沖刺南外英語思維專題訓(xùn)練4解析卷

“沖刺南外”英語思維專題訓(xùn)練四解析卷姓名成績10、ratioandproportion（比和比例）1.TheratioofpriceoftwogoodsAandBis7:3,iftheirpriceriseupby70yuan,thentheratioofpricewillbe7:4,whattheoriginalpriceofthesetwogoodsrespectively?【解析】差不變，把這兩個比化成差相等的比，即7:3=21:9；7:4=28:16；一份就是70÷（28-21）=10.甲原來有10×21=210；乙有10×9=90.2.Thereisagroupofstudentsplayinggamesontheground,andtheratioofboysandgirlsis3:2.Then6girlscomeoutoftheclassroomandjointhem,andtheratioofboysandgirlsbecome5:4.Whataretheoriginalnumbersofboysandgirlsrespectively?【解析】男生人數(shù)不變，把這兩個比化成前項相等的比，即3:2=15:10；5:4=15:12，一份就6÷（12-10）=3（人）。原來男生有3×15=45人；女生有3×10=30人。AtraingoesfromAtoBinthespeedof50km/h,whenitarrivedatastation,thedistanceitpassedis10kmmorethanonefifthofthetotaldistance.Thenitwentonforanother2.4hours,andtheratioofthedistanceithadpassedandtheremainingjourneyis1:2.What’sthetotaldistancebetweenAandB?【解析】轉(zhuǎn)化成分?jǐn)?shù)應(yīng)用題來解答，先走了全程的1/5多10千米，再走2.4小時即走了2.4×50=120千米，這時行了的路程和剩下的比是1:2，即行了全程的1/3，所以全程就是（10+120）÷（1/3-1/5）=975（千米）ThepriceofcandyAandcandyBarerespectively10.8yuanperkilogramand14.8yuanperkilogram.Mixthesetwokindofcandiesandthepricebecome12.3yuanperkilogram.What’stheratioofweightofcandyAandB?【解析】用十字交叉法來解答：（14.8-12.3）：（12.3-10.8）=5:3.5.Asshowninthefigure,inthetriangleABC,DC:BC=2:5,BO:OE=4,What’sAE:EC?【解析】假設(shè)三角形AOB的面積為4，則三角形AOE的面積為1；連接OC。因為BD：DC=3:2，則三角形AOB面積：三角形AOC面積=3:2，三角形AOC的面積就是4÷3×2=8/3；三角形COE的面積為8/3-1=5/3；AE：EC=1:5/3=3:511、Logicalreasoning（邏輯推理）6、AmongXiaoZhao,XiaoQianandXiaoSun,thereisaworker,adoctorandateacher.It’sknownthatXiaoSunisolderthantheteacher,XiaoZhaoandthedoctorhavedifferentages,andthedoctorisyoungerthanXiaoQian.Pleasefindouttheworker,thedoctorandtheteacherrespectively？【解析】列表推理。工人醫(yī)生教師趙×錢×孫×√×再按年齡排一下序：錢＞醫(yī)生（孫）＞教師，則趙是教師；錢是工人。7.LiZhiming,ZhangBinandWangDaweichosedifferentworkaftergraduation（畢業(yè)）,andoneofthemisajournalist（記者）.Someoneaskedabouttheirworkoneday,LiZhimingsaidthat“I’majournalist.”,ZhangBinsaid:“I’mnotajournalist.”,whileWangDaweisaid:”LiZhimingtoldalie.”.Ifonlyoneofthemtoldthetruth,thenwhoisajournalist？【解析】矛盾法推理。李志明和王大為的話互相矛盾，必有一真一假。因為只有一個人說真話，則張斌的話是假話，他說“我不是記者”，則他就是記者。8.A,B,CandDtakepartinatabletenniscontest,andeverytwoofthemshouldplayagame.TheresultisthatAbeatD,andA,BandCwinthesametimes.HowmanytimesdoesDwin?【解析】四個人單循環(huán)要打3+2+1=6場比賽。A、B、C贏的場數(shù)相同，只能都贏了1場或2場。如果都贏了1場，則D贏了6-3=3場，就表示D是全贏，這和A勝了D矛盾。所以A、B、C各贏了2場，D贏了6-2×3=0場。9.Therearefourlittlerabbitswhoseagearedifferentandrangedfrom1to4.Twoofthemcantalk,nomatterwhospeak,it’suntruewhenit’saboutrabbitsolderthanthetalkerandit’salwaystruewhenit’saboutrabbitsyoungerthanthetalker.RabbitAsays:”RabbitBis3yearsold.”,andrabbitCsays:”TheageofRabbitAisnot1.”.Pleasefindoutagesofthesefourrabbits.【解析】假設(shè)A的話是對的，則B是3歲，A是4歲，這樣C比A小，他要說假話，而他說“A不是1歲”，這是真話，推出矛盾了。所以A的話是假話，他說“B是3歲”，B就不是3歲，并且A要比B小，B就是4歲（B不能是2歲，為什么？）；而C說A不是1歲，所以A是2歲，C是3歲，D是1歲。Thereare3familiesthatallhaveonechild,threechildrenareXiaoHong(girl),XiaoLing(girl)andXiaoDong(boy),threefathersareMrWang,MrLiandMrZhang,andthreemothersareWangPing,ZhaoQinandXiaoYanrespectively.Andit’sknownthat:(1)ChildrenofMrWangandZhaoQinbothtakepartinthegirl’sswimmingteam;(2)ThegirlofMrLi’sfamilyisn’tXiaoLing;(3)MrZhangandXiaoYanisn’tinafamily.Pleasefindoutparentsandchildofthesethreefamilyrespectively.【解析】列表推理。王萍趙琴肖艷老王××√小玲老李×√×小紅老張√××小東12、Projectproblem（工程問題）11.Acanfinishaprojectin20daysalone,whileBcanfinishthesameprojectin30daysalone.AandBhaddonetheprojecttogetherforafewdays,thenBaskedforleaveforseveraldaysandAkeptdoing,andtheprojectwouldbedonein16daysfromthebeginningtotheend.HowmanydaysdidBleavefor?【解析】（1-16/20）÷1/30=6；16-6=10（天）12.AandBprocessabatchofpartstogether,theyfinishedonethirdofthetotalin2days.IttakesA10daystofinishprocessingthesepartsalone.HowmanydayswillittakeforBtofinishprocessingthesepartsalone?【解析】工效和是1/3÷2=1/6；1÷（1/6-1/10）=1513.IttakesA9hourstofinishanassignmentaloneandittakesB12hourstohavetheassignmentdonealone.Iftheyworkintheturnof“A,B,A,B......”andworkanhoureveryturn.Howlongwillittakethemtofinishtheassignment?【解析】周期工程。A、B各干一小時，一個周期做了1/9+1/12=7/36；單位“1”里最多有5個這樣的周期，還剩1/36，這時輪到A干，需要1/36÷1/9=1/4（小時），共用了5×2+1/4=10又1/4小時。14.IfpipeAandpipeBareopenatthesametime,theycanfillthepoolin6hours;ifpipeBandpipeCareopenatthesametime,theycanfillthepoolin4hours.NowweopenpipeBfor6hours,andopenpipeAandpipeCfor2hoursatthesametime,thenwecanfillthepool.IfweopenpipeBalone,howlongwillittaketofillthepool?【解析】把B的6小時分成三個2小時。整個過程，相當(dāng)于A、B合干2小時，B、C合干2小時，B又單獨做了2小時，即B的每小時做（1-2/6-2/4）÷2=1/12，單獨做完工作需要12小時。15.Thereisaroad,whichteamAcanfinishitalonein15daysandteamBcanfinishitalonein12days.Afterworkingtogetherfor4days,teamBwastransferredaway,andteamAkeptworkingontheroaduntilit’sfinished.HowmanydaysdidteamAworkintotal?【解析】（1-4/12）÷1/15=10（天）Ca