2015-2019美国数学大联盟杯赛Math League6年级及答案

2015-2016年度美田“数学大联盟2015-2016年度美田“数学大联盟杯赛”（中国赛区）（初赛时间；2015年11月14日，考试时间90分钟，总分200分灼为我个人独立完成的成果｀否则应接受本次成续无效的处罚 如果怎同意遵守以上协议请在装订线内签选择题：每小题5分，答对加5分，答错不扣分，共200I.(20x」+6){20X]5 D)ITimlovest()workoutinthegym)Thegymchargeshim$100foraoae-time1-egistrationfeeandthen$4 C) D)4x104+Qxl03+3xl02+2xl01=2016X B) lttookmetwiceasmuchtimelodophysicshomeworkthantodocalculushomework.Ididmyphysicshomeworkin9000seconds.Howlong,inhours,didittakemetodothecalculushomework? B) C) D)Ineedtopack1l2booksusinglargeandsmallboxes,Alargecanstore5books.Whatistheleastlmustspendonboxestopackallll2books? C) D) B) C) Whichofthefollowing.isnota B) C) D)maybe_1_cmtall. B) C) D)Theareasofanisoscelesrighttriangleandarectanglearethesame.Thetrianglehasalegof6.The B) I0.Whenanintegei-isdividedby3,theremaindercannotbe B) ll26x56x103＝乌 B) C)10 D)1012.ApeTfectsquaTecannothaveexactly_j_positiveA) D) D)calculatorforsalefor$50.Hethenincreasedthesalpriceby25%sincehewasverygr沈dy.Whennooneby上 C) C) Ofthefollowing,whichisclosestto(22v,)/(52'16)? B)1008x992=lOOO"，-

Jackistheweallhiestpersonintheto叩！Hehas$280morethanJill.ThemoneyJillhasisonly60%ofthemo1JeyJackhas.Jackhas$.1... C) D)SquareA'sperimeteris9timesaslargeasthatofSquareB.IfthelengthofasideofSquareBis1,whatistheareaofSqllareA? B) C) D)sbebuys_J_bMkstotal. B) D)ThedigitsofanumberNareallIs.[fNisdivisibleby3and11,Ncanhave_j_山 A) B) ThentimberNwhenroundedtothenearesthundredthis2016.WhenroundedtothenearestthousandthNisatmost C) D) Whatfractionofthefactorsin65"xIW5are C) D)Fig11reAisacirclewithradius6FigureBisabt)unded的micirclewithradius6.Whatistheratiooft:he B)2: C)2兀兀＋ D)叶2:2Rotatingafigu沁225°clockwiseandthen1170°counterclockwiseisthesameasrotatingthefigure_.1_ C) D)Threediffe,entl.inesandasquarecanhaveatmost_J_pointsofinte,se>Ctions[Note:Theverticesofthesquaredonotcounta�inle,se,ctions.] C) D)Onanumberline,theKingTortoisestandsatI7andtheQueenHarestandsal1.TheyarebothmovingtotherightThetortoise'sspeedisJrn/sandthehare'sspeedis7m/s.Theymeetat C) Ifthes111nofalltheiI仆egersfrom64to126is5985whatisthe�urnofthefirs!63positive ThepossiblescoresonecangelontheAIMElestisanintegerfromOto15.100studentsinmyschoolappearsmostfrequentlyinaseriesofnumbers.) Whichofthefollowingnumbersisnotdi.visibleby4,9,and FourpairsoftwinsenteraraflleeventThereare70wayslopick4winnersThereare_1__waysto Nisatwo-digit.number.WhenNisdividedbyits011esdigit,thequotientis8and!heremainderis1WhenNi�dividedbyitstensdigit,thequotientis11andthe.remainderi�2.Whatisthevalueof1V? C) C) D)C)Itcosts$350tobuy3broccolo7banana�andI.pearItco$450tobuy4broccolo,IObananas,andIpear.HowmuchdoesitcosttobuyIbroccoli,IbananaandIpear? C) D)Mike,Lucy,andJerryvisitedsomeofcitiesX,Y,andMike:"1visitedmorecitiesthanLucy.Ihaven'tvisitedcityZ."Lucy:·'Ihaven'tvisitedcityY"Jeny:'Thereisonecitythatallthreeofusvisited." B)LucyvisitedcityXC)LucyvisitedcityZ D)LucyvisitedcitiesXand38进步先生在不断提高他的考试成绩．他前两次考试的平均分是86,前三次考试的平均分是87,前匹次考试的平均分是88,他第四次考了多少分？A) B) C) D)39做家务是迪的兴趣．迪每8天进行次大扫除，每11天洗次衣服．如果星阴天迪做了两件家务，那么下一次她做两件家务会是哪一天？A)星期 B)星期 C)星期 D)星期40将I,2,...,13,这13个不同的自然数监新排成行，记作a1=13,a2=l凸并使01+a只．．a..能被a炉1整除(Ir:=1,212),求a3+an B) C) D)选择题；每小题5分，答对加5分，答错不扣分，共200分，答案请填涂在答愿卡上．l2.C)B)trape乙A)D)A)B)JO2:2兀叶叶2:2135D)7LucyvisitedcilyXLucyvisitedcityZLucyvisitedcitiesXand40（六年级（2016年11月20日，考试时间90分钟，总分200分均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。5分，答对加5分，答错不扣分，200分，答案请填涂在答题卡I.IfIgive28coinstoeachofmy8friendsIwillhave3coinsleftover.Ihave_J_ 8)Tothenearestten,54.545

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D)3Alwantstofinishreadinghisbookatexactly7P.M.Hehas36pageslefttoread,andhecanread4pagesevery9minutes.Atwhattimeshouldhestartreading?5.++ B)6:19 C)6:445.++ Ihave3jarswithI00jellybeansineach,and6jarswith250jellybeansineach.Whatistheaveragenumberofjellybeansineachjar? Thegreatestcommonfactorof1234and20I7 D)2488HowmanywholenumbersfromIOIto199havebothaneventensdigitandanevenones Asquareandanequilateraltrianglehavethesameside-lengths,andthetotaloftheirperimetersis42Whatistheareaofthesquare? 8)l0.ThesquareofaprimeCANNOTbe

D)divisibleby92016-数学大联盟杯(20000x30000x40000x50000)-c-(I000x2000x3000x2016-数学大联盟杯 8)10 C)49 D)50Ifthecircumferenceofacertaincircleisdividedby兀，thequotientis8.Iftheareaofthesamecircleisdividedby兀，thequotientis D)Acarthatwaspricedat$20000isonsalefor$16000.Thatisapricereduction exactly$15,Ibought..1_plums.

Thereareonlywhitecarsandblackcarsinagarage.Iftheratioofwhitecarstoblackcarsis3to8Thereciprocal lplusthesquareoflminusthecube l l8、丿B)D)l8、丿B)D) C) D)Howmanywhole-numberfactorsdoes8640 0.125%of25%of128

Thereareoverl000studentsatmyschool.Whenthenumberofstudentsisdividedbyl0,theremainderis3.Whenthenumberisdividedby13,theremainderis3.Whatistheremainderwhenthenumberisdividedby130?IamtravelingatI00kmperhour.HowfarwillItravelin18 D) 8) Thepriceofacomputergoesup20%,thendown40%,thenup20%.Afterallthreechanges,thefinalpriceis__J__ofthestartingprice?

Whenwrittenasadecimalnumber,100x102016100has_J_小 ThearithmeticaverageofI,I,and-:- B)

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l EachsideofsquareS,pentagonP,andhexagonHisaninteger.Iftheperimeterofeachfigureisthesame,theperimetercouldbe Aunitfractionisafractionwhosenumeratorislandwhosedenominatorisawholenumber.numberofunitfractionsbetween- an.100

PumpsAandBworkingtogethercandrainmyfilledpoolin6hours,pumpsAandCworkingtogethercandrainitin8hours,andpumpsBandCworkingtogethercandrainitin12hours.Ifall3pipesworktogether,myfilledpoolcanbedrainedin_.1_hours Theareasof3facesofarectangularsolidare20squareunits,24squareunitsand30squareunits.Thevolumeofthissolid,incubicunits,is Inacertain2-persongame,eachplayer,inturn,removes1,2,3,4,5,or6coinsfromapileuntilnocoinsremain.Theplayertakingthelastcoinloses.Ifthegamebeginswith2016coins,howmanycoinsshouldthefirstplayertakeonthefirstturnsothatthefirstplayerwillwinwithperfectplayduringthewholegame? InhowmanywayscanIarrange7differentbooksonashelfsothatmy3favoritebookswillbenexttooneanotherwithnootherbooksbetweenthem? Thenumberofpeanutssoldatthecircusinthepast20yearsisthesameasthehighestpowerof2thatdividestheproductofthefirst50positiveintegers.Thenumberofpeanutssoldatthecircusinthepast20yearsisWhatisthemaximumvalueofchangethatyoucanhaveinUScoins(pennies,nickels,dimes,andquarters)withoutbeingabletogivesomeoneexactchangeforaone-dollarbill? Whatisthesumofthedegree-measuresofthe9anglesmarked

Allthepos山veintegersnforwhich2,i23n+1isdivisibleby6arelistedinincreasingorder.What "DeathRay"tower.TowerAcanfireabeamofenergyfivetimesinfiveseconds.TowerBcan

apos巾vefiretentimesintenseconds.Beamsarefiredoneconsecutivebeamsareconstant.AssumeittakesTowerBt2secondstofire12beams.Whichofthet,< B)t1=C)t,> D)Non-是0A)226 8)251 C)279 D)282“数学大联盟杯赛”（中“数学大联盟杯赛”（中国赛区）初赛答案（六年级l2l2l3l3l5:396:196:448:21l2488D)divisibleby10495023410 66110129176l-卢 8181任 8 1201251301310A凶m 2m c幻 m o m 2m 2mm6 7 8 9 0l l l lA)t,<t,=t,>Non-226251279282（六年级（初赛时间：201711月26日，考试时间90分钟，总分200分答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。选择题：每小题5分，答对加5分，答错不扣分，共2001和ckanyintegergreaterthanIDoubleittwicethentripletheresult.Thefinaloutcomeis..1_ofyourstartinginteger. Barrylistenedtotheradiofor3hoursand36minutes.Roundedtothenearest10forhowmanyminuteswasBarry

Divide99by22togetaquotientandremainder.Dividethatremainderbyquotient,andthenewremainder Amanhadfivepiecesofchain,eachmadeupofthreelinks,figurebelow.Hewantedtojointhefivepiecestogethertomakeabigchainoffifteenlinksandwenttoablacksmithtoseehowmuchitwouldcost."Well,"saidtheblacksmith,"lwillchargeyou50centsforcuttingalinkand$1.00forweldingalink.Anybendingthatisrequiredisfree."Giventhoseprices,whatisthesmallestamountofmoneyforwhichthejobcouldbeNote:Inachain,eachlinkisconnectedtooneortwoother C

Abeesatontheheadofahorseriderwhosehorsewastrottingeastboundatasteadyfivemilesperhour.Somedistanceaheadonthesamepath,anotherhorseandriderwereapproachingwestbound,alsoatfivemilesperhour.Whenthetwohorseswere20milesapart,thebeeleftthefirsthorseriderandflewtowardthesecondhorseatarateoftenmilesperhour.Uponreachingthesecondhorse,thebeeimmediatelyturnedaroundandflewbackatthesameratetothefirsthorse.Ifthebeekeptupthisperformanceuntilthetworidersmet,howfar(inmiles)didhetravelfromthemomentheleftthe D)NoneoftheWhichofthefollowingisthesumoftheprimefactorsof Ifthelengthofthelongestsideofatriangleis18,whichofthefollowingcouldnotbethelengthofitssecond-longestside? C)l2 Myfinalscoreinacompetitionistheaverageofmyscoreson5rounds.Togetafinalscoreof88aftergetting84,80,and92onthefirst3rounds,whatmustbemyaveragescoreforthelast2rounds? MrRicehadbreakfastonedayatarestaurantwithMrWheatWhenitcametimetopaythebill,itwasfoundthatMrRicehadasmanyone-dollarbillsasMr.Wheathadquarters.(MrRicehadone-dollar础sonlyandMrWheathadquartersonly.)RatherthaneachmanpayingseparatelyMrRicepaidhisshareoftheb仆1$6,toMrWheat.AtthatpointMrWheathadfourtimesasmuchmoneyasMr.Rice.HowmuchmoneydidMrRicehaveatthebeginning? I0.ProfessorPeachteacheschemistrytocleverkids.Theratiooffreshmentootherstudentsinhisclassis3:8.ThetotalnumberofstudentsinProfessorPeach'sclasscouldbe11.440-,-220 Mr.Bogsworthonceleftawillwhichread:ToBobtwiceasmuchastoBetty.ToBrian,twiceasmuchastoBob.ToB仆I,twiceasmuchastoBrian.

Ipaid$5andgot5quarters,5dimes,and5nickelsinchange.I OnesideofTodd'struckisaperfectrectanglewithanareaof12m2.Ifitslengthis3timesitswidth,thenitsperimeteris8 B)12 C)16 D)20Ifabirdinthehandisworthtwointhebush,andabirdinthebushisworthfourinthesky,then4birdsinthehandareworth_J_birdsinthesky. Oneachofthefourshelvesofmybookcaseisadifferentprimenumberofbooks.Therecouldbeatotalof...1__booksonmyshelves. SevenyearsagoIrealizedthatmyagewouldbetripledtwelveyearsfromthen.HowoldamI HowmanyfractionswithanumeratorofIandawhole-numberdenominatoraregreaterthan0.0IandlessthanI? manytimesdoIwritethele甘erE?l6 B theareaoftheactualparkis_J_kn12.C)10

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Ifmyluckynumberdividedbyitsreciprocalis100,thenthesquareofmyluckynumberis D)Aboyandhissisterwerewalkingdownthestreetoneafternoonwhentheymetakindoldman.When Afarmerwasaskedhowmanypigshehad."Well,"hesaid,"ifIhadjustasmanymoreagain,plushalf 15%of80is40% mycyclingspeed.Iftheridetotheparktook15minutes,whatdistancedidItravelfromthebeachtothe1545

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Thegreatestintegerpowerof20thatisadivisorof5W50v D)20 _ C) C) PiratePercyhas300coinsinhischest.OftheSpanishcoins,20%aregoldIfI00ofthecoinsaregoldbutnotSpanishand70ofthecoinsareneithergoldnorSpanish,howmanySpanishgoldcoinsareinPercy'schest?

8) 二1gsednainve9)rffeirufoevahsreb二1gsednainve9)rffeirufoevahsrebmnd06)C0sl。w.ItlgdF?UItfol.d5BydanwooHth．3)53uatg4DISCAthrtnCrfiIOngr冗iulU兀5 5++eahrtf0 00- 5)BDaeelrariechetriquatg4DISCAthrtnCrfiIOngr冗iulU兀5 5++eahrtf0 00- 5)BDaeelrariechetriqhar.Dsu1ddnarBofAecre.aclthi2 5om))A Se CB．63oTheareaofABCD

Amillionisalargenumber,a"I"followedby6zeros.AgoogolisalargeC)a"l"followedbyonehundredzeros.Agoogolplexisalargenumber,a"l"followedbyagoogoIofzeros.Agoogolplexianisalargenumber,a"l"followedbyagoogolplexofzeros.C)D)noneofthe10D)noneofthepositiveintegraldivisorsofn"? lengthofthebaseofthetrianglewiththelargestarea?“数学大联盟杯赛”（中国赛区）（六年级选择题：每小题55200 D)lIO.D.812162010100D)D)153045135D)20B)105兀D)50+5 DADA10D)noneoftheD)noneofthe2018-2019年度美国“大联盟”(MathLeague)（六年级（活动日期：20181125日，答题时间：90分钟，总分：200分答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。选择题：每小题5分，答对加5分，答错不扣分，共200I.(2x4x8)—2=4x Alsleepsdailyfor3timesasmanyhoursasheisawake.ForhowmanyhoursdoesAlsleepdaily? C)

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ofanhourearlyforhernoonappointment.AtwhattimedidAngel11:18 8)11:20 C)11:40 D)11:42Theproductoftheleastandgreatestpositiveoddfactorsof2019 B) TheaveragevalueofthetenwholenumbersfromOthrough9 B) 2019X3+201973=2019X(3 8)

D) B)3x D)Whatistheareaofasquareifone-thirditsside-lengthis C) OnaMondaymysurfclubhad20members.Ifthenumberofmembersdoubledeachday,onwhatdaydidmyclubfirsthaveover2018members? B) originaldecimal. Theperimeterofarectanglewitharea2019andintegralside-lengthsisgreatestwhenitslengthandwidthdifferby8) 8)5-、丿-3、�l-3、丿l_6、．丿5-、丿-3、�l-3、丿l_6、．丿I6.9x90x900x9000=9x

D)9000Whatisonelessthantheproduct-18xA)- 8)- C)- D)-Myfirstnamehas60%asmanyle甘ersasmylastname.Myfirstnamecould Whatistheleastpossiblesumoftwointegerswhoseproductis12? , 16-dozeneggsthatarenotcracked.Whichofthefollowingisnearestinvalueto8 8)8 C)8 D)8l

Whichofthefollowinghastheleast Arectangularprismis5mlong,4mwide,and6mhigh.WhatisthesumofthelengthsofitsC)8015 B)60 D)120C)8044

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IwrotethefirstI00positiveintegersinorder,andthenerasedevery"I"Ihadwritten.HowmanydigitsdidIerase? B) 31.Whatisthedifferencebetweentheproductandthesumofthenonzerodigitsof2010whenitiswrittenindecimalform?Inthesequence

D)2x—,—, 17 —,—, previousterm'snumeratorandadding1tothepreviousterm'sdenominator.Howmanytermsinthissequencearepositiveintegers?Twocongruentrectangularcardspartiallyoverlap.Theareaofoverlap1sasquarewitharea4,andthetotalareaoftheregionsofthefacesofthetwocardsthatdonotoverlapis12.Whatistheareaoflfthemeanofthreepositiveintegersis5,thentheproductofall3integersisatWhatisthesumofthedigitsoftheleast3-digitintegerwhosesquareisa6-digit D)lIfthesumoftwoconsecutiveevenintegersis2018,whatistheirlessthanC)biggerthanl009andlessthan

segmentdrawnfromavertexoftherectangletothemidpointoftherectangle'slongerside(asshown)haslength5? D)circular12-hourclock? D)valueofN-M?

Whatisthedigitsumofthesmallestintegergreaterthan237forwhicheachdigitoftheintegerisaprimenumber?llll丿A4l丿C4l丿C2018-2019年度美国大联盟

(MathLeague)（六年级选择题：每小题5分，答对加5分，答错不扣分，共200(248.Alsleepsdailyfor3/4oftheday.Therefore,Alsleepsfor18hours36=6X6=(-6)X(-6).20x(J9-1)=20x19+20x(-1)Since

of60minutesis18minutes,Angelarrived18minutesbefore12p.m.;that'sll:42ll:18ll:2011:4011:42Thesumofthefirsttenwholenumbersis45.Theiraverageis4.5.2019X3+2019X1/3=2019X(3+1/3).B)C)3x4If1/3theside-lengthis4,theside-lengthis12andtheareais144.aMonday.Theperimeterisgreatestwhenthelengthis2019andthewidthisl.Thedifferencebetweenisatmost2018.670D)Using6pals,3palshaveatleastlpet,and-::-ofthem,orlpal,hasmorethanlpet.ThefractionTheaverageof0.5,l.5,and2.5isl.5;theaverageofland2isalsoC)29000B)-C)-D)-12=土1X土12=土2X土6土3X土4;theleastsumis1(-12)-13.Sinceeachcartoncontains8eggsthatarenotcracked,3cartonscontain2dozeneggsthatarenotcracked.Ineed24cart