2015-2019美国数学大联盟杯赛Math League5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200 B) 2.Eveiyprimehasexactly_J_positiveA) B)

4or3"IfIanswered34outof40questionsonmymathtestcorrectly,Ianswered_1_ofthequestion�120+3+4x120+3+4x B) C) D)昙10x20x30x4024)( B)10 C) D)IOOOOneofmyboxescontainsIpencilandtheotherseachcontain5pencils.thr,eare101pencilsinmyboxes,howmanyboxesdoIhave?／_`` B) ／_``Anelectricalcompanyimports2016lightbulbs.Unfortunately25%ofthosearedamaged.Howmanylightbulbsa「enot"damaged1 C) 50x(1.6+24)isthesquareB)-A)-B)- C) D)I0.'J:eopeoples1andinaline.Countingfromtheleft·,fonystandsatthe5thposition.CountingfromC)Tight,whichpositionisC)Onateamworkproject,Jackcontributed217ofthetotalamountofwork,Jillcontributed1/4ofLhework,Patcontributedl/5ofthework,andMauc0111ributedtherest.WhocontributedIhemosttowardthis B) C) D)Whichoftbefollowingnumbersisafactor B) D)A)22X4X8X16X)2XA)2

D2C)Onagameshow,AlwonfourtimesasmuchasBob,andBobwonfourtimesasmuchasCy.[fC)$1536,howrm1chdidAl,Bob,andCywin Thesumoftwocompositescannot B) C) D)Ifaandbarepositiveinlege『ssuch甘atalb517thena+b Whatisthegreatest(Jddfactorofthenumberofhomsinallthedaysoftheyear2015? B)365 C)1095 IfthecurrentmonthisFebmary,whatmonthwillitbel199999rnonthsfromJan B) C) Twoanglesarecomplemen.tary.Oneoftheseanglesis36°lessthantheother.Wl1atisthemeasureofthelargerangle? B) C) D)(Thesquarerootof16)+(thecuberootof64)+(the4throotof2561- B) D)21In凶BC,m乙A-1忆BIIILB-III乙CWhatis!hedegreemeasureof B) D)22,Forevery3mathbooksIbought,Tbought2biologybooks.Ibought55booksinall.Howmanyofthosearemathbooks?A) B) Johnwroteanumberwhosed.igitsconsistsentirelyofIs.Thisnt1mberwasacompositenumber_munbercouldcontain B) Flegs,then5Sels"'_J_Plegs. B) IfthelengthofarectangularprismwithvolumeVisdoubledwhilethewidthandtheheightarehalved,lbevolumeofthenewprismwillbe B) C) RickandRoyeachstandsatdifferent:endsofa、trnightroad!batis64mlongTheynmtowardeachother.Rick'sspeedis3m/sandRoy'sspeedis5mis.Theywi.11meetin? C) Iftheareaofacertaincircleis2016,itsradiusC)2016/兀

s.q1t{4032尔Inatoyshop,thecostofaTeddyBea『is200%asmuchasthatofatoytn1inThecostofatoytrninis B) D)Intheseqnence20J6,225,14I,66.432,99,1458...,eachtermaftertheirsttermisthesumofthe C) D)Whatisthesumofall!hepositivedivigors2巾－ B)211- C)212- 0)213-3l.Ittakes4hoursforMikeandLucytofin.shatask.IttakesLucyandJerry5hou飞tofinishlhesameAndittakes6hoursforMikeandJe可tofinishthesametaskLucy沺dJerryfirstworkonthetaskforlhourand45minutes.ThenMiketakesoverthetaskonhisown.Howmanymorebou飞doesittakefor B) D)1fyousellaclothatitscurrentprice,youget$40profit.ThetotalprofityougetsellinglOclothesat70%ofitscurrentpriceis四uallothetotalprofityougetselling20clothesat$82percloth.Whatisthecurrentpriceofacloth? B) C) The1eare6ident:icalsquaresi11!hefigtireonthe1ightThesidelengthofeach.qae.sIOfallthetrianglescon斗trnt:tedbyconnectingthreeofthe18whichhasatleastoneverticalorhorizontalside? B) D)PickupNnumbe飞fromIto2015inclusively,suchthatthesm.ofanythreeoftheNm1mbersisdivisibleby24.WhatisthemaximumvalueofN? D)35汤如有一件花了64关金买来的衬衫，他打算以比原价高出25％的价格出售，他会卖出多少 B) C) D)满足以下条件的最小整数是多少：除以3余2，除以5余4，除以7余6凸 37，飞人以每小时360 C) 38，设A为一个可整除11但不可整除10的正整数，若B为一个颠倒A数位的整数，那么B必须被几 B) C) DA,B,C39珍妮花50美金买了一条围巾。她一开始准备以60美金卖出，然后把价格增加25%,再把新的价格减少20％并且出售凸在这笔交易之中，她凸

D)亏了10关40,A,B两袋子里分有若I个，袋B袋数比是4：巨A袋中取个A袋球和B袋球的数呈之比变为8:3;再从B袋中取出若l-·个球放入A袋后，A袋球和B袋球的奻噩之比变为9:2。两个袋子里最少一？A) B) C) 2015-2016年度美国“数学大联2015-2016年度美国“数学大联盟杯（中国赛区）初赛选择题；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． 4orIO000D)lOOOA)-D)lO.B)B)IL22ID)C)32CC)33sqrt(2016尔D)1008/210-2ll-212-ID)D)D)A,B,CB2016-数学大联盟杯（五年级2016-数学大联盟杯学生诚信协议：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55200Whichofthefollowinghasthegreatest 8) C)20 D)20+ 8)20I ABizz-Numberisapositiveintegerthateithercontainsthedigit3orisamultipleof3.Whatisthevalueofthe10thBizz-Number? Theperimeterofanisoscelestrianglewithside-lengthsIandI008 8) Howmanyintegerslessthan2017aredivisibleby16butnotby Jonhasacertainnumberofpens.Ifhedistributedthemevenlyamong4students,hewouldhave3leftJoncouldhaveis C) Whichofthefollowingnumbersisnotdivisibleby 8) Whichofthefollowingisbothaperfectsquareandaperfect36 B)36 C)36xS D)39xS 8) themgot4's,25%ofthemgot3's,and15%ofthemgot2's.Howmanystudentsgotl's?ooox52011=looox52011=l8)8)I%of1/10of10000is_1_percentgreaterthanI sideofSareequal?兀： B)兀： C)兀： D)兀： Ifthesumofthreeprimenumbersis30,whatisthelargestpossiblevalueofanyofthethree dollars,didIspendintotal? 8) Howmanypos山veoddfactorsdoes25x35x55 Thenumberofscalenetriangleswithperimeter15andintegralside-lengths and3460,respectively? 8) Eachtennafterthe1stterminthesequenceI,5,9,...is4morethanthepreviousterm.Thegreatestterminthissequencethatis<1000andthatleavesaremainderof1whendividedby6is writeareprime? Ifapaintingmachinepaintsataspeedof1m2/sec,itsspeedis600 8)600060000 D)600000ofSquareCisthreetimesthatofSquareB.TheareaofSquareCis..1_timesthatofSquareA Ifthetime17minutesagowas19:43,whatwillbethetime17minutesfrom 28和ckanyintegergreaterthanI00andsubtractthesumofitsdigitsfromtheintegerThelargestintegerthatmustdividetheresultisA) roomborninthesamemonthis. IfM,A,T,andHaredifferentdigitssuchthatMATH+HTAM=12221,whatisthevalueofM+A+T+ If10forks,20knives,and30spoonscost$360,and30forks,20knives,and10spoonscost$240,what Write,insimplestreducedform,thevalue hissixopponentsexactlyonce.Sofar,AlhasplayedImatch.Barbhasplayed2matches.CalhasplayedmanymatcheshasGregplayedatthispoint? nothreeoftheseintegerscouldbethelengthsofthesidesofthesame D)lquarters)withoutbeingabletogivesomeoneexactchangeforaone-dollar 36小罗星期一工作了2个小时。在那之后的每一天，他的工作时间是前一一 37苏珊花了一天中的－的时间做英语作业，－的时间做数学作业，请问她这一 38下面哪个数是11,111,111和llllll,111,111的公约数 39设n是一任意自然数。若将n的各位数字反向排列所得自然数n1与n相等，则称n为一回文数。例如，若n1234321,则称n为一回文数；但若n1234567,则n不是回文数。请问在10000 8) C)40汤姆建了两个塔。塔A发射5次能最波5秒。B发射l0次能量波需要正好l0秒。能量波是间隔发送的，间隔是相同的。假设塔A发射l2次能晕波需要t1秒，塔B发射l2次能量波需要t2秒。t,<l2B)t1 C)t1

D)“数学大联盟杯赛”（中国赛区）初赛答（五年级 20xD)20+D)36X36X36X539x5C)冗D)兀600600060000600000A)t1<t,=t1>（五年级选择题：每小题5分，答对加5分，答错不扣分，共200Thesmallestpossiblesumoftwodifferentprimenumbers Thegreatestcommonfactoroftwonumbersis3.Theproductofthesetwonumbersmustbedivisible Thesumof5consecutiveone-digitintegersisat Howmanytwo-digitmultiplesof10arealsomultiplesof12 D)exactly

eachchapterhasthesamewholenumberofpages,thenthetotalnumberofchaptersIhaveleftcouldbe Whatisthegreatestoddfactorof44x55x63 35X55 D)36X55

Whatisthesumofthefactorsof D)Theleastcommonmultipleof8and12isthegreatestcommonfactorof120 JanuaryhasthegreatestpossiblenumberofSaturdayswhenJanuaryIoccursonanyofthefollowingdaysoftheweekexcept B) C) D)Thenumberthatisl0%ofl000islOmorethanl0% B)222 C)444 D)8885hours?35 B)40 C)42 D)45displayedonmywatch65minuteslater?7:20C)8:20(2018x2017)+(2018xI)=

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8)80兀40Ofthefollowing,whichexpressionhasthegreatestnumberoffactorsthataremultiplesof2018x Whenthesumofthefactorsofaprimenumberisdividedbythatprimenumber,theremainder B) Forhowmanydifferentpairsofunequalpos山veintegerslessthan10istheleastcommonmultipleofthenumberslessthantheirproduct? Exactly—ofthestudentsinmyclasshaveatleastonebrother,and-=-haveatleastonesister. l-chavenosiblings,whatfractionofthestudentsinmyclasshaveatleastonebrotherandatleastonel-c3）D4-5、丿B6、�AEachday,SalswimsalapIsecondfasterthanonthedaybefore.IfSalswimsalapin60minutesonthe1stday,onwhatdaydoesheswimalapinI3）D4-5、丿B6、�AC)36lC)36l

20I72018X20172019=20I7LX20I7' BotharcsABandADarequartercirclesofradius5,figureontheright.ArcBCDisasemi-circleofradius5.WhatistheareaoftheregionABCD?

B)105D)50+Forevery$5IearnfrommyjobIsave$2Forevery$4Isavefrommy」ob,Iamgivenanadditional$1frommyparentstoaddtomysavingsHowmuchmustIearninordertohave$40insavings?

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RAAmillionisalargenumber,a"I"followedby6zeros.Agoogolisalargenumber,a"I"followedbyonehundredzeros.Agoogolplexisalargenumber,a"l"followedbyagoogolofzeros.Agoogolplexianisalargenumber,a"l"followedbyagoogolplexofzeros.AgoogolplexianisRA10 B)

Anintegraltriangleisatrianglewithpositiveintegralside-lengthsandapos山vearea.Suchatrianglecanhaveaperimeterassmallas3Whatisthenextsmallestpossibleperimeterofanintegraltriangle? 2literof2%fatmilk+3literof3%fatmilk=5literof_J_fat Oneday,amotoristcametoahillthatwasten-miledriveuponesideandaten-miledrivedowntheother.Hedroveupthehillatanaveragespeedof30milesperhour.Howfastwillhehavetodrivedowntheothersidetoaverage60milesperhourfortheentire20-miledistance?30milesper90milesper

60milesperD)NoneoftheWhatistheweightofafish们tweighstenpoundsplushalfits B) Withoutusingpennies,howmanydifferentcombinationsofcoins(nickels,dimes,quarters)willmake30cents? Amanonceboughtafinesuitforwhichhepaid$30morethan-:-ofitsprice.Howmuchdidheforthe Afatherisfivetimesasoldashisson.Infifteenyearshewillbeonlytwiceasold.Howoldisthefatheratpresent? Ittakes30minutestocompletelyfillatank.If,however,aholeallows—ofthewaterthatisthetanktoescape,howlongwillitthentaketofillthe “数学大联盟杯赛”（中国赛区）（五年级选择题：每小题55200I.D)35X36XIll222444888354042457:207:258:208:25D)(2018+10223458120806040113） ） ）DABCD．62B)B)79、丿）79、丿））） ．）D BCD．52B)105兀D)50+5cRDAcRDA8)（五年级（活动日期：2018年11月25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2002018+2019=20+18+20+19+ If1/3ofmyhatsarered,and36arenotred,Ihave_.1_87）87）A2）CThesumofthemeasuresofthe2smallestanglesofatrianglecould B)135 C)121 D)612018=2QX_J_+18xA) A)EveryEnglishletterappearsinmy2018-letterpasswordatleastonce.TheletterAappearsatmost_J__ Whichofthefollowingistheproductof2consecutive Theleastintegerwithaprimenumberofdifferentprimefactors Ihave5coinsconsistingofpennies,nickels,anddimes.IfIhaveatleastIofeachtypeofcoin,theleastpossiblevalueofmy5coinsisExactly...1_different3-digitareacodescanbemadeusingonly2sand3s,withatleastone2andone3ineachareacode.Howmanymultiplesof10arefactorsof10

A) A)Myteamhadtowinacertainnumberofgamestomakeittothefinals,andwewonhowmanywinsdidweneed? Whatisthegreatestcommonfactorof1x3x5x7x9and2x4x6x8x The2ndactofa3-actplayis1/3thelengthoftheentireplay.Ifthe1stactistwiceaslongasthe3rd,whatfractionoftheplayisthe3rdact?

Ifldoublemyspeedof12000m/hr.,mynewspeedwill200 B)400C)600 D)2400Whichofthefollowingcouldbetheperimeterofanequilateraltrianglewithintegralside- ThegreatestofIOconsecutivepositiveintegersisaprimenumber.Whatistheleastpossiblesumof One-fourthofEd'sballoonspopped,with2balloonspoppingevery3minutes

Whatisthegreatestcommonfactorof68and8Theexpression1002018canbewrittenastheproductofexactly二＿primeC)2x

Howmanyintegershaveasquarerootgreaterthan15andlessthan 8)22＝霾

Eachdayforamonth,Sullywakesup5minutesearlierthanhedidthedaybefore.IfSullywokeupat Theproductofallfactorsof21equals (1234+0+1234+1+1234+2+1234+3+1234+4)—5 B)1234+ C)1234+ D)1234+Onanumberline,twodifferentintegersareeachthesamedistancefrommyfavoriteintegerandhaveasumof144.Whatismyfavoriteinteger? LastyearIspent$180for80pairsofshades.ThisyearIspent$180for5fewerpairsofthesameshades.HowmuchdidthepriceperpairincreasesinceIboughtthemlastyear? Idroveataconstantspeedof60km/hr.withoutstopping.Atexactly5:00p.m.Ihadtraveled318km.AtwhattimedidIstartdriving?10:42C)12:42

11:42D)1:42wasoneofthese9numbers.Whenmysumwasdividedby11,theremaindercouldnothave ofthelast4digitsonthefirstline? Theproductofallthefactorsofanintegergreaterthanlequalsthecubeofthatinteger.Whatistheleastintegerforwhichthisistrue? Xi0;-(iX23X25XXi0;-(iX23X25X...X297X bothlanes? Icountedbackwardsoutloudfrom2018byones.WhenIsaidmy50thmultipleof8,howmanynumbershadIcounted? D)1+7=18.Howmanyluckyyearsaretherebetween2018and2108? 3.0C)4.5

4.0D)9.0thepatternwouldbe 2018-2019年度美国“大联盟”(MathLeague)（五年级选择题：每小题5分，答对加5分，答错不扣分，共200 (2018-20-18)+2019-20-19=1980+1980=3960.8)ThenumberofredhatsishalfthenumberthatarenotIfthemeasuresofthe2smallestanglesofatrianglewere30and31degrees,thelargestanglewouldbe119degreesfeveryEnglishletterexceptAappearedexactlyonce,thenAwouldappear2018-25=1993Thenumber6hastwoprimefactors,2and3.pennies,1nickel,and1dime.Thecommonfactorsare1,3,5,and15.Thegreatestis15Since2400=16100,itistheproductofexactly100sixteens.Iftheplayis90mins.,the2ndactis30mins.Thatleaves60mins.forthe1stand3rdacts.The1stactw