.59,3.7, . . .A)5.02B)5.24C)5.13D)4.91Answer:C92)The11th term of3,6,12, . . .A)6144B)12,288C)1024D)3072Answer:D93)The 8th term of 1, 12, 14 , . . .A) 12B)1128C)1512D)164Answer: B94) The 9th term of 14, 18 ,116, . . .A)11024B)12048C)1256D)172Answer: A95) The 7th term of 18, 6, 2, . . .A)227B)2729C)281D)2243Answer: CUse logic to solve the problem.96) How much dirt is there in a hole 6 feet wide by 8 feet long by 10 feet deep?A) 480 ft3B) 48 ft3C) NoneD) 60 ft3Answer: C97) In India, water lilies grow extremely fast. In one pond, a lily grew so fast that each day it doubled the area itcovered. In 30 days it covered the pond. How long would it take 2 such lilies to cover the pond?A) 29B) 7C) 15D) 30Answer: ASHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.98) Which is heavier, a pound of soap bubbles or a pound of soap?Answer: They both weigh a pound.99) Farmer Higgs owns 5 brown pigs, 3 white pigs, and one black pig. How many of Higgs' pigs can say that it isthe same color as another pig on Higgs' farm?Answer: None. Pigs can't talk.100) Dick and Tom find a long drainage pipe in a vacant lot. It is big enough so that each boy can just manage tosqueeze into it and crawl from one end to the other. If Dick and Tom go into the pipe from opposite ends, is itpossible for each boy to crawl the entire lengthof the pipe and come out the other end?Answer: Yes. First Dick crawls through in one direction. After he comes out, Tom crawls through it the other way.12

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101)Why are1977pennies worth almost twenty dollars?Answer:One thousand, nine hundred,seventy-sevenpennies are worth $19.77, which is almost twenty dollars.102)If it takes6minutes to hard-boil3goose eggs when dropped into boiling water, how long will it take tohard-boil 6 goose eggs?Answer: The same time, 6 minutes.MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.103) If the hometown baseball team scored 2 runs every inning played, and the visiting team scored 1 run everyinning played, what was the final score?A) Home: 18Visitors: 9B) Home: 0Visitors: 0C) Home: 16Visitors: 9D) Home: 18Visitors: 8Answer: C104) During vacation time, two students met on a train. One asked the other how old he was. He replied, "The daybefore yesterday I was 15, and next year I will have my 18th birthday." On what date of the year did the twostudents meet?A) Feb 29B) Dec 31C) Jan 1D) Feb 28Answer: C105) A farmer had a stone weighing 40 pounds that he used to weigh pigs, but the stone broke into 4 pieces. Thefarmer found to his surprise that with the four pieces, he could weigh any whole number from 1 to 40. What dideach of the 4 pieces weigh?A) 1, 3, 7, and 29 lbB) 1, 3, 9, and 27 lbC) 1, 4, 8, and 27 lbD) 1, 4, 9, and 26 lbAnswer: BUse problem solving strategies to solve the problem.106) I'm thinking of a number between 4 and 10. If I square my number and find the difference of the digits, I willend up with the cube root of my number. What is my number?A) 4B) 15C) 9D) 8Answer: D107) A mouse is at the bottom of a 10-foot-tall clock. Every hour he climbs up 3 feet. But when the clock strikes atthe hour, he falls back 1 foot. If the mouse starts climbing at 8 a.m., at what time to the nearest minute will itreach the top of the clock?A) 12:40 p.m.B) 1:10 p.m.C) 12:30 p.m.D) 1:00 p.m.Answer: A108) A rabbit grows so that every 2 months it doubles in weight. However, the rabbit will never go over 75 pounds.If a bunny is born on July 15th, weighing 2 pounds, in which month will it weigh 46 pounds?A) JulyB) AprilC) MarchD) MayAnswer: B109) Donna is older than Steve but younger than Brenda. Kelly is younger than Brandon. What is the first letter in thename of the oldest person?A) SB) DC) BD) KAnswer: C13

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110)The number of dogs and chickens on a farm add up to 12. The number of legs between them is 28. How manydogs and how many chickens are on the farm if there are at least twice as many chickens as dogs?A) 4 dogs, 8 chickensB) 2 dogs, 10 chickensC) 6 dogs, 6 chickensD) 3 dogs, 9 chickensAnswer: B111) A boxer takes 3 drinks of water after each of the first three rounds of a championship fight. After the fourthround he increases the number of drinks by 1. If he continues to increase his drinks by 1 after each round, howmany drinks will he take between the 14th and 15th rounds?A) 15 drinksB) 10 drinksC) 12 drinksD) 14 drinksAnswer: D112) What's the easiest way to heat a pan of water for 9 minutes when you have only a 6-minute hour-glass timerand a 21-minute hour-glass timer?A) Start the 6-min timer. When it's halfway through start heating the water. When it runs out turn it over andheat the water until it runs out again.B) Start both timers. When the 6-min one runs out, turn it over. When it runs out again, start heating thewater until the 21-min timer runs out.C) Start both timers. When the 6-min timer runs out, start heating the water. Continue until the 21-min timerruns out.D) Can't be done.Answer: B113) There is a number between 100 and 115, such that if you find the sum of the cubes of the digits, subtract thissum from 99, divide the result by 3, and add the digits once more, you get 2. What is the number?A) 114B) 102C) 105D) 113Answer: A114) There is a number between 2 and 8, such that if you raise any of the remaining numbers to the power of thisnumber, the units digit of the result will always be equal to the base. What is the number?A) 8B) 3C) 2D) 5Answer: DSolve the problem.115) If you raise 9 to the 387th power, what is the units digit of the result?A) 9B) 6C) 1D) 7Answer: A116) If you raise 4 to the 214th power, what is the units digit of the result?A) 4B) 2C) 6D) 8Answer: C117) Sally and Karl work at different jobs. Sally earns $7 per hour and Karl earns $5 per hour. They each earn thesame amount per week but Karl works 2 more hours. How many hours a week does Karl work?A) 9B) 11C) 5D) 7Answer: D118) An average library contains at least 50 and at most 250 books. How many library owners must be polled to becertain that at least two owners have the same number of books in their libraries?A) 200 ownersB) 203 ownersC) 202 ownersD) 201 ownersAnswer: C14

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119)A cell has at least 3 and at most 47 nucleii. How many cells must a scientist view under his microscope to becertain that at least two cells have the same number of nucleii?A) 46 cellsB) 45 cellsC) 44 cellsD) 47 cellsAnswer: A120) A girl asks her father how many ties he has and he answers with a riddle: "Seven-eighths of my ties plus five."How many ties does her father have?A) 50B) 35C) 45D) 40Answer: D121) When 5 gallons of gasoline are put into a car's tank, the indicator goes from 18of a tank to 34 . What is the totalcapacity of the gasoline tank?A) 12 gallonsB) 6 gallonsC) 8 gallonsD) 10 gallonsAnswer: C122) five painters can paint two rooms in 7 hours. How many rooms can a painter paint in 1 hour?A) 14 roomsB)710of a roomC)235of a roomD)514 of a roomAnswer: C123) Ethan was asked by his teacher to subtract 10 from a certain number and then divide the result by 5. Instead, hesubtracted 5 and then divided the result by 10, giving an answer of 25. What would his answer have been if hehad worked the problem correctly?A) 49B) 51C) 50D) 24.5Answer: ADetermine the number of figures (of any size) in the design.124) Squares (of any size)A)13B) 12C) 18D) 17Answer: D15

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