2021年大联盟(Math League)国际夏季五年级数学挑战活动二

PAGEPAGE102021美国"大联盟"(MathLeague)国际夏季数学挑战活动2021MathLeagueInternationalSummerChallengeGrade5,SpeedQuestions1.(2021÷5)+(2021÷5)+(2021÷5)+(2021÷5)+(2021÷5) =A)2020 B)2021 C)2022 D)8084Kirokthedragonhas2021scalesonhisneck,3031scalesonhiswings,and5051scalesontherestofhisbody.WhatisthetotalnumberofscalesonKirok’sbody?A)1013 B)7073 C)10103 D)100103Whatistheremainderwhen(7+77+777+7777)isdividedby7?A)0 B)1 C)4 D)1234FouroutofeveryfivedentistsrecommendHiGlotoothpaste.IfIask100dentistswhethertheywouldrecommendHiGlotoothpaste,howmanyofthedentistswillrecommendit?A)25 B)30 C)50 D)80Whatistheperimeterofasquarethathasanareaof64?A)16 B)24 C)32 D)646.4×5×101=1010×?A)2 B)20 C)101 D)1010Eachangleofarectangleis?degreesgreaterthaneachangleofanequilateraltriangle.A)30° B)60° C)90° D)120°Itis2021hoursaftermidnight.Whattimeisit?A)5AM B)7AM C)5PM D)7PMIf20%ofanumberis50,whatis40%ofthesamenumber?A)30 B)60 C)100 D)150Asherides,SirReginaldvonPrimeisgoingtoplantaflageverytimethetotaldistancehehasriddenisaprimenumberofkm.Howfarwillhehavegonewhenheplantshis11thflag?A)23km B)29km C)31km D)37kmThegreatestcommonfactorof43×52and53×72isA)5 B)52 C)53 D)55Howmany2-digitoddnumbersdonothave3aseitherdigit?A)32 B)36 C)40 D)44Myaveragescoreonthe3testsI’vetakensofaris85.WhatscoredoIhavetogetonthenexttoraisemyaveragescoreto88?A)94 B)95 C)96 D)97Nanknitsnewtopsfornewborns.Todaysheknittedonemoretopthanyesterday.ThenumberoftopssheknittedinthetwodayscombinedcouldbeA)12 B)23 C)34 D)1008dozensocks=?pairsofsocksA)24 B)36 C)48 D)96Aboyisinlinewith30peoplebehindhimandtwiceasmanyaheadofhim.Howmanypeopleareinthisline?A)60 B)61 C)90 D)91Ifthesumof6consecutiveintegersis255,whatisthesumofthegreatestandtheleastoftheintegers?A)38 B)43 C)81 D)85Paolaranthe300mfromherdoortothebusin20seconds.Whatwasherspeedinkm/hr?A)15 B)20 C)34 D)54Whatistheproductofallthepositivedivisorsof64?A)64 B)8×642 C)8×643 D)644double,mysister’sagewilltriple,andmybrother’sagewillquadruple!Whatisthesumofouragesnow?A)32.5 B)55 C)90 D)100.5Thegreatestprimefactorofthenumberofsecondsin2197hoursisA)11 B)13 C)17 D)19InthecountryofLatka,6simkasareworth25ibidasand2ibidasareworth15yatabes,IfIpay12simkasforachickenthatispricedat365yatabes,howmanyyatabesshouldIexpectinchange?A)10 B)12 C)13 D)15Alighthousecanbeseenfromatmost50kmonaclearnightbutfromatmost20kmduringfog.Thegreatestviewingdistanceonaclearnightiswhatpercentofthegreatestduringfog?A)40 B)60 C)150 D)250Whatisthegreatestpossiblenumberofpointsofintersectionsofacircleandarectangle?A)2 B)4 C)6 D)8Howmanysquaresofintegershave3digits?A)20 B)21 C)22 D)23Alwritesthefirst20%ofhisreportonMonday,then30%oftheremainingreportonTuesday.WhatpercentoftheentirereportthatAlbeganonMondayremainstobewrittenonWednesday?A)44% B)50% C)54% D)56%27.42×44×46×48=A)240 B)41024 C)1630 D)6430Zakshuffledtogetherfourdecksofcardsandstarteddealingthemout.Surprisingly,thesuitscameoutinapatternthatrepeatedasfollowsuntilthe26thclubappeared:club,diamond,heart,club,heart,diamond,club,diamond,heart,club,heart,diamond,HowmanycardsmustZakdealinordertohavedealt26oftheclubsuit?A)75 B)76 C)78 D)84Mylocalicecreamshopoffers15differentflavorsoficecream.IfIwanttwoscoopsoficecream,eachscoopadifferentflavor,howmanycombinationsoftwoscoopsoficecreamarepossible?A)29 B)30 C)105 D)210Inezmultiplied21bytheproductof2121s.Thenshesubtracted21fromthattimes.Withwhatnumberdidsheendup?A)0 B)2120 C)2121+212 D)2122–212Whatisthegreatestnumberofprimefactors(notnecessarilyalldifferent)thatathree-digitnumbercanhave?A)5 B)6 C)8 D)9Howmanyofthefirst2021evenpositiveintegersaredivisibleby6?A)336 B)337 C)673 D)674Maestromustbeabletodividethebirdsinhisall-birdchoirinto6,7,and8equalwantsa3-digittotalnumberofbirds.Inall,howmanysuch3-digitnumbersarepossible?A)2 B)3 C)4 D)5If25peopletake27hourstocatchallthebirds,atthatratehowlongwouldittake45peopletocatchallthebirds?A)9hrs B)15hrs C)18hrs D)21hrsWhatistheleastnumberofconsecutivepositiveintegersstartingwith1thatmustbemultipliedtogethertogetamultipleof2021?A)22 B)80 C)90 D)105(2+4+8)2=A)(3+4+5)2(4+5+6)×2(1+2+4)2×4D)22+42+82Eachequilateraltriangleshownhasaperimeterof9.Whatistheperimeterofthefigure?A)6 B)8 C)10 D)12Thebaseofanisoscelestrianglewithintegralsidesis12.Whatcouldbetheperimeter?A)20 B)22 C)24 D)26Emmacountedupfrom0by1severysecondfor5minutes,andthendownby1severysecondfor2minutes.Whatnumberdidsheendon?A)180 B)240 C)360 D)480Whatisthe200thnumberinthesequence1,1,1,2,1,3,1,4,1,5,...?A)1 B)100 C)101 D)2002020isdivisibleby?differentprimenumbers.A)2 B)3 C)4 D)5Thelargeranglebetweentheminutehandandthehourhandofacircularclockat1:10PMmeasuresA)300° B)315° C)330° D)335°Howmanyprimenumberslessthan50havereciprocalsthatareterminatingdecimals?A)1 B)2 C)3 D)4Redpensaresoldat3for$1andblackpensaresoldat4for$1.50.Alicebought12redpensand24blackpens.Shepaidforthemwitha$20bill.Howmuchchangedidshereceive?A)$7 B)$9 C)$13 D)$16Thenumber1000hasonly16positivewholenumberfactors.Theproductofall16ofthesefactorsisA)108 B)1016 C)1024 D)1032Theaverageof21consecutiveintegersis31.ThelargestoftheseintegersmustbeA)40 B)41 C)51 D)5247.(221×1000)+(221×100)+(221×10)+(221×1)isdivisiblebyA)2 B)3 C)4 D)1148.314159272–314159262=31415926+?A)0 B)31415927 C)31415928 D)31415925Eachkmofa5kmrace,myhorse’saveragespeeddecreased1km/hr.IfIaveraged5km/hratfirst,ittookme?minutestofinish.A)120 B)137 C)216 D)685Imakeastraightcutthrougharectangularpieceofpaperandgettwopieces.WhenImakeastraightcutthroughoneofthesetwopieces,Ithenhavethreepieces.Altogether,thenumberofedgesonthesethreepiecescannotbeA)8 B)9 C)10 D)1151.

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17 D)noneofthese154A)4 B)25 C)50 D)100Ifthetotalvalueofanequalnumberofpennies,nickels,anddimesis$3.20,whatisthevalueofthenickelsalone?A)40cents B)60cents C)80cents D)100centsWhatistheonesdigitof22021?A)2 B)4 C)6 D)8Thesumof50consecutivewholenumbersequalsthesumof25otherconsecutivewholenumbers.Ifthesmallestofthe50numbersis2021,thesmallestofthe25numbersisA)4079 B)4103 C)2021 D)2070IfBisthe