2022年大联盟(Math League)国际夏季五年级数学挑战活动二（含答案）

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10

SpeedQuestions,Grade5

2022MathLeagueInternationalSummerChallenge(Unofficialversion,forreferenceonly)

Note:

ListedbelowarethefourtypesofcoinscurrentlybeingmintedinUnitedStates.

Penny:1¢

Nickel:5¢

Dime:10¢

Quarter:25¢

1.1%of1%=

1

1%

11000

1%

100

Answer:D

2.200%of? isaprime.

1

2

3

5Answer:A

1

3. 1 =

1

2+

2+

2

13

25

29

512

Answer:D

Findthemissingnumber:44×55=4×5.

?

11

22

45

D)121

Answer:D

TheaverageofsixconsecutivewholenumberscouldbeA) 361

3

B)441

6

C)481

2

54Answer:C

If5%ofacertainnumberis16,then25%ofhalfthenumberis

2

4

40

80Answer:C

Ali’scrystalballgrantstwo-fifthsofone-fifthofallwishes.Thisis？ofallwishes.

35

225

8

60Answer:C

Afteragirlspends1

3

ofhermoneyandloses1

2

oftheremainder,shethenhas$10

left.Shestartedwith

A) $30

B)$45

C)$50

D)$60Answer:A

Whichofthefollowingfractionshasthegreatestvalue?

A) 51100

B)152

300

52103

5099

Answer:A

If5applescostthesameas4oranges,findtheratioofthecostof1appletothecostof1orange.

A) 5:9

B)4:9

C)5:4

D)4:5

Answer:D

Theleastcommonmultipleof1,2,3,4,5,6,7,8,9,and10is

A) 1

B)1260

C)2520

D)3628800

Answer:C

Bywhatfractionalpartof4

5

does3

5

exceed2?

5

15

14

25

35

Answer:B

Inarighttrianglewhoseareais12,eachlegisaslongasthesideofacertainsquare.Whatistheareaofthesquare?

12

24

48

D)144

Answer:B

Findthelastdigitof19831984.

1

2

3

9Answer:A

Ihave5coinsofequalvalueinmyleftpocket,and2coinsofequalvalueinmyrightpocket.Ifthetotalvalueofthecoinsineachpocketisthesame,myleftpocketcontains

pennies

nickels

dimes

quartersAnswer:C

Acirclehasanareaof36π.Whatistheareaofthesmallestsquarethatcansurroundthiscircle?

18

48

72

D)144

Answer:D

Thenumber1000hasonly16positivewholenumberfactors.Theproductofall16ofthesefactorsis

A) 108

B)1016

C)1024

D)1032

Answer:C

18.1112131202112022

1

0

1

D)1011

Answer:B

IfBo’sscorewas8/10ofAl’s,andCy’sscorewas3/4ofBo’s,thentheratioofAl’sscoretotheaverageofBo’sandCy’sscoreswas

A) 10:7

B)7:10

C)5:3

D)3:5

Answer:A

Jackpicks3litersofberriesin8minutes.Jillpick4litersofberriesin10minutes.Workingtogether,howmanyberriescantheypickin1minute?

79

718

819

3140

Answer:D

5%iswhatpercentof0.1?A) 10%

B)50%

C)200%

D)500%

Answer:B

Thelengthofaradiusofacircleisdecreasedby10%.Thiscausestheareatobedecreasedby

A) 19%

B)20%

C)21%

D)25%

Answer:A

999999

Thehundredsdigitof is

3

5

7

9Answer:D

Anantcrawlsoutsideasquareofside1cm,atalltimesremainingexactly1cmfromtheboundaryofthesquare.Insquarecm,theareaboundedbyonecompletecircuitoftheantismostnearlyequalto

7

8

9

10Answer:B

Fromnoononedaytillnoon2dayslater,howmanytimeswillthehourhandofaclockpassthe1o’clockmark?

2

3

4

48Answer:C

Thereciprocalof1.01isA) 0.101

B)1.01

C)0.99

D)100

101

Answer:D

If,every2seconds,aunicyclewheelofradius1mrollsoncearoundwithoutslipping,whatisthewheel’saveragegroundspeed?

0.5m/sec

m/sec

2m/sec

4m/sec

Answer:B

ThevolumeofcubeⅠis331m3lessthanthevolumeofcubeⅡ.Ifanedgeof

cubeⅠis10meters,anedgeofcubeⅡis

14meters

13meters

12meters

11metersAnswer:D

29.727272727272727?

72

73

77

78

Answer:A

Whichofthefollowingfigurescannotbefoldedalongthedottedlinestoformacube?

A)

B)

C)

D)

Answer:D

WhenIturnmycalculatorupsidedown,thedigits0,1,2,5,6,8,and9stillappearasdigits.Forexample,WhenIturnmycalculatorupsidedown,65259remainsthesame—thatis,itstays65259.Howmanywholenumbersbetween100and1000remainthesamewhenIturnmycalculatorupsidedown?

A) 6×7

B)6×5

C)6×5×6

D)6×7×6

Answer:B

Foreachwholenumbern1,listallthefractionsbetween0and1with

denominatornandawholenumbernumerator.Thelist,whichbegins

1,1,

2 3

2,1,

3 4

2,3,

4 4

1,…,continuesinincreasingorderforeachdenominator.The100thsuch

5

fractionis

846

946

1046

1146

Answer:C

Ifthehandsonaroundclockmovedcounterclockwise,towhatnumberwouldtheminutehandpoint20minutesbeforethehourhandpointedtothe3?

4

7

8

11Answer:A

IfMandNarepositivetwo-digitnumbers,then,ofthefollowingfractions,theonewiththelargestvalueis

NM

N1

M1

N1

M

NM1

Answer:B

Findtheareaofthetrapezoidbelow.

44

48

90

D)100

Answer:A

IfA)

a0

ab

and

b0,whichofthefollowingmustbetrue?

ab

ba0

ab0

Answer:C

37.299(2)99

A) 099

B)299

C)2198

D)499

Answer:A

Thefirst1000primesaremultipliedtogether.Thisnumbermustbedivisibleby

A) 10

B)100

C)1000

D)101000

Answer:A

Twosidesofatrianglehavelengths9and11.Ifnotwosidesofthetrianglehaveequallengths,theperimetercouldbe

21

23

29

31Answer:B

Toformacertainsequence,therulesare:

Ifanumberiseven,divideby2togetthenextnumber;

Ifanumberisodd,multiplyby3,thenadd1tothenextnumber.

Startingwith12,thefirstfewtermsare12,6,3,10,5,16,…Inthisparticularsequence,the100thtermis

1

2

3

4Answer:A

If

x3

representsanevennumber,thenwhichofthefollowingwillalways

representanoddnumber?

x1

6x4

3x5

5x8

Answer:D

Anumberisroundedtothenearestwholenumber.Theoriginalnumberisthenroundedtothenearestten.Thedifferencebetweenthe2newnumbersformedcannotbe

3

4

5

6Answer:D

Howmanyofthefirst1992primenumbershavereciprocalswhicharelessthan0.05?

A) 1972

B)1984

C)1985

D)1988

Answer:B

Ifxpeoplecandoajobinddays,howlongwouldittakeypeopletodothesamejob?

x

yd

xdy

yxd

ydx

Answer:B

Thereare2red,3blue,and4greenmarblesinabag.Itakeonemarbleatatimeoutofthebagwithoutlooking.WhatistheleastnumberofmarblesImusttakeouttobesurethatIhave3ofthesamecolor?

3

5

7

9Answer:C

IfPatisA) 20%

B)25%

C)30%

331%tallerthanLee,thenLeeiswhatpercentshorterthanPat?

3

D)331%

3

Answer:B

Howmanydifferentintegershavereciprocalswhosevaluesaregreaterthan

19 andlessthan

1998

78

79

84

85Answer:D

98?

1998

Whatistheremainderwhentheproductofalltheprimenumbersbetween1and100isdividedby4?

3

2

1

0Answer:B

Asshown,avertexofasquarewithsidesoflength2,andthecenterofacircle

witharadiusof2,coincide.Whatistheareaoftheshadedregion?

A) 44

B)24

C)34

D)

Answer:B

Whatisthequotientoftheleastcommonmultipleofthefirst40positiveintegersdividedbytheleastcommonmultipleofthefirst30positiveintegers?

A) 1147

B)2294

C)36704

D)89466

Answer:B

InProfessorTuffguy’smathematicsclass,36studentstookthefinalexam.Iftheaveragepassinggradewas78,theaveragefailinggradewas60,andtheclassaveragewas71,howmanyofthesestudentspassedthefinal?

14

22

24

29Answer:B

FrankandAlicewenttoa“BringaSnack”party.Frankspent10pennies+16dimes.AlicespentasmuchasFrank,buther26coinsconsistedofonlyquartersandnickels.HowmanynickelsdidAlicespend?

16

20

22

24Answer:D

Intheorderedsequence1,2,2,3,3,3,4,4,4,4,…,eachpositiveintegernoccursinablockofnterms.IfIaddthereciprocalsofalltheterms,inorderbeginningwiththefirstterm,thenatsomepointthesumwillbe

A) 98.1

B)99.25

C)100.5

D)102.75

Answer:B

Ifnisapositiveinteger,n！istheproductofthefirstnpositiveintegers.For

example,

4！432124.Ifuandvarepositiveintegersand

u!v!56,thenv

couldequal

6

8

56

57Answer:A

Ifthelengthsofthesidesofarectangleareintegers,andifonesides