2018加拿大滑铁卢大学高斯数学竞赛真题(CEMC).docx

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1、2018加拿大滑铁卢大学高斯数学竞赛真题(CEMC)Scoring:Thereisnopenaltyforanincorrectanswer.Eachunansweredquestionisworth2,toamaximumof10unansweredquestions.PartA:Eachcorrectanswerisworth5.1.Whatnumbershouldbesubtractedfrom21togive8?(A)12(B)13(C)14(D)15(E)162.Inthediagram,thepiechartshowstheresultsofasurveyaskingstudent

2、stochoosetheirfavouritefruit.100studentsweresurveyed.Howmanystudentschosebanana?(A)40(B)80(C)100(D)20(E)60Banana20%Apple40%Orange40%3.Aclassbeginsat8:30a.m.andendsat9:05a.m.onthesameday.Inminutes,whatisthelengthoftheclass?(A)15(B)25(C)35(D)45(E)754.Asquarehasanareaof144cm2.Thesidelengthofthesquareis

3、(A)288cm(B)72cm(C)48cm(D)12cm(E)36cm5.Ifthereisnotax,whichofthefollowingcostsmorethan$18topurchase?(A)Five$1itemsand?ve$2items(B)Nine$1itemsandfour$2items(C)Nine$1itemsand?ve$2items(D)Two$1itemsandsix$2items(E)Sixteen$1itemsandno$2items6.Whichofthefollowingnumbersliesbetween3and4onanumberline?(A)52(

4、B)114(C)115(D)134(E)1357.Anenvelopecontains2sun?owerseeds,3greenbeanseeds,and4pumpkinseeds.Carrierandomlychoosesoneoftheseedsfromtheenvelope.WhatistheprobabilitythatCarriechoosesasun?owerseed?(A)29(B)59(C)97(D)79(E)198.Ifx=4andy=3x,thevalueofyis(A)12(B)24(C)7(D)81(E)49.Themeasureofoneangleofanisosce

5、lestriangleis50?.Themeasuresoftheotheranglesinthistrianglecouldbe(A)50?and90?(B)40?and50?(C)50?and80?(D)30?and100?(E)60?and70?10.The26lettersofthealphabetarewritteninorder,clockwisearoundacircle.Theciphertextofamessageiscreatedbyreplacingeachletterofthemessagebytheletterthatis4lettersclockwisefromth

6、eoriginalletter.(ThisiscalledaCaesarcipher.)Forexample,themessageZAPhasciphertextDET.WhatistheciphertextofthemessageWIN?(A)ALN(B)ZLN(C)AMR(D)AMQ(E)ZMQPartB:Eachcorrectanswerisworth6.11.Acubehasexactlysixfacesandtwelveedges.Howmanyverticesdoesacubehave?(A)4(B)5(C)6(D)7(E)812.Whatisthesurfaceareaofa1c

7、mby2cmby2cmrectangularprism?(A)10cm2(B)20cm2(C)12cm2(D)24cm2(E)16cm22cm2cm1cm13.Atafactory,11410kgofriceisdistributedequallyinto3260bags.Afamilyuses0.25kgofriceeachday.Howmanydayswouldittakethisfamilytouseuponebagofrice?(A)9(B)12(C)13(D)14(E)1514.DaliasbirthdayisonaWednesdayandBrucesbirthdayis60days

8、afterDalias.OnwhatdayoftheweekisBrucesbirthday?(A)Monday(B)Tuesday(C)Friday(D)Saturday(E)Sunday15.Karlhas30birds.Someofhisbirdsareemusandtherestarechickens.Karlhandsout100treatstohisbirds.Eachemugets2treatsandeachchickengets4treats.HowmanychickensdoesKarlhave?(A)10(B)15(C)25(D)20(E)616.Theintegers1t

9、o32arespacedevenlyandinorderaroundtheoutsideofacircle.Straightlinesthatpassthroughthecentreofthecirclejointhesenumbersinpairs.Whichnumberispairedwith12?(A)28(B)27(C)23(D)21(E)2917.Inthediagram,theareaoftheshadedmiddleringis6timestheareaofthesmallestcircle.Theareaoftheunshadedouterringis12timestheare

10、aofthesmallestcircle.Whatfractionoftheareaofthelargestcircleistheareaofthesmallestcircle?(A)13(B)16(C)112(D)118(E)11918.Thereareseveralgroupsofsixintegerswhoseproductis1.Whichofthefollowingcannotbethesumofsuchagroupofsixintegers?(A)?6(B)?2(C)0(D)2(E)619.Theheightsof4athletesonateamare135cm,160cm,170

11、cm,and175cm.Laurissajoinstheteam.Onthenewteamof5athletes,themodeheightoftheplayersisequaltothemedianheightwhichisequaltothemean(average)height.HowtallisLaurissa?(A)135cm(B)160cm(C)170cm(D)175cm(E)148cm20.Inthediagram,PQRisisosceleswithPQ=PR.Whatisthevalueofx?(A)110(B)90(C)95(D)100(E)105PQR95x120Part

12、C:Eachcorrectanswerisworth8.21.The?gureconsistsof8identicalsmallparallelograms,joinedasshown.Includingthese8smallparallelograms,howmanyparallelogramsappearinthis?gure?(A)29(B)30(C)26(D)27(E)2822.Inajar,thereare50coinswithatotalvalueof$5.00.Thecoinsarequarters(worth$0.25each),dimes(worth$0.10each),an

13、dnickels(worth$0.05each).Thenumberofnickelsinthejaristhreetimesthenumberofquarters.Thenumberofdimesisonemorethanthenumberofnickels.Howmanyquartersareinthejar?(A)7(B)6(C)5(D)9(E)823.Thedigitsfrom1to9arewritteninordersothatthedigitniswrittenntimes.Thisformstheblockofdigits1223334444999999999.Theblocki

14、swritten100times.Whatisthe1953rddigitwritten?(A)4(B)5(C)6(D)7(E)824.Thenumber2018isusedtocreatesix-digitpositiveintegers.Thesesix-digitintegersmustcontainthedigits2018togetherandinthisorder.Forexample,720186isallowed,but209318and210893arenot.Howmanyofthesesix-digitintegersaredivisibleby9?(A)28(B)27(C)31(D)34(E)2225.Inthetriangle,eachofthenumbers1,2,3,4,5,6,7,8isplacedintoadi?erentcircle.Thesumsofthenumbersoneachofthethreesidesofthetriangleareequaltothesamenumber,S.Thesumofallofthedi?erentpossiblevaluesofSis(A)85(B)99(C)66(D)81(E)67