2024 年袋鼠數(shù)學(xué)競(jìng)賽 等級(jí)E（中國(guó)區(qū)）

2024MathKangarooJuniorLevelD(China)1、Whichofthefollowingstringscannotbetransformedintothestringontherightwithoutcutting?請(qǐng)問(wèn)下列哪條繩子在不切割的情況下，無(wú)法變成右圖所示的樣式？A.B.C.D.E.2、Ashapeismadeofequal-sizedpentagonaltiles.Whichofthefollowingtilescanbeplacedinthespaceintheshapetoproducetwoclosedcurves?右側(cè)圖形由尺寸相同的五邊形瓷磚組成．請(qǐng)問(wèn)將下列哪塊瓷磚放入這個(gè)圖形的空白處可以形成兩條封閉曲線？A.B.C.D.E.3、Thefirstdiagramshowsarhombus.Theareaofthefirstdia-gramisincreasedbyaddingtworight-angledtriangles,asshown.Bywhatpercentagehastheareaincreased?如圖所示，第一個(gè)圖形為菱形，加上兩個(gè)直角三角形之后，圖形面積有所增加．請(qǐng)問(wèn)面積增加了百分之幾？A.20%B.25%C.30%D.40%E.50%4、Whatisthevalueof20×242×0+2×4請(qǐng)問(wèn)20×242×0+2×4A.12B.30C.48D.60E.1205、Juliocutsoffthefourcornersofaregulartetrahedron,asshown.Howmanycornersdoestheshapethatremainshave?如圖所示，Julio切掉了一個(gè)正四面體的四個(gè)角．請(qǐng)問(wèn)余下圖形有多少個(gè)角？A.8B.9C.11D.12E.156、Riahasthreecountersmarked1,5and11,asshown.Shewantstoplacethemsidebysidetomakeafour-digitnumber.Howmanydifferentfour-digitnumberscanshemake?Ria有三個(gè)籌碼，分別標(biāo)記有1、5和11，如圖所示．將三個(gè)籌碼并排放置組成一個(gè)4位數(shù)，請(qǐng)問(wèn)Ria可以得到多少個(gè)不同的4位數(shù)？A.3B.4C.6D.8E.97、Afruitbowlcontainsfivetypesoffruit

,

,

,

and

.Allikes

.Boklikes,

,

and

.Camlikes

,

,

,and

.Donlikes

,

and

.Evalikes

and

.Thefruitissharedsothateveryonegetsadifferenttypeoffruitandeveryonegetsatypeoffruitthattheylike.Whogets?一個(gè)果籃里有5種水果：、、、、．Al喜歡．Bok喜歡、、、

．Cam喜歡、、、．Don喜歡、、．Eva喜歡、．大家分享這些水果時(shí)，每個(gè)人拿到的水果都不同且都是自己喜歡的水果．請(qǐng)問(wèn)誰(shuí)拿到了？A.AlB.BokC.CamD.DonE.Eva8、Theweightrestrictionnoticeforanelevatorsaysitcancarryeither12adultsor20children.Accordingtotheweightrestrictions,whatisthelargestnumberofchildrenthatcanrideintheelevatorwithnineadults?電梯超載提示標(biāo)明，該電梯能承載12名成年人或20名兒童．根據(jù)該提示，如果該電梯已經(jīng)搭載了9名成年人，那么最多還能搭載多少名兒童？A.3B.4C.5D.6E.89、Fourdifferentpositiveintegersareplacedonagridandthencoveredup.Theproductsoftheintegersineachrowandineachcolumnareshowninthediagram.Whatisthesumofthefourintegers?在一個(gè)網(wǎng)格中放入4個(gè)不同的正整數(shù)，然后將其遮蓋．右圖中顯示的數(shù)字分別為每行和每列中的整數(shù)之積．請(qǐng)問(wèn)這4個(gè)整數(shù)的總和是多少？A.10B.12C.13D.14E.1510、Thelengthofasetoffourwell-parkedandfittedsupermarkettrolleysis108cm.Thelengthofasetoftenwell-parkedandfittedsupermarkettrolleysis168一排4輛整齊停放的超市手推車的長(zhǎng)度為108cm．一排10輛整齊停放的超市手推車的長(zhǎng)度是168A.60B.68C.78D.88E.9011、Carinabakedacakeandcutitintotenequalpieces.Sheateonepieceandthenarrangedtheremainingpiecesevenly,asshown.Whatisthesizeoftheanglebetweenanytwopieces?Carina將自己烤的蛋糕等分為10塊．她吃了一塊，然后將剩下的9塊均勻分布，如圖所示．請(qǐng)問(wèn)任意兩塊相鄰的蛋糕之間的角度是多少？A.5°B.4°C.3°D.2°E.1°12、Wernercanmakea4×4square,wherethesumofthenumbersinallfourrowsandallfourcolumnsisthesame,fromthethreepiecesshown

andonefurtherpiece.Whichofthefollowingpiecesisneededtocompletehissquare?Werner做了一個(gè)4×4的正方形，這個(gè)正方形中每行、每列的4個(gè)數(shù)字之和相同．正方形可分成四塊碎片，其中三塊碎片為：．請(qǐng)問(wèn)下列哪個(gè)選項(xiàng)是該正方形的最后一塊碎片？A.B.C.D.E.13、Asquarehasside-length10m.Itisdividedintopartsbythreestraightlinesegments,asshown.TheareasofthetwoshadedtrianglesareAandB.WhatisthevalueofA?B如圖所示，一個(gè)邊長(zhǎng)為10m的正方形被三條線段切分．其中兩個(gè)陰影三角形的面積分別為A和B．請(qǐng)問(wèn)A?BA.0B.1C.2D.5E.1014、Paulathepenguingoesfishingeverydayandalwaysbringsbacktwelvefishforhertwochicks.Eachday,shegivesthefirstchicksheseessevenfishandgivesthesecondchickfivefish,whichtheyeat.Inthelastfewdaysonechickhaseaten44fish.Howmanyhastheotherchickeaten?企鵝Paula每天都出門捕魚(yú)，并且總是會(huì)給她的兩只企鵝幼崽帶回12條魚(yú)．每一天，Paula會(huì)給她看到的第一只企鵝幼崽喂7條魚(yú)，給看到的第二只企鵝幼崽喂5條魚(yú)．在過(guò)去的幾天中，其中一只企鵝幼崽一共吃掉44條魚(yú)．請(qǐng)問(wèn)另一只企鵝幼崽一共吃了多少條魚(yú)？A.34B.40C.46D.52E.5815、Johanhadalargenumberofidenticalcubes.Hemadethestructureontherightbytakingasinglecubeandthenstickinganothercubetoeachface.Hewantstomakeanextendedstructureinthesamewaysothateachfaceofhisoriginalstructurewillhaveacubestucktoit.Howmanyextracubeswillheneedtocompletehisextendedstructure?Johan有許多相同的立方體．他選取其中一個(gè)立方體，然后將其他立方體貼在該立方體的各個(gè)面上，最終形成右側(cè)所示結(jié)構(gòu)．接下來(lái)，他想用同樣的方式制作一個(gè)擴(kuò)展結(jié)構(gòu)，使得原結(jié)構(gòu)的每一面上都貼上一個(gè)立方體．請(qǐng)問(wèn)Johan還需要多少個(gè)立方體才能完成這個(gè)擴(kuò)展結(jié)構(gòu)？A.18B.16C.14D.12E.1016、Akangaroojumpsupamountainandthenjumpsbackdownalongthesameroute.Itcoversthreetimesthedistancewitheachdownhilljumpasitdoeswitheachuphilljump.Goinguphill,itcovers1metreperjump.Intotal,thekangaroomakes2024jumps.Whatisthetotaldistance,inmetres,thatthekangaroojumps?一只袋鼠跳上山，然后按照同樣的路線跳下山．它下山時(shí)每次跳躍的距離是上山時(shí)每次跳躍距離的三倍．袋鼠上山時(shí)每次跳躍的距離是1米．袋鼠上下山總共跳了2024次，請(qǐng)問(wèn)袋鼠總共跳躍了多少米？A.506B.1012C.2024D.3036E.404817、Gerardcutsalargerectangleintofoursmallerrectangles.Theperimetersofthreeofthesesmallerrectanglesare16,18and24,asshowninthediagram.Whatistheperimeterofthefourthsmallrectangle?Gerard將一個(gè)大矩形切割成4個(gè)小矩形．其中三個(gè)小矩形的周長(zhǎng)分別為16、18、24，如圖所示．請(qǐng)問(wèn)第四個(gè)小矩形的周長(zhǎng)是多少？A.8B.10C.12D.14E.1618、Watermakesup80percentofthemassoffreshmushrooms.However,watermakesuponly20percentofthemassofdriedmushrooms.Bywhatpercentagedoesthemassofthemushroomdecreaseduringdrying?新鮮蘑菇中的水分占總質(zhì)量的80%，但干蘑菇中的水分只占總質(zhì)量的20%．請(qǐng)問(wèn)在曬干過(guò)程中，蘑菇的質(zhì)量減少了百分之幾？A.60B.70C.75D.80E.8519、Terithetilerisplanningtomakealarge,squaremosaicfloorwitharepeatingpattern,usinghexagonalandtriangulartiles,arrangedasshowninthediagram.泥瓦匠Teri計(jì)劃按照一定的規(guī)律將六邊形瓷磚和三角形瓷磚拼接成一個(gè)大塊正方形馬賽克地板，排列方式如圖所示．Shethinksshewilluse3000hexagonaltilestomakethewholefloor.Approximately,howmanytriangulartileswillsheneed?Teri認(rèn)為鋪成這樣一整塊地板需要用3000塊六邊形瓷磚．請(qǐng)問(wèn)Teri大約需要用多少塊三角形瓷磚？A.1000B.1500C.3000D.6000E.900020、Ninecardsnumberedfrom1to9wereplacedfacedownonthetable.Aleksa,Bart,ClaraandDeindraeachpickeduptwoofthecards.Aleksasaid"Mynumbersaddupto6".Bartsaid"Thedifferencebetweenmynumbersis5".Clarasaid"Theproductofmynumbersis18".Deindrasaid"Oneofmynumbersistwicetheotherone".Allfourmadeatruestatement.Whichnumberwasleftonthetable?九張編號(hào)為1到9的卡牌正面朝下放在桌子上．Aleksa，Bart，Clara和Deindra每個(gè)人都從桌子上挑選2張牌．Aleksa說(shuō)：“我拿到的卡牌上的數(shù)字相加等于6．”Bart說(shuō)：“我拿到的卡牌上的數(shù)字之差是5．”Clara說(shuō)：“我拿到的卡牌上的數(shù)字的乘積為18．”Deindra說(shuō)：“我拿到的卡牌上的其中一個(gè)數(shù)字是另一個(gè)數(shù)字的兩倍．”如果他們4個(gè)人說(shuō)的都是真的，那么請(qǐng)問(wèn)桌子上剩余卡牌上的數(shù)字是什么？A.1B.3C.6D.8E.921、Thedigits0-9canbedrawnwithhorizontalandverticalsegments,asshown.Gregchoosesthreedifferentdigits.Intotal,hisdigitshave5horizontalsegmentsand10verticalsegments.Whatisthesumofhisthreedigits?用橫線和豎線表示數(shù)字0-9，如圖所示．Greg從中選取三個(gè)不同數(shù)字．他選取的數(shù)字一共包含5條橫線和10條豎線．請(qǐng)問(wèn)他選取的三個(gè)數(shù)字之和是多少？A.9B.10C.14D.18E.1922、Tarekwantstoshadetwofurthersquaresonthediagramshownsothattheresultingpatternhasasingleaxisofsymmetry.Inhowmanydifferentwayscanhecompletehispattern?Tarek想將下圖中的另外兩個(gè)方格涂黑，使得最終所得圖形只有一條對(duì)稱軸．請(qǐng)問(wèn)他能用幾種不同的涂法來(lái)完成他想要的圖形？A.2B.3C.4D.5E.623、Thediagramshowsthreesemi-circlesinsidearectangle.Themiddlesemi-circletouchestheothertwosemi-circleswhich,inturn,eachtouchashortersideoftherectangle.Thelargestsemi-circlealsotouchesoneofthelongersidesoftherectangle.Theshortestdistancesfromthatsideoftherectangletotheothertwosemi-circlesare5cmand7cmrespectively,asshown.Whatistheperimeter,in圖中展示了一個(gè)矩形中有三個(gè)半圓．中間的半圓與兩側(cè)的半圓相切，兩側(cè)的半圓分別與矩形的一條短邊相切，同時(shí)，最大的半圓與矩形的一條長(zhǎng)邊相切，且這條長(zhǎng)邊到另外兩個(gè)半圓的最短距離分別為5cm和7cm，如圖所示．請(qǐng)問(wèn)這個(gè)矩形的周長(zhǎng)為多少A.82B.92C.96D.108E.12024、Agroupof50studentssitinacircle.Theythrowaballaroundthecircle.Eachstudentwhogetstheballthrowsittothe6thstudentsittinganti-clockwisefromwheretheyaresitting,whocatchesit.Fredacatchestheball100times.Inthattime,howmanystudentsnevergettocatchtheball?50名學(xué)生坐成一圈，然后繞著這個(gè)圓圈傳球．每名拿到球的學(xué)生會(huì)把球傳給從自己所在位置起逆時(shí)針?lè)较蛏系牡?名學(xué)生．Freda共接到100次球．在這段時(shí)間里，有多少名學(xué)生從來(lái)沒(méi)有接到過(guò)球？A.0B.8C.10D.25E.4025、Donggyuwantstocompletethediagramsothateachboxinthemiddleandtoprowswillcontaintheproductofthevaluesinthetwoboxesbelowitandeachboxcontainsapositiveinteger.Hewantsthevalueinthetopboxtobe720.Howmanydifferentvaluescantheintegerntake?Donggyu想完成右圖，使得中間行和頂行中的每個(gè)方格都包含其下方緊鄰的兩個(gè)方格內(nèi)的數(shù)字之積，且每個(gè)方格內(nèi)均為正整數(shù)．他希望頂行方格中的數(shù)字為720，那么請(qǐng)問(wèn)整數(shù)n可以有多少個(gè)不同的數(shù)值？A.1B.4C.5D.6E.826、FarmerFiissellingchickenandduckeggs.Shehasbasketsholding4,6,12,13,22,and29eggs.Herfirstcustomerbuysalltheeggsinonebasket.Finoticesthatthenumberofchickereggsshehasleftistwicethenumberofduckeggs.Howmanyeggsdidthecustomerbuy?農(nóng)夫Fi正在賣雞蛋和鴨蛋．她有很多個(gè)籃子，里面分別裝有4、6、12、13、22、29個(gè)蛋．第一位顧客買了其中一個(gè)籃子中所有的蛋．此時(shí)Fi注意到在剩下的蛋中，雞蛋數(shù)量是鴨蛋數(shù)量的兩倍．請(qǐng)問(wèn)這位顧客買了多少個(gè)蛋？A.4B.12C.13D.22E.2927、Threeanglesα,β

andγ

aremarkedonsquaredpaper,asshown.Whatisthevalueof

α+β+γ?如圖所示，方格紙上標(biāo)記有α、β、γ三個(gè)角．請(qǐng)問(wèn)α+β+γ的值是多少？A.6B.7C.75D.90E.1228、CaptainFlintaskedfourofhispiratestowriteonapieceofpaperhowmanygold,silverandbronzecoinswereinthetreasurechest.Theirresponsesareshowninthediagrambutunfortunatelypartofthepaperwasdamaged.Onlyoneofthefourpiratestoldthetruth.Theotherthreeliedinalltheiranswers.Thetotalnumberofcoinsis30.Whotoldthetruth?海盜船長(zhǎng)Flint要求他的4位船員在一張紙上記錄下藏寶箱中金幣、銀幣、銅幣的數(shù)量．船員們的記錄如下圖所示，但不幸的是，紙張出現(xiàn)了部分破損．四位船員中只有一位是如實(shí)記錄，其他三位記錄的數(shù)字全部都是虛假的．已知硬幣的總數(shù)量為30枚．請(qǐng)問(wèn)哪位船員記錄的數(shù)字是真實(shí)的？A.TomB.AlC.PitD.JimE.wecannotbesure無(wú)法確定29、AlexdrivesfrompointAtopointB,thenimmediatelyreturnstoA.BobdrivesfrompointBtopointA,thenimmediatelyreturnstoB.Theytravelonthesameroad,startatthesametimeandeachtravelsataconstantspeed.Alex'sspeedisthreetimesBob'sspeed.Theypasseachotherforthefirsttime15minutesafterthestart.Howlongafterthestartwilltheypasseachotherforthesecondtime?Alex開(kāi)車從A點(diǎn)到B點(diǎn)，然后又立刻返回A點(diǎn)．Bob開(kāi)車從B點(diǎn)到A點(diǎn)，然后又立刻返回B點(diǎn)．他們?cè)谕粭l路上行駛，同一時(shí)間出發(fā)，并且勻速前行．Alex的速度是Bob的三倍．他們出發(fā)15min后第一次相遇．請(qǐng)問(wèn)他們?cè)诔霭l(fā)多久之后會(huì)第二次相遇？A.20minB.25minC.30minD.35minE.45min30、InthepentagonABCDE,∠A=∠B=90°,AE=BCandED=DC.FourpointsaremarkedonABdividingitintofiveequalparts.Thenperpendicularsaredrawnthroughthesepoints,asshowninthediagram.Thedarkshadedregionhasanareaof13cm2在五邊形ABCDE中，∠A=∠B=90°，AE=BC，ED=DC．在線段AB上標(biāo)出4個(gè)點(diǎn)，將其分成5等份．然后經(jīng)過(guò)這4點(diǎn)做垂線，如圖所示．深色陰影區(qū)的面積為13cm2A.45B.47C.49D.58E.601、【答案】B;【解析】OnlyforB,tworingsareformedthatmustpassthrougheachotheranditisimpossibletodothiswithoutcuttingthestring.【標(biāo)注】2、【答案】C;【解析】Notethatalltilesarerotatedby180°.Nootherrotationcanmakethetilefitasthepentagonaltilehasexactlytworightangles.【標(biāo)注】3、【答案】E;【解析】Theinitialfigurecanbedividedintofourrighttrianglesofthesamearea,andtheinitialfigureintosixtriangles,thustheproportionin6/4,thatis3/2=1.5,thereforeithasincreasedby50%.【標(biāo)注】4、【答案】D;【解析】20×24【標(biāo)注】5、【答案】D;【解析】Atetrahedronhasfourcorners.Threesidesmeetateachvertex.Everycutcornertherforgivesthreenewcorners.Soifallfouroldcornersarecutoff,4×3=12newcornersarecreated.【標(biāo)注】6、【答案】B;【解析】Youcanmake1511,1115,5111and1151.Noticethat,normallyyoucanmake3?2?1=6numbers,butwhen1and11arenexttoeachother,theorderisnotimportant,soyoulose2possibilities.【標(biāo)注】7、【答案】E;【解析】Ifwewantthateveryonegetsthefruitshe/helikesthenAlgetstheappleandEvagetsthecherries.【標(biāo)注】8、【答案】C;【解析】Weneedtodeterminehowmanychildrencanbeintheelevatorinsteadof12?9=3adults.Ifinsteadof12adultstherecanbe20children,theninsteadoffourtimeslessadultstherecanbefourtimeslesschildren,i.e.20:4=5【標(biāo)注】9、【答案】C;【解析】Inthetoprow,weeitherhavea2anda3,ora1anda6.Ifweplacethe2inthetopleftsquare,wewillneedtorepeata2inthebottomleftsquaresothisisnotpossible.Ifweplacea3ora6inthetopleftsquare,itgivesafractioninthebottomleft.Hence,wemustplacea1inthetopleftsquare.Fromhere,wecanfillinthewholegridasfollows.Alternativesolution:Inthetopleftsquarewemustwriteacommondivisorof4and6,itmaybeonly1or2.Ifwewritethe2inthetopleftsquare,wewillneedtorepeata2inthebottomleftsquaresothisisnotpossible.So,itremainsonly1forthetopleftsquare.Fromhere,wecanfillinthewholegridasfollows:【標(biāo)注】10、【答案】C;【解析】Thedifferenceinlengthbetween4trolleysand10trolleysequals60cm.Adding10?4=6trolleysmeansadding60cm.So,addingoneextratrolleymeansadding60cm:6=10cmAlternativesolutionLetthelengthofonetrolleyequalxcmandlettheleftpartofthefirst(fromleft)trolley,whichisnotcoveredbyothertrolleys,equalycm.Thelengthofasetoffourwell-parkedtrolleysconsistsofthreepartsyofthefirstthreetrolleysandthelengthxoftheforthtrolley.Thus,3y+x=108.Analogously,fortentrolleyswehave9y+x=168.Itfollowsthat6y=168?160=60andy=10cm【標(biāo)注】11、【答案】B;【解析】Theangleofeachpieceis360°10=36【標(biāo)注】12、【答案】A;【解析】Oneofthegivenpieceshasarowoffournumberswithsum2+1+3+1=7.Thereforethesumofthenumbersinthewholesquareis4×7=28.Thesumsofthenumbersonthethreepiecesare7,8and8andhenceapiecewherethenumberssumto28?7?8?8=5isrequired.Oftheoptionsgiven,theonlyonewithasumof5isA.Thediagrambelowshowshowthesefourpiecesfittogethertomakethesquare.【標(biāo)注】13、【答案】A;【解析】AreasA+CandB+Careequalsincebotharehalfthesquare.SoA?B=(A+C)?(B+C)=0.【標(biāo)注】14、【答案】D;【解析】Theonlywayachickcanhaveeaten44fishintotalistohaveeaten5fishsixtimesand7fishtwice.Thereforeithadeatenfishon8days.ThenumberoffishPaulabroughtbackonthose8dayswas8×12=96.Hencethenumberoffisheatenbythesecondchickwas96?44=52.【標(biāo)注】15、【答案】A;【解析】Thereare30facestocover.Addingacubeintooneofthe"angles"aboutoneedgeoftheinnermostcubeofthestructurecovers2(inner)facesatthesametime.Thereare12edgesofthisinnermostcube,hencewith12cubesyoucoverthese24innerfaces.Tocovertheoutermostfacesyouneed6morecubes,hence18cubesaltogether.【標(biāo)注】16、【答案】D;【解析】Letudenotethenumberofuphilljumpsanddthenumberofdownhilljumps.Sincethekangaroocoversthreetimesthedistancewitheachdownhilljumpasitdoeswitheachuphilljump,itwillmakethreetimesasmanyuphilljumpsasitdoesdownhilljumps.Thereforeu=3d.Sincewearetoldthatu+d=2024.Thereforethetotaldistance,inmetres,thatthekangaroojumpsis506×3+3×506×1=3036.【標(biāo)注】17、【答案】B;【解析】Fromthediagram,itcanbeseenthattheperimeteroftherectangleinthetopleftandtheperimeteroftherectangleinthebottomrighttogetherareequaltotheperimeterofthelargerectangle.Thesameargumentistruefortheperimeteroftherectangleinthebottomleftandtheperimeteroftherectangleinthetopright.Therefore

24+?=18+16,andhence

?=10.【標(biāo)注】18、【答案】C;【解析】Consider100gramsoffreshmushrooms.Since80%ofthisiswater,theremainderhasamassof20grams.Whendried,this20gramsnowrepresents80%ofthetotalmassandsothe20%thatiswaterhasamassof5grams.Thereforethetotalmassofthedriedmushroomsis25gramsandhencethedecreaseis75gramsor75%oftheoriginalmass.AlgebraicSolution:LetthemassofthewaterinthedriedmushroomsbeXgrams.Sincethisrepresents20%ofthetotalmass,themassoftheremainderfourtimesasmuchandsois4Xgrams.However,this4Xgramsrepresentsonly20%ofthemassoffreshmushroomsandhencethemassofwaterinthefreshmushroomsisfourtimesasmuchandsois16Xgrams.Thereforethepercentagedecreaseinthemassis(16X+4X)?(4X+X)【標(biāo)注】19、【答案】D;【解析】Eachhexagonissurroundedbysixtriangles,andeverytriangletouchesthreehexagons.Thereare6/3=2trianglesperhexagon,soapproximately6000altogether.【標(biāo)注】20、【答案】E;【解析】Sinceallfourmadeatruestatement,thenumbersonAleksa'scardswere1and5or2and4,thenumbersonBart'scardswere1and6,2and7,3and8or4and9,thenumbersonClara'scardswere2and9or3and6andthenumbersonDeindra'scardswere1and2,2and4,3and6or4and8.SupposethenumbersonAleksa'scardswere2and4.ThenthenumbersonClara'scardscouldonlybe3and6.However,thiswouldnotleaveanypossiblecardsforDeindra.Thereforethenumbersonleksa'scardswere1and5.NowsupposethenumbersonClara'scardswere2and9.ThenthenumbersonDeindra'scardscouldonlybe3and6.However,thiswouldnotleaveanypossiblecardsforBart.ThereforethenumbersonClara'scardswere3and6.FinallysupposethenumbersonBart'scardswere4and9.HoweverthisleavesnopossiblecardsforDeindra.ThereforethenumbersonBart'scardswere2and7,leavingcardsnumbered4and8forDeindra.Hencethecardnumbered9isleftonthetable.【標(biāo)注】21、【答案】A;【解析】Eachdigithas0,1,2or3horizontalsegments,sothetotalof5canbeobtainedas5=2+2+1or5=3+1+1or5=3+2+0.However,thefirstoptionisnotpossiblesinceonly0hastwohorizontalsegments.Thesecondoptionisnotalsopossible,sinceonly4and7haveonehorizontalsegment,andthedigits4and7haveatotalof3+2=5verticalsegments,meaningthethirddigitwouldneedtohave5verticalsegmentsandthemaximumpossibleis4.Thereforetheremustbe3,2,and0horizontalsegmentsinthedigits.Onlydigit1hasnohorizontalsegmentsandonlydigit0hastwohorizontalsegmentsandtheyhavesixverticalsegmentsbetweerthem.Thereforethefinaldigithasthreehorizontalsegmentsandfourverticalsegmentsandsoisdigit8.Hence,thesumofthedigitsis8+0+1=9.【標(biāo)注】22、【答案】E;【解析】Thesingleaxisofsymmetrycanbehorizontal,vertical,diagonalfromtoplefttobottomrightanddiagonalfrombottomlefttotopright.Inthefirstthreecases.Tarekcanonlyshadetwofurthersquaresinonewaytogiveasymmetricalpattern.However,inthefinalcase,therearethreepossiblewaystocompleteasymmetricpattern.Hence,Tarekcancompletehispatternin1+1+1+3=6differentways.【標(biāo)注】23、【答案】B;【解析】Let?cmbethelengthoftheunknownsideoftherectangle.Thereforetheradiofthethreesemi-circles,in

cm,are?,??5and??7.Therefore,byconsideringthelongersideoftheectangle,wehave2(?+??5+??7)=36.Thishassolution?=10.Thereforetheperimetertherectangle,incm,is2?(36+10)=92【標(biāo)注】24、【答案】D;【解析】Inorderforastudenttoreceivetheballagainafterpassingiton,theballmustbypassamultipleof50students.Astheballiscatchedbyevery6thstudent,itmustalsohavebypassedamultipleof6studentsatanygiventime.Therefore,theballmustbypass150(theLCMof50and6)studentsforthefirststudenttoreceivetheballagain.Beforethisoccures,theballhasbeenpassedto150/6=25studentsandwecanbesurethatnotwostudentsarethesamebecausethiswouldtakeatleast150passes.Afterthefirststudentreceivetheballagainandstartpassingitaroundforthesecondtime,thepassingpatternrepeatitselfandthesame25playerswillgettheballagain,meaningtheother25playerswillnevertouchtheball.【標(biāo)注】25、【答案】D;【解析】Letaandbbethemissingvaluesintheboxesintheleft-handsideandright-handsideofthebottomrowrespectively.Thereforethevaluesintheboxesinthemiddlerowareanandbnandthev