【微臣数学难题班讲义集锦

难题集锦A1.Ifjandkareevenintegersandjk,whichofthefollowingequalsthenumberofevenintegersthataregreaterthanjandlessthank?A.(k-j-2)/2B.(k-j-1)/2C.(k-j)/2D.k-jE.k-j-12.m=10#$+2,whenmisdividedby11,theremainderisr.QuantityArQuantityB33.Inasinglelineofpeoplewaitingtopurchaseticketsforamovie,therearecurrently10peoplebehindShandra.If3ofthepeoplewhoarecurrentlyinlineaheadofShandrapurchaseticketsandleavetheline,andnooneelseleavestheline,therewillbe8peopleaheadofShandrainline.Howmanypeopleareinthelinecurrently?4.AandBareindependentevents,andtheprobabilitythatbotheventsoccuris1/2.WhichofthefollowingcouldbetheprobabilitythateventAoccurs?Indicateallsuchprobabilities.A.0B.1/4C.1/2D.3/4E.15.Howmanypositiveintegerslessthan10,000aresuchthattheproductoftheirdigitsis210?A:24B:30C:48D:54E:726.Fromagroupof8people,itispossibletocreateexactly56differentk-personcommittees.Whichofthefollowingcouldbethevalueofk?Indicateallsuchvalues.A.1B.2C.3D.4E.5F.6G.77.Yesterday’sclosingpricesof2,420differentstockslistedonacertainstockexchangewerealldifferentfromtoday’sclosingprices.Thenumberofstocksthatclosedatahigherpricetodaythanyesterdaywas20percentgreaterthanthenumberthatclosedatalowerprice.Howmanyofthestocksclosedatahigherpricetodaythatyesterday?A.484B.726C.1,100D.1,320E.1,6948.Ofthestudentsinaschool,20percentareinthesciencecluband30percentareintheband.If25percentofthestudentsintheschoolareinthebandbutarenotinthescienceclub,whatpercentofthestudentswhoareinthescienceclubarenotintheband?A.5%B.20%C.25%D.60%E.75%9.ThecompanyatwhichMarkisemployedhas80employees,eachofwhomhasadifferentsalary.Mark’ssalaryof$43,700isthesecond-highestsalaryinthefirstquartileofthe80salaries.Ifthecompanyweretohire8newemployeesatsalariesthatarelessthanthelowestofthe80salaries,whatwouldMark’ssalarybewithrespecttothequartilesofthe88salariesatthecompany,assumingnootherchangesinthesalaries?A.Thefourth-highestsalaryinthefirstquartileB.ThehighestsalaryinthefirstquartileC.Thesecond-lowestsalaryinthesecondquartileD.Thethird-lowestsalaryinthesecondquartileE.Thefifth-lowestsalaryinthesecondquartile10.xisapositiveinteger.Whenxisdividedby2,4,6,8,theremainderis1.QuantityAxQuantityB2411.Whichofthefollowingcouldbethesumofthreeconsecutiveintegers?A.29B.46C.57D.92E.10012.𝑥&𝑦(𝑧*equalstheproductof154and56,z𝑦𝑥 𝑎𝑛𝑑 𝑎𝑏𝑐,thenwhatisthevalueof𝑎2𝑏3𝑐4?A.1024B.2048C.8624D.22528E.cannotbedeterminedbytheconditiongiven13.If1≤𝑛≤100,and678$isamultipleof4butnotamultipleof3,thenwhichofthefollowingcouldbetrue?Indicateallpossiblevalues.A.nisevenB.nisoddC.nisprimeD.nisamultipleof3E.nisamultipleof414.f,g,hareconsecutiveprimenumberssuchthatfghQuantityAQuantityBf+g+h3g15.kisapositiveintegerand225and216arebothdivisorsofk.Ifk=2&3(5*,wherea,bandcarepositiveintegers,whatistheleastpossiblevalueofa+b+c?A.4B.5C.6D.7E.816.xisanintegergreaterthan3.QuantityAthenumberofevenfactorsof2xQuantityBthenumberofoddfactorsof3x17.Inhowmanywayscan16differentgiftsbedividedamongfourchildrensuchthateachchildreceivesexactlyfourgifts?A.16=B.(4!)=C.16!/ (4!)=D.16!/4!E.4BC18.If867B+86=36,thenn=A.1/3B.1/2C.3/5D.2/3E.4/519.If55percentofagroupofpeoplehavebrownhairand80percentofthesamegroupdonothaveredhair,what’sthefractionofthosewhodonothavebrownhairhaveredhair?A.1/4B.4/11C.4/9D.5/9E.4/520.LastyearMelaniahadatotalof$20000investedintwomutualfunds,CapitalGrowthFundandVentureIndexFund.Attheendoftheyear,sheanalyzedherinvestmentsandfoundthatherearningsonhersharesofCapitalGrowthFundwerethreetimeshalfofherearningsonherinvestmentinVentureIndexFund.Ifsheearnedatotalof$1250onherinvestmentsinthetwofunds,andhadthreetimesasmuchmoneyinvestedinCapitalGrowthFundasinVentureIndexFund,whatpercentinterestdidMelaniaearnonherinvestmentinVentureIndexFund?A.0.075B.0.01C.7.5D.10E.50021.Thefunctionfisdefinedbyf(27$$)=3𝑥$-x+5QuantityA:f(4)QuantityB:7522.QuantityA:180+aQuantityB:b+c23.Theaverageofthreedifferentpositiveintegersis6.QuantityATheproductofthethreeintegersQuantityB2524.ListKconsistsof16positivenumbers.ListMisobtainedfromlistKbymultiplyingeachnumberinlistKby-1QuantityAThestandarddeviationofKQuantityBThestandarddeviationofM25-26arebasedonthegraphgiven.25.Howmanyoftheage-groupseachaccountedformorethan15percentofthetotalnumberofoccupationalinjuriesinStateXin1998?A.OneB.TwoC.ThreeD.FourE.Five26.In1998,ifone-halfoftheoccupationalinjuriesinthecombined34-andunderage-groupswereincurredbymen,whatwasthenumberofoccupationalinjuriesincurredbymeninthecombined35-and-overage-groups?A.33,500B.31,900C.30,500D.25,400E.21,70027.Forthe55-64age-groupin1998,theaverage(arithmeticmean)numberofwork-hourslostperoccupationalinjurywas48.5.Ifaworkweekis40work-hours,whichofthefollowingisclosesttothetotalnumberofworkweekslostduetooccupationalinjuriesinthe55-64age-groupin1998?A.4500B.5200C.5500D.5900E.630028.Inagraduatingclassof236students,142tookalgebraand121tookchemistry.Whatisthegreatestpossiblenumberofstudentsthatcouldhavetakenbothalgebraandchemistry?29.P,Q,andRarethreepointsinaplane,andRdoesnotlieonlinePQ.Whichofthefollowingistrueaboutthesetofallpointsintheplanethatare