冲刺南外英语思维专题训练3解析卷

“冲刺南外”英语思维专题训练三解析卷姓名成绩Newton'sproblem（牛顿问题）1.Themeadowiscoveredwithgrass,andthegrasskeepsgrowinconstantspeed.Grassonthemeadowcanbeeatenupby9cowsin20daysorby15cowsin10days.Thenhowmanydayswillittakefor18cowstoeatupthegrass.【解析】9×20=180；15×10=150；（180-150）÷（20-10）=3；150-3×10=120；120÷（18-3）=8（天）2.Awellpoursoutwaterinconstantspeedcontinually（不断）.Ittakes30minutestodrainthewaterifweuse8pumps,whileittakesahourifweuseonly5pumps.Todrainthewaterinthewellin18minutes,howmanypumpsdoweneed?【解析】8×30=240；5×60=300；（300-240）÷（60-30）=2；240-2×30=180；180÷18+2=12（架）Supposetheamountofresourcesgrowneachyeariscertain.It’sknownthatalltheresourcesonearthwillbeusedupby11billionpeoplein90years,orusedupby9billionpeoplein210years.Toguaranteetheresourcesonearthenoughtomakethehumanreproductionhowmanyshouldtheworld’spopulationbecontrolledwithin?【解析】11×90=990；9×210=1890；（1890-990）÷（210-90）=7.5（十亿）Theexhibitionhallopensdoorat9:00,butsomebodywaitinlinetoenterearlier.Fromthefirstvieweron,theamoutofviewersarrivedperminuteisequal.If3entrancesareopen,therewillbenowaiterby9:09,andif5entrancesareopen,therewillbenowaiterby9:05.Whendidthefirstviewerarrive?【解析】3×9=27；5×5=25；（27-25）÷（9-5）=0.5；25-5×0.5=22.5；22.5÷0.5=45（分）；9:00-45分=8:155.Threecarswhosespeedarerespectivelyfast,mediumandslowsetofffromAtoBatthesametimetocatchabike,theirspeedare24km/h,20km/h,19km/h.Ittakesthefastcar6hoursandthemediumcar10hourstocatchupwiththebike.Thenhowlongdoesittaketheslowcartocatchupwiththebike?【解析】24×6=144；20×10=200；（200-144）÷（10-6）=14；200-14×10=60；60÷（19-14）=12（小时）inclusion-exclusionprinciple（容斥原理）6.Among62students,11ofthemcanplaythepiano,56ofthemcanblowclarinetand4studentscanplayneither.What’sthenumberofstudentscanplayboth?【解析】62-4=58；11+56-58=97、Aforeignlanguageclasshas40students,andthestudentshavetolearnonelanguageamongEnglish,Japanese,Germanatleast.Thereare20studentswholearnEnglish,12studentswholearnJapanese,and18studentswholearnGerman.Besides,5studentslearnbothEnglishandJapanese,2studentslearnbothJapaneseandGermanandnobodylearnsthreelanguages.HowmanystudentslearnbothEnglishandGerman？【解析】20+12+18-5-2-x=40；x=3Amongnaturalnumbersfrom1to500,howmanynumberscanbedivisiblebyneither3nor5?【解析】【500/3】=166；【500/5】=100；【500/15】=33；166+100-33=233；500-233=2679.Thereare46studentsinaclass,40studentscanridebike,38studentscanplaytabletennis,35studentscanplaybadmintonand27studentscanswim.What’sthenumberofstudentswhocanallthefoursportsatleast?【解析】46-40=6；46-38=8；46-35=11；46-27=19；6+8+11+19=44；46-44=2（人）9.Markwordproblems（分数应用题）10.Numberaishalfofthesumofb,candd,numberbisone-thirdofa,candd,numbercisa-quarterofa,bandd.It’sknownthatd=130,whatthesumofa,b,candd?【解析】甲占总数的1/3；乙占总数的1/4；丙占总数的1/5；丁占总数的1-1/3-1/4-1/5=13/60，这就是130对应的分率，则总数是130÷13/60=600ofthenumberofpeachtreesisequaltoofthenumberofpeartrees,thesumoftreesis141.What’sthenumberofpeachtreesandpeartreesrespectively?【解析】根据条件可以求出桃树和梨树的比是：=20:27；一份就是141÷（20+27）=3（棵）；桃树有3×20=60（棵）；梨树有3×27=81（棵）Grade6choosesofthenumberofboysand12girlstotakepartinmathcompetition,thenumberofboysleftis2timesasthenumberofgirls.It’sknownthatthenumberofstudentsingrade6is156.Thenwhatarenumbersofboysandgirlsrespectively？【解析】用份数来思考。假设把男孩总数看成11份，则女孩总数是这样的（11-1）÷2=5份加12人，则一份就是（156-12）÷（11+5）=9（人）；男孩有9×11=99（人）；女孩有9×5+12=57（人）Thenumberofboysis25lessthanofthetotalnumberofstudentsinXinminelementaryschool,andthenumberofgirlsis15lessthanofthetotalnumber.What’sthetotalnumberofstudentsinXinminelementary？【解析】设学生总数为x人，则列方程为x-25+x-15=x，解得x=2520Alibraryowns1880booksofthreekinds,theyareliteraturebooks,sciencebooksandcomicbooks.Nowoftheliteraturebooksand50sciencebooksareborrowedandtakenaway,butanother40newcomicbooksareboughtandbroughtintothelibrary,thenthenumberofeachkindisthesame.Whataretheoriginalnumbersofthreekindsrespectively?【解析】把相等的数设为x本，则甲种原来有x本，乙种书有x+50本，丙种书有x-40本；列方程为x+x+50+x-40=1880，解得x=510。甲种有510×=850（本）；乙种书有510+50=560（本）；丙种书有510-40=470（本）Boysinthemathcompetitionare28morethangirls,andallthegirlsgetprize,whileonly3/4thboysgetprize.Besides,42studentsgetprize.Howmanyboysandgirlstookpartinthemathcompetitionrespectively？【解析】设原来女孩有x人，则原来男孩有x+28人。列方程为x+（x+28）=42；解得x=12.男孩有12+28=40（人）Hereis105litersofwaterand2containers.Thewatercanfilledinto