2015-2019美国数学大联盟杯赛Math League3-4年级及答案

（三四年级（初赛时间；2015年11月14日，考试时间60分钟，总分200分选择题：每小题5分，答对加5分，答错不扣分，共200I.Todayisacrazyshoppingdayformygym.Ibought50soccerballsat$24each,andIbought24basketballsat$34each.HowmuchdidIspendintotal? B) D)1fthelasttwodigilsofanumberare"84",thenthenumbeTmL1�tbedivisible 9mathbooksareforsaleatatotalof$117.12dictionar.iesareforsaleatatotalof$!08.Thepriceforonemathhookis...1___morethanthecostofonedictionary. B) D)Whichofthefollowinglistspulsthethreetypesofanglesinascendingorder,accordingtotheirdegreeRight,acute, B)Obtuse,right,C)Acute,right, D)Obtuse,acute,AmyisstandinginastraightlineofpeopleThereare200peoplelandingatherleftandthereare300peoplestandingatherright.Howmanypeoplea，色intheline? B) D)16 B) C) 3(846(58)6 B) Theunitsdigitofaperfectsquarecannot ,

B) C) 0)I0.Theunitsdigitoftheprod11ctoftwoconsecutiveinteger�cannut B) D)6th B) C) D)Apeifectnumberisapositiveintegerwhichisequalto由esumofitsproperpositivediviso飞．Forexample,6isaperfectnumbersince6=I23.Whichofthefollowingisaperfect1111111ber? B) C) D)Theproductofthefirst36positiveintege兀is,C)divisible

divisiblebyD)divisibleby

也应比SuperPatwasmnning1.001km.HetookabreakaftereveryIIkm B) C) D)TommtgagemycaI,paidhalfofitspriceinthefirstmonththenpaidII(Jofitsoriginalpriceinthe B)$15,000C)$20,000D)6 B)6 C)12 D)12ofI001thatislargerthanI? B) C) D)be555minutesfromnowusing24-hournotation?08 B) C)20: D) B) C) B) C) D)�mailer B) D) D)Whichoftbefollowingnumbersisdivisibleby3butnotdivisibleby B) C) D) B) D)tornnthisdistance? B) C) D)theapplesinthebasketinmorethanIOdays,andthenumberofapplesiteatsonthelastdayis3.1fitapplesiteatsonthelastdayis2.Howmanyapplesarethereinthebasket? B) C) Nisatwo-digitnumber]\/dividedby2isstillatwo-digitnumber.Misatwo-digitnumbera几戏witchingtheonesdigitandtensdigitofN/2.TheproductofsevenandhalfofMiseql!la!toNWhatis B) .ProfessorTonyhas9hatseachtaggedwithoneofthenumbersl109respectivelyProfessorTonyletswhichhatsarethrownaway).Eachs.tudentcanseethenumbersonthehatsofotherstudents,butnotthenumbeonhisownhai.ThenProfessorTonywritesanumberontheblackboardandtellseachstudentto C) D)365天里有多少个l000 B) C) D)3I在孮斯食堂里，每份晚餐有8个肉丸和3块蒜蓉而包。今天卖出的构丸数呈比卖出的蒜蓉而包数昼多600,今天琼斯卖出了多少份晚餐？ B) C) D)一个奇数乘3以后将会是二质 B)合 C)奇 D)偶把123456789除以10000的淌转化为小数以）旬十位和于分位的积是多少 B) D)33，前6C) C)在小镇大学里，学生们的专业是音乐、美术，或两者。如果有500个学生是音乐专业，600个学生是美术专业，300个学生是音乐和美术专业，那么大学里有多少个学生？ B) C) D)35如果你花30分钟做了35道题目，那么用同样的速度．你做315 C) D)一个物体的2016度逆时针旋转，与它的多少度顺时针旋转是一样的 前10个正整数的积，末尾有几个C) C)有几个正三位数祸足个位数是十位数和百 D)一一共是60辆，则在这一整条索道上（双向）共有多少辆缆车？30 B)60 C)6l 一个程序员给编号为1-40的40个机器人写好程序，让它们来判断某句话的对错程序员为了提高准确率，在它们都进行过一次判断后，让从编号为1的机器人开始，修改自己的如果其余39个机器人多，则自己的回答也为“对“，否则回答错＂。如果品开始有20个机20＇＇，并且“对“。那么这40个机器人按序修改自己的答案后， 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．l B)C)3D)Right,acute,Obtu.se,right、Acute,right,Obtuse,acute,A)B)A)B)D)I.I.D)l2.divisiblebydivisiblebydivisiblebyC92知应比C)$20,00066121220IID)C)D)201SC)D)CC)4.5A)39,B)606l12040D)（三年级（2016年11月20日，考试时间90分钟，总分200分学生诚信协议：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，我确定以下的答案选择题：每小题55200I. 8) D)Ofthefollowing,立＿anglehasthelargestdegree- 8)an C)a lO203040＿＝50+6070

D)aD)D)2016-数学大联盟杯Yinrounded2017tothenearesttens.Yanrounded2017tothenearesthundreds.Thedifferencebetweentheirtwonumbers2016-数学大联盟杯 8) D)6metres+_J_centimetres+6millimetres=6666 D)A3by12rectanglehasthesameareaasarectanglewithl B)2 C)3 D)5byInJenandBerry'sicecreamshop,12scoopsofvanillaicecreamaresoldfor$36,16scoopsofchocolateicecreamaresoldfor$64,18scoopsofstrawberryicecreamaresoldfor$81,andIOscoopsofminticecreamaresoldfor$35.Whichflavoristhemostexpensiveperscooptobuy? 8) D)Thesumof123456and654321isnotamultiple C) D)Tomisamathlover!Inhismathclass,hewrotethephrase"MATHISFUN"9999times.Whatisthel00thletterhewrote? Whichofthefollowingcanbewrittenastheproductoftwodifferentprime 8) D)Aliensarehugefansofcookies.Analienhasthreehands.Eachhandhasfourlargefingers,andeachfingercanholdfivecookies.Atmost,howmanycookiescansixaliensholdintheirhands 8)360C)420Therangeofasetofnumbersisthedifferencebetweenthegreatestandtheleastnumberintheset.ThenumbersinsetAarel0,20,30,40,and50.IfeachnumberinsetAisdoubledandthenincreasedbyl0, B)80C)90100+200+300+400=(25+50+75+100)X B)16C)32Whatistheproductofthenumberofsidesofahexagonandthenumberofsidesofan 8)35C)42 l7.Theproductoftwodifferentprimescannot

3X2017=_]_720J7-;-

Thirtyyearsfromnow,myagewillbetripled.Myagenow WhenIreversethedigitsofanynumberthatisamultipleof3butnotamultipleofI0,thereversednumberisalwaysamultipleof If3teachersate12cookieseachand2studentsate14cookiesintotal,whatistheaveragenumberof ForeverypenthatStevebought,healsobought3pencilsand5highlighters.Ifhebought6pencils,howmanypencilsandhighlightersdidhebuyalltogether? to6? Theaverageofonethousandandonemillion10 B)100 C)500 D)500TworectangleshavethesameareaIfthelengthofthefirstoneishalfthelengthofthesecondonethenthewidthofthefirstoneis立＿timesthewidthofthesecondone. Johnlovescollectingstamps!Ifhedividesthenumberofstampshehasby32,thenhewillhave30remainingstamps;ifhedividesthenumberofstampshehasby9,hewillhave7remainingstamps;ifhedividesthenumberofstampshehasby7,hewillhave5remainingstamps.Howmanystamps,atleast,doesJohnhave? Eachofthe40studentsinMr.Talent'sclasspossessesatleastoneofthethreeskills:singing,dancing,andacting.If28studentsknowhowtosing,26studentsknowhowtodance,and31stt1dentsknowhowtoact,atleasthowmanystudentspossessallthreeskills? JackisagiftedathletewhohastrainedhardfortheOlympicmarathon.Inthelasthundredyardshefindstheinnerstrengthtoincreasehispaceandovertakestherunnerinthesecondplace.Butthen,withthefinishinglinejustaway,heisovertakenbytwootherrunners...

InasequenceofIOnumbers,theaverageoftheIOtermsis13.Iftheaverageofthefirstthreetermsis7andtheaverageofthenextfourtermsisI0,whatistheaverageofthelastthreeterms? If1apple,2bananas,and3cherriescost$9intotal,3apples,2bananas,and1cherrycost$7intotal,whatisthetotalcost,indollars,of1apple,1banana,and1cherry? Iftheperimeterofarectangleis32,whatisthemaximumpossiblevalueforits Inaclassof40students,30studentsgetA'sonthemathtestand20studentsgetA'sontheEnglishtestsAtleasthowmanystudentsgetA'sonbothtests? I2315 8) 36个三角形的两条边的长度分别为1011,A)l9 C)l7 D)l637从1到20的20个整数，每个整数除以6,所得的余数的总和是多少？ 明在考试中获得95分，那么他答对了多少道题？ 9+99+999+9999+...+9999999999（最后一项有10位数字）8)8)40约翰的钱比吉尔多20美元。他们两个总共有42美元。请问约翰有多少美元？ （三年级选择题：每小题5分，答对加5分，答错不扣分，共200分， ananaalby2by3by5byI10100500500B)B)（三年级（初赛时间：20171126日，考试时间90分钟，总分200分学生诚信协议：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，我确定我所填写的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。I.5+6+7+1825+175 C) JohnandJillhave$92intotal.JohnhasthreetimesasmuchmoneyasJill.HowmuchmoneydoesJohn Tomisabasketballlover!Onhisbook,hewrotethephrase"ILOVENBA"I00times.Whatisthe500th An8by25rectanglehasthesameareaasarectanglewith4by10by

6byWhatisthepos山vedifferencebetweenthesumofthefirstl00pos山veintegersandthesumofthenext Youhaveaten-footpolethatneedstobecutintotenequalpieces.Ifittakestensecondstomakeeachcut,howmanysecondswillthejobtake? Amyrounded2018tothenearesttens.Benrounded2018tothenearesthundreds.Thesumoftheirtwonumbersis Whichofthefollowingpairsofnumbershasthegreatestleastcommon C) Forevery2pencilsDanbought,healsobought5pens.Ifhebought10pencils,howmanypensdidhe TwentydaysafterThursday C)WednesdayOfthefollowing,..1__anglehastheleastdegree-an 8)an C)a D)aEverystudentinmyclassshoutedoutawholenumberinturn.Thenumberthefirststudentshoutedoutwas1.Theneachstudentafterthefirstshoutedoutanumberthatis3morethanthenumberthepreviousstudentdid.Whichnumberbelowisapossiblenumbershoutedoutbyoneofthestudents? Aboyboughtabaseballandabat,paying$1.25forbothitems.Iftheballcost25centsmorethanthebat,howmuchdidtheballcost? 2hours+_.1_minutes+40seconds=7600 Inthefigureontheright,pleaseputdigits1-7inthesevencirclessothatthethreedigitsineverystraightlineaddupto12.Whatisthedigitinthemiddlecircle? If5adultsate20appleseachand3childrenate12applesintotal,whatistheaveragenumberofapplesthateachpersonate?

Whatistheperimeterofthefigureontheright?Note:Allinteriorinthefigurearerightanglesor

Thirtypeoplearewaitinginlinetobuypizza.Thereare10peopleinfrontofAndy.Susanisthelastpersonintheline.HowmanypeoplearebetweenAndyandSusan?Thirty-ninehoursafter9:00AM

B)12:00 C)8:00200+400+600+800=(}+2+3+4)X

11...11(thenumberconsistingof2016l's)isnotamultiple C) D)lllllTheaverageoftwothousandsandtwomillions

Atrianglehasthesameareaasasquare.Ifthelengthofabaseofthetriangleisthesameasside-lengthofthesquare,andtheheightofthetriangletothebaseis4,whatistheareaofthe

WhenVoltafoundafieldintheshapeofanisoscelestriangle,shewassoexcitedthatsheranalaparoundallthreesides.Twosidesofthefieldhavelengthsof505meach,andthethirdsidehasawhole-numberlength.WhatisthegreatestpossibledistancethatVoltamighthaveruninonelap?25X66=75Thenumberthathasanoddnumberofwholenumberdivisors Inasequenceof8numbers,theaverageofthe8termsis15.Iftheaverageofthefirstthreetermsis16andtheaverageofthenexttwotermsis15,whatistheaverageofthelastthreeterms? Allyearsbetween2000and2050thataredivisibleby4areleapyears.Nootheryearsbetween2000and2050areleapyears.Howmanydaysaretherealltogetherinthe17yearsfrom2010to2026?

Thesumofthehundredsdigitandthetensdigitof2357 Whichoftheexpressionsbelowhasthegreatestvalueof(quotientx27-c-57-c-

47_,_6Ihavesomedimesandnickels,andtogetherthesecoinsareworth$3.IfIreplaceeverynickelwithaquarter,Iwillhave$5.HowmanydimesdoIhave? Igetis9,Iputthatwholenumberonmylistoffavoritenumbers.Ofthewholenumbersfrom1000to9999,howmanywouldIputonmylistoffavorite

TheproductofallprimenumbersbetweenIandIO

D)noneoftheWhatistheaverageof12,14,16,and 8) C) D)WhenJonshoutsoutawholenumber,Alshoutsouttheproductofitsdigits,shoutsouttheproductofthedigitsofthenumberAlshoutedout,andCyshoutsouttheproductofthedigitsofthenumberBarbshoutedout.WhenCyshoutsout18,whatnumbermightJonhaveshoutedout?Eachbigboxcontains3mediumboxes,eachmediumboxcontains2smallboxes,andeachsmallboxcontains5apples.Howmanybigboxesarenecessaryfor1200apples? 2lAEighteenyearsfromnow,myagewillbe4morethantwicemycurrentage.Myag2lA6lCEachtimeWandawavedherwand,4morestarsappearedonherdress(whichstartedwithnostars).Afterseveralwaves,Wandamultipliedthetotalnumberofstarsthenonherdressbythenumberoftimesshehadwavedherwand.Thisproduct6lCcannot