GRE（QUANTITATIVE）综合模拟试卷6（共160题）

GRE（QUANTITATIVE）综合模拟试卷6（共8套）（共160题）GRE（QUANTITATIVE）综合模拟试卷第1套一、数值比较题(本题共6题，每题1.0分，共6分。)1、标准答案：A知识点解析：InthisquestionyouareaskedtocomparethepriceatwhichEmmasoldthebicyclewith$140.Fromtheinformationgiven,youcanconcludethatEmmaspentatotalof75+27=102dollarsbuyingandrepairingthebicycleandthatshesolditfor40percentmorethanthe$102shespentbuyingandrepairingit.Ifyounoticethat140is40percentmorethan100,youcanconcludethat40percentmorethan102isgreaterthan40percentmorethan100,andtherefore,QuantityAisgreaterthanQuantityB.ThecorrectanswerisChoiceA.(Ifyousolvetheprobleminthisway,youdonothavetocalculatethevalueofQuantityA.)AnotherwaytosolvetheproblemisbyexplicitlycalculatingthevalueofQuantityAandcomparingtheresultwith$140directly.Since40percentof102is(0.4)(102)=40.8,itfollowsthatQuantityA,thepriceatwhichEmmasoldthebicycle,is102.00+40.80=142.80dollars.ThusQuantityA,$142.80,isgreaterthanQuantityB,$140,andthecorrectanswerisChoiceA.2、标准答案：C知识点解析：Inthisquestionyouareaskedtocomparetheareaoftheshadedregionwith36.YouaregiventhatbothPQRVandVRSTaresquareswithsidesoflength6.Therefore,youcanconcludethatthelengthofQSis12,andtheareaoftheshadedrighttrianglePQSis1/2(12)(6),or36.ThusQuantityAisequaltoQuantityB,andthecorrectanswerisChoiceC.3、标准答案：A知识点解析：Beforemakingthecomparisoninthisproblem,youneedtoanalyzetheinformationgiventoseewhatittellsyouaboutthevalueofQuantityA,thepropertytaxin2009onahomeinTownXthathadanassessedvalueof$160,000.Onewayofdoingthisistodeterminethevalueoftheconstantpandthenusethatvaluetocalculatethetaxonthehomethathadanassessedvalueof$160,000.Sinceitisgiventhatahomethathadanassessedvalueof$125,000hadapropertytaxof$2,500,youcanconcludethatpisequalto,or2%.Onceyouknowthatthepropertytaxis2%oftheassessedvalue,youcandeterminethattaxonthehomethathadanassessedvalueof$160,000was2%of160,000,or3,200.ThecorrectanswerisChoiceA.Anotherwaytocalculatethepropertytaxonahomewithanassessedvalueof$160,000isbysettingupaproportion.BecausethetaxrateisthesameforeachhomeinTownX,youcanletthevariablexrepresentthetaxforthehomeassessedat$160,000andsolveforxasfollows.ThecorrectanswerisChoiceA.4、标准答案：D知识点解析：Onewaytoapproachthisquestionistopluginvaluesforoneofthevariablesanddeterminethecorrespondingvaluefortheothervariable.Onewaytoplugin:Plugineasyvalues.Forexample,youcanpluginx=0andfindthatthecorrespondingvalueofyis-1;thenyoucanpluginy=0andfindthatthecorrespondingvalueofxis-1.Sinceinthefirstcasexisgreaterthanyandinthesecondcaseyisgreaterthanx,thecorrectanswerisChoiceD,therelationshipcannotbedeterminedfromtheinformationgiven.Asecondwaytoplugin:Ifyouprefertoalwayspluginvaluesofxtodeterminecorrespondingvaluesofy,youcanbeginbywritingtheequationx+y=-1asy=-x-1.Writingitinthisformmakesiteasiertofindthecorrespondingvaluesofy.Youcanstartbyplugginginthevaluex=0.Forthisvalueofx,thecorrespondingvalueofyisy=-1,andtherefore,xisgreaterthany.Ifyoucontinueplugginginavarietyofvaluesofx,somenegativeandsomepositive,youwillseethatsometimesxisgreaterthanyandsometimesyisgreaterthanx.Ifyouinspecttheequationy=—x-1,youcanconcludethatsincethereisanegativesigninfrontofthexbutnotinfrontofthey,foreachvalueofxthatisgreaterthan0,thecorrespondingvalueofyislessthan0;therefore,foreachx>0,xisgreaterthany.Whataboutnegativevaluesofx?Aquickinspectionoftheequationy=—x-1allowsyoutoconcludethatifx<-1,theny>0,soyisgreaterthanx.Soforsomevaluesofxandythatsatisfytheequation,xisgreaterthany;andforothervalues,yisgreaterthanx.Therefore,therelationshipbetweenthetwoquantitiesxandycannotbedeterminedfromtheinformationgiven,andthecorrectanswerisChoiceD.5、标准答案：B知识点解析：Youaregiventhatthreenumbers,r,s,andt,areconsecutiveoddintegersandthatrInthelaststepofthesimplification,youcaneasilyseethat3<5.Ifyoufollowthesimplificationstepsinreverse,youcanseethattheplaceholderineachstepremainsunchanged,soyoucanconcludethatQuantityBisgreaterthanQuantityA,andthecorrectanswerisChoiceB.Simplification2:Sincethenumbersappearsinbothquantities,youcanbeginthesimplificationbysubtracting5frombothsidesoftherelationshipandthenexpresstintermsofr.Thestepsinthissimplificationcanbedoneasfollows.Inthelaststepofthesimplification,youcaneasilyseethat1<3.Ifyoufollowthesimplificationstepsinreverse,youcanseethattheplaceholderineachstepremainsunchanged,soyoucanconcludethatQuantityBisgreaterthanQuantityA,andthecorrectanswerisChoiceB.Notethatinthissolution,thefactthatrisoddisnotused;whatisusedisthefactthattheconsecutiveoddintegersdifferby2.6、标准答案：A知识点解析：Notethattheslopeofeachofthelinesispositive,sinceeachlinerisesasitgoestotheright.Sincetheslopesofbothlinesarepositiveandlinekrisesfaster(orissteeper)thanlinet,linekhasthegreaterslope,andthecorrectanswerisChoiceA.Youcanalsousethedefinitionoftheslopetoarriveatthecorrectanswer.Slopecanbedefinedastheratioof"rise"to"run"betweenanytwopointsonaline,wheretheriseistheverticaldistancebetweenthepointsandtherunisthehorizontaldistance,andtheslopeisrespectivelypositiveornegativedependingonwhetherthelinerisesorfallswhenviewedfromlefttoright.BecausebothlinespassthroughpointPonthey-axis,theyhavethesamerisefromPtothex-axis.However,linetintersectstheX-axisatagreatervaluethanlinek.Thus,therunoflinelfromthey-axistothex-interceptisgreaterthantherunoflinek.Whentheslopeisexpressedasaratio,bothlineshavethesamenumerator(rise),butlinelhasagreaterdenominator(run).Thegreaterdenominatorresultsinalesserfractionandalesserslopeforlinel.Therefore,thecorrectanswerisChoiceA.二、计算题(本题共7题，每题1.0分，共7分。)7、Inthefigureabove,whatisthevalueof?A、2B、3C、4D、5E、6标准答案：C知识点解析：Thesumofthemeasures,indegrees,ofthethreeinterioranglesofanytriangleis180°.Asshowninthefigure,thethreeanglesofthetrianglehavemeasuresofx°,y°,andz°,sox+y+z=180.Therefore,=4,andthecorrectanswerisChoiceC.8、Acertainstoresellstwotypesofpens:onetypefor$2perpenandtheothertypefor$3perpen.Ifacustomercanspendupto$25tobuypensatthestoreandthereisnosalestax,whatisthegreatestnumberofpensthecustomercanbuy?A、9B、10C、11D、12E、20标准答案：D知识点解析：Itisfairlyclearthatthegreatestnumberofpensthatcanbeboughtfor$25willconsistmostly,ifnotentirely,of$2pens.Infact,itisreasonabletobeginbylookingathowmanyofthe$2pensthecustomercanbuyifthecustomerdoesnotbuyany$3pens.Itiseasytoseethatthecustomercouldbuy12ofthe$2pens,with$1leftover.Ifthecustomerbought11ofthe$2pens,therewouldbe$3leftoverwithwhichtobuya$3pen.Inthiscase,thecustomercouldstillbuy12pens.Ifthecustomerbought10ofthe$2pens,therewouldbe$5leftover.Only1ofthe$3penscouldbeboughtwiththe$5,sointhiscase,thecustomercouldbuyonly11pens.Asthenumberof$2pensdecreases,thetotalnumberofpensthatthecustomercanbuywith$25decreasesaswell.Thusthegreatestnumberofpensthecustomercanbuywith$25is12.ThecorrectanswerisChoiceD.9、Ify=3xandz=2y,whatisx+y+zintermsofx?A、10xB、9xC、8xD、6xE、5x标准答案：A知识点解析：Itisnotnecessarytofindtheindividualvaluesofx,y,andztoanswerthequestion.Youareaskedtorewritetheexpressionx+y+zasanequivalentexpressionintermsofx.Thismeansthatyouneedtousetheinformationprovidedaboutyandztoexpressthemintermsofthevariablex.Thevariableyisalreadygivenintermsofx;thatis,y=3x;andbecausez=2y,itfollowsthatz=(2)(3x)=6x.Usingsubstitution,youcanrewritetheexpressionasfollows.x+y+z=x+(3x)+(6x)=(1+3+6)x=10xThecorrectanswerisChoiceA.10、Acertainshippingservicechargesaninsurancefeeof$0.75whenshippinganypackagewithcontentsworth$25.00orlessandaninsurancefeeof$1.00whenshippinganypackagewithcontentsworthover$25.00.IfDanusestheshippingcompanytoshipthreepackageswithcontentsworth$18.25,$25.00,and$127.50,respectively,whatisthetotalinsurancefeethatthecompanychargesDantoshipthethreepackages?A、1.75B、2.25C、2.5D、2.75E、3标准答案：C知识点解析：Notethattwoofthepackagesbeingshippedhavecontentsthatareworth$25.00orless.Therefore,eachofthemhasaninsurancefeeof$0.75,foratotalof$1.50.Thethirdpackagehascontentsworthover$25.00,andithasaninsurancefeeof$1.00.Therefore,thetotalinsurancefeeforthethreepackagesis$1.50+$1.00=$2.50,andthecorrectanswerisChoiceC.11、If55percentofthepeoplewhopurchaseacertainproductarefemale,whatistheratioofthenumberoffemaleswhopurchasetheproducttothenumberofmaleswhopurchasetheproduct?A、11to9B、10to9C、9to10D、9to11E、5to9标准答案：A知识点解析：Notethatbecause55percentofthepeoplewhopurchasetheproductarefemales,itfollowsthat45percentofthepeoplewhopurchasetheproductaremales.Therefore,theratioofthenumberoffemaleswhopurchasetheproducttothenumberofmaleswhopurchasetheproductis55to45,or11to9,andthecorrectanswerisChoiceA.12、Intherectangularsolidabove,TU=3,UV=4,andVR=Whatistheareaoftheshadedrectangularregion?______标准答案：10知识点解析：Tofindtheareaoftheshadedrectangularregion,youneedtomultiplythelengthoftherectangularregionbyitswidth.Inthisquestionyouaregiventhelengthsofthreeedges:TU=3,UV=4,andVR=2.NotethatVRisthelengthoftheshadedrectangle.Tofindthewidthoftheshadedrectangle,youneedtofindeitherRSorVT.NotethatVTliesonthefrontfaceoftherectangularsolid.ItisthehypotenuseofrighttriangleVUT.YouknowthatUV=4andTU=3,sobythePythagoreantheoremyoucanconcludethatVT==5.Therefore,theareaoftheshadedrectangularregionis(5)(2)=10.Thecorrectansweris10.13、Alistofnumbershasameanof8andastandarddeviationof2.Ifxisanumberinthelistthatis2standarddeviationsabovethemean,whatisthevalueofx?x=______标准答案：13知识点解析：Youaregiventhatxis2standarddeviationsabovethemean,8.Becausethestandarddeviationofthenumbersinthelistis2.5,itfollowsthatxis(2)(2.5),or5unitsabovethemean8.Therefore,x=8+5=13,andthecorrectansweris13.三、图表题(本题共1题，每题1.0分，共1分。)14、Thecirclegraphaboveshowsthedistributionof200,000physiciansbyspecialty.Whichofthefollowingsectorsofthecirclegraphrepresentmorethan40,000physicians?Indicateallsuchsectors.A、PediatricsB、InternalMedicineC、SurgeryD、AnesthesiologyE、Psychiatry标准答案：A,B,C知识点解析：Oneapproachtosolvethisproblemistofindoutwhatpercentof200,000is40,000andthencomparethispercentwiththepercentsgiveninthecirclegraph.Because=0.2,itfollowsthat40,000is20%of200,000,andanyspecialtythathasmorethan20%ofthedistributionhasmorethan40,000physicians.Thisistrueforthespecialtiesofpediatrics,internalmedicine,andsurgery.ThecorrectanswerconsistsofChoicesA,B,andC.GRE（QUANTITATIVE）综合模拟试卷第2套一、计算题(本题共8题，每题1.0分，共8分。)Evaluatethefollowing.(a)15-(6-4)(-2)(b)(2-17)÷5(c)(60÷12)-(-7+4)(d)(3)4-(-2)3(e)(-5)(-3)-15(f)(-2)4(15-18)4(g)(20÷5)2(-2+6)3(h)(-85)(0)-(-17)(3)1、标准答案：19知识点解析：暂无解析2、标准答案：-3知识点解析：暂无解析3、标准答案：8知识点解析：暂无解析4、标准答案：89知识点解析：暂无解析5、标准答案：0知识点解析：暂无解析6、标准答案：1296知识点解析：暂无解析7、标准答案：1024知识点解析：暂无解析8、标准答案：51知识点解析：暂无解析二、图表题(本题共7题，每题1.0分，共7分。)PERCENTOFFEMALEFACULTYANDPERCENTOFMALEFACULTYATUNIVERSITYX,BYFIELDTotalfemalefaculty:200Totalmalefaculty:2509、MediumQuestionThereare275studentsinthefieldofengineeringatUniversityX.Approximatelywhatistheratioofthenumberofstudentsinengineeringtothenumberoffacultyinengineering?A、8to1B、10to1C、12to1D、14to1E、20to1标准答案：A知识点解析：Accordingtothegraph,2percentofthefemalefacultyand12percentofthemalefacultyareintheengineeringfield.Todeterminethetotalnumberoffacultymembersinengineering,youneedtoadd2percentof200,whichis4,to12percentof250,whichis30,toget34.Thus,theratioofthenumbersofstudentstofacultyinengineeringis275to34,whichisapproximatelyequalto280to35,or8to1.ThecorrectanswerisChoiceA.10、MediumQuestionApproximatelywhatpercentofthefacultyinhumanitiesaremale?A、35%B、38%C、41%D、45%E、51%标准答案：E知识点解析：Youneedtodeterminethenumbersoffemaleandmalefacultyinthehumanitiesfield.Accordingtothegraph,17percentofthe200females,or34,and14percentofthe250males,or35,areinhumanities.Thus,thefractionofhumanitiesfacultywhoaremaleis,orapproximately0.507.Asapercent,theanswerchoicethatisclosestto0.507is51percent.ThecorrectanswerisChoiceE.11、HardQuestionForthebiologicalsciencesandhealthsciencesfacultycombined,1/3ofthefemaleand2/9ofthemalefacultymembersaretenuredprofessors.Whatfractionofallthefacultymembersinthosetwofieldscombinedaretenuredprofessors?标准答案：24/87知识点解析：Youneedtodeterminethenumberoffemalefacultyandthenumberofmalefacultyinthecombinedgroup.Accordingtothegraph,5percentofthefemalefaculty,or10,and10percentofthemalefaculty,or25,areinthebiologicalsciences.Similarly,16percentofthefemalefaculty,or32,and8percentofthemalefaculty,or20,areinthehealthsciences.Whenyoucombinethegroups,yougetatotalof42females(10+32)and45males(25+20),whichisatotalof87faculty.Thetenuredfacuhyare1/3ofthe42females,or14females,and2/9ofthe45males,or10males.Thus,thereare24tenuredfaculty,andthefractionthataretenuredprofessorsis24/87.Thecorrectansweris24/87(oranyequivalentfraction).VALUEOFIMPORTSTOANDEXPORTSFROMCOUNTRYT,2000-200912、Forwhichoftheeightyearsfrom2001to2008didexportsexceedimportsbymorethan$5billion?Indicateallsuchyears.[A]2001[B]2002[C]2003[D]2004[E]2005[F]2006[G]2007[H]2008标准答案：A，B，C，F，G，H知识点解析：Notethatforallyearsshown,thedollarvalueofexportsisgreaterthanthedollarvalueofimports.Foreachyear,thedifferencebetweenthedollarvalueofexportsandthedollarvalueofimportscanbereaddirectlyfromthegraph.Thedifferencewasmorethan$5billionforeachoftheyears2001,2002,2003,2006,2007,and2008.ThecorrectanswerconsistsofChoicesA,B,C,F,G,andH.13、MediumQuestionWhichofthefollowingisclosesttotheaverage(arithmeticmean)ofthe9changesinthevalueofimportsbetweenconsecutiveyearsfrom2000to2009?A、$260millionB、$320millionC、$400millionD、$480millionE、$640million标准答案：E知识点解析：Theaverageofthe9changesinthevalueofimportsbetweenconsecutiveyearscanberepresentedasfollows,wherethefunctionv(year)representsthevalueofimportsfortheindicatedyear.Notethatinthenumeratorofthefraction,eachterm,withtheexceptionofv(2000)andv(2009),appearsfirstaspositiveandthenagainasnegative.Thepositiveandnegativepairssumto0,andthefractionsimplifiesto.Readingthevaluesfromthegraph,youcanapproximatethevalueofthesimplifiedfractionas0.644billiondollars.Theanswerchoicethatisclosestto$0,644billionis$640million.ThecorrectanswerisChoiceE.14、MediumQuestionIn2008thevalueofexportswasapproximatelywhatpercentgreaterthanthevalueofimports?A、0.4B、0.6C、0.7D、1.2E、1.4标准答案：E知识点解析：ThedifferencebetweenthevalueofexportsandthevalueofimportsexpressedasapercentofthevalueofimportsisIn2008thevalueofimportswasapproximately$5billionandthevalueofexportswasapproximately$12billion,sothevalueofthefractionisapproximately,or7/5.Sincethefractionisgreaterthan1,expressingitasapercentwillgiveapercentgreaterthan100.Thefractionisequalto1.4,or140percent.ThecorrectanswerisChoiceE.15、HardQuestionIfitwerediscoveredthatthevalueofimportsshownfor2007wasincorrectandshouldhavebeen$5billioninstead,thentheaverage(arithmeticmean)valueofimportsperyearforthe10yearsshownwouldhavebeenapproximatelyhowmuchless?A、$200millionB、$50millionC、$20millionD、$7millionE、$5million标准答案：A知识点解析：Toanswerthisquestion,youdonotneedtocomputeeitherofthetwo10-yearaveragesreferredtointhequestion;youjustneedtocalculatethedifferencebetweenthetwoaverages.Theaveragevalueofimportsforthe10yearsshowninthegraphisfoundbyaddingthe10valuesandthendividingthesumby10.Thevalueofimportsin2007is$7billion.Ifthatamountwere$5billioninstead,thenthesumofthevalueswouldbe$2billionless.Ifthesumwere$2billionlessthanwhatitwas,thentheaveragewoulddecreaseby2billiondividedby10,or=200,000,000.Theaveragewouldthereforebe$200millionless,andthecorrectanswerisChoiceA.AmorealgebraicapproachtotheproblemistoletSrepresentthesum,inbillions,ofthe10valuesofimportsinthegraph.Theaverageofthe10valuesisS/10.NotethatS-2representsthesum,inbillions,ofthe10valuesadjustedforthe$2billioncorrectionfor2007.Theaverageoftheadjustedsumis.ThedifferencebetweenthetwoaveragesisThedifferenceis0.2billiondollars,or$200million.ThecorrectanswerisChoiceA.GRE（QUANTITATIVE）综合模拟试卷第3套一、数值比较题(本题共5题，每题1.0分，共5分。)1、标准答案：A知识点解析：InthisquestionyouaregiventhatmachineR,workingaloneatitsconstantrate,producesxunitsofaproductin30minutes.Sinceitiseasytoseethat3hoursis6times30minutes,youcanconcludethatQuantityAis6x.Youcancompare6xwithQuantityBintwoways.One:Intheadditionalinformationcenteredabovethequantities,youaregiventhatmachineS,workingaloneatitsconstantrate,producesxunitsoftheproductin48minutes,soyoucanconcludethatmachineScanproduce6xunitsoftheproductin(6)(48)minutes,or4.8hours.Soin4hours,machineSproduceslessthan6xunits,andQuantityBislessthan6x.Two:First,convert48minutesto4/5hour,thenfindthenumberof48-minuteperiodstherearein4hoursbycomputing=5.Thus,QuantityBis5x.Eitherway,QuantityAisgreaterthanQuantityB,andthecorrectanswerisChoiceA.2、标准答案：B知识点解析：Inthisproblemyouareaskedtocomparetheaveragewiththemedianofthe120numbersinlistZ.SincelistZconsistsofthenumbersinlistsXandYcombined,itisreasonabletotrytousetheinformationaboutlistsXandYtocalculatetheaverageandthemedianofthenumbersinlistZ.Todeterminetheaverageofthe120numbersinlistZ,youcanusetheinformationgivenabouttheindividualaveragesofthenumbersinlistsXandY.BecauselistsXandYeachcontain60numbers,theaverageofthenumbersinlistZistheaverageoftheindividualaveragesofthenumbersinlistsXandY.Thus,theaverageofthenumbersinlistZis,or4.9.Todeterminethemedianofthe120numbersinlistZ,firstnotethatlistZcontainsanevennumberofnumbers,sothemedianofthenumbersinlistZistheaverageofthemiddletwonumberswhenthenumbersarelistedinincreasingorder.Ifyoulookatthenumbersinthetwolists,youwillseethatthe60numbersinlistXarealllessthanorequalto5,andthe60numbersinlistYareallgreaterthanorequalto6.Thus,thetwomiddlenumbersinlistZare5and6,andtheaverageofthesenumbersis,or5.5.Therefore,themedianofthenumbersinlistZis5.5,andthisisgreaterthantheaverageof4.9.ThecorrectanswerisChoiceB.3、标准答案：D知识点解析：Youaregiventhatthecirclehasadiameterof10,andfromthefigureyoucanassumethatpointsA,B,C,andDlieonthecircleintheordershown.However,becausefiguresarenotnecessarilydrawntoscale,youcannotassumeanythingelseaboutthepositionsofpointsA,B,C,andDonthecircle.Therefore,togetanideaofhowvariouspossiblepositionsofthesefourpointscouldaffecttheareaofquadrilateralABCD,itisagoodideatoseehowthefigurecanvarybutstillhavepointsA,B,C,andDinthesameorderasinthefigureabove.Onewaythatyoumightvarythefigureistoevenlyspacethefourpointsalongthecircle,asshownbelow.AnotherwayistodrawpointsAandCoppositeeachother,withpointsBandDclosetopointC,asshownbelow.FromthesefiguresyoucandrawsomebasicconclusionsabouttheareaofABCD.IfpointsAandCareoppositeeachother,withpointsBandDveryclosetopointC,theareaofquadrilateralABCDisverycloseto0.Clearly,theareacanbelessthan40(QuantityB).IfpointsA,B,C,andDareevenlyspaced,theareaisnotcloseto0.Howdoestheareacomparewith40?TocalculatetheareaofABCD,drawthediametersACandBDinthefigure.Thetwodiametersareperpendicularbisectorsofeachother,sotheydivideABCDintofourrighttriangles,asshown.Theareaofeachoftherighttrianglesis(1/2)(5)(5),or12.5.Thus,theareaofABCDis(4)(12.5),or50.Sincetheareaofthequadrilateralinthefirstfigureislessthan40andtheareaofthequadrilateralinthesecondfigureisgreaterthan40,therelationshipcannotbedeterminedfromtheinformationgiven.ThecorrectanswerisChoiceD.4、标准答案：B知识点解析：Youaregiventhatx2y>0,whichmeansthattheproductofthetwonumbersx2andyispositive.Recallthattheproductoftwonumbersispositiveonlyifbothnumbersarepositiveorbothnumbersarenegative.Thesquareofanumberisalwaysgreaterthanorequalto0.Inthiscase,x2cannotequal0becausetheproductx2yisnot0.Thus,x2ispositiveanditfollowsthatyisalsopositive.Youarealsogiventhatxy2<0,whichmeansthattheproductofthetwonumbersxandy2isnegative.Theproductoftwonumbersisnegativeonlyifoneofthenumbersisnegativeandtheothernumberispositive.Inthiscase,y2cannotbenegativebecauseitisthesquareofanumber,anditcannotbe0becausetheproductx2yisnot0.Thus,y2ispositiveandsoxmustbenegative.Becausexisnegativeandyispositive,ymustbegreaterthanx,andthecorrectanswerisChoiceB.5、标准答案：C知识点解析：Inthisquestionyouarenottoldwhetherallofthe9,000peopleattendingthegamewerestudents.Letzbethenumberofpeopleattendingthegamewhowerenotstudents.Thepeopleattendingthegamecanbebrokendownintothreegroups:studentsfromCollegeC,studentsnotfromCollegeC,andpeoplewhowerenotstudents.Thiscanbeexpressedalgebraicallyas9,000=x+y+z,wherexrepresentsthenumberofstudentsfromCollegeCattendingthegameandyrepresentsthenumberofstudentsattendingthegamewhowerenotfromCollegeC.Therefore,9,000-x-y=zisthenumberofpeopleattendingthegamewhowerenotstudents.ThecorrectanswerisChoiceC.二、计算题(本题共8题，每题1.0分，共8分。)6、Ifx0,whichofthefollowingisequivalentto?A、x2B、x3C、x4D、x5E、x6标准答案：D知识点解析：Tosimplify,itcanbehelpfultowrite(x2)3as(x2)(x2)(x2)inthegivenexpression;thatis,.Becausex0,bothnumeratoranddenominatorcanbedividedbyx2,andtheexpressionsimplifiestox(x2)(x2),which,bytherulesofexponents,isequaltox5.Anotherwaytosimplifytheexpressionusingtherulesofexponentsdirectlyisasfollows.ThecorrectanswerisChoiceD.7、Thefigureaboveshowsthegraphofthefunctionfinthexy-plane.Whatisthevalueoff(f(-1))?A、-2B、-1C、0D、1E、2标准答案：D知识点解析：Notethattofindf(f(-l)),youmustapplythefunctionftwice,firsttofindthevalueoff(-1)andthentofindthevalueoff(f(-l)).Tofindthevalueoff(-l),findthepointonthegraphofthefunctionfwhosex-coordinateisx=-1.Thispointhasy-coordinatey=2.Therefore,thevalueoff(-1)is2,andf(f(-1))=f(2).Nextyouneedtofindthevalueoff(2).Tofindthevalueoff(2),findthepointonthegraphwhosex-coordinateisx=2.Thispointhasy-coordinatey=1.Therefore,f(2)=1,andbecausef(f(-1))=f(2),youcanconcludethatf(f(-l))=1.ThecorrectanswerisChoiceD.8、If=1,whichofthefollowingstatementsdescribesdintermsofn?A、dis4lessthann.B、dis4morethann.C、dis3/7ofn.D、dis2timesn.E、dis5timesn.标准答案：E知识点解析：Todescribedintermsofn,youneedtosolvetheequation=1ford.Tosimplifytheequation,youcanbeginbymultiplyingbothsidesby7n-dandthenproceedasfollows.d-3n=7n—dd=10n-d2d=10nd=5nThecorrectanswerisChoiceE.9、Byweight,liquidAmakesup8percentofsolutionRand18percentofsolutionS.If3gramsofsolutionRaremixedwith7gramsofsolutionS,thenliquidAaccountsforwhatpercentoftheweightoftheresultingsolution?A、10%B、13%C、15%D、19%E、26%标准答案：C知识点解析：LiquidAmakesup8percentoftheweightofsolutionRand18percentoftheweightofsolutionS.Therefore,3gramsofsolutionRcontain(0.08)(3),or0.24gramofliquidA,and7gramsofsolutionScontain(0.18)(7),or1.26gramsofliquidA.Whenthetwosolutionsaremixed,theresultingsolutionweighs3+7,or10gramsandcontains0.24+1.26,or1.5gramsofliquidA.ThismeansthatliquidAmakesup1.5/10,or15/100,or15percentoftheweightoftheresultingsolution.ThecorrectanswerisChoiceC.10、Ofthe700membersofacertainorganization,120arelawyers.Twomembersoftheorganizationwillbeselectedatrandom.Whichofthefollowingisclosesttotheprobabilitythatneitherofthemembersselectedwillbealawyer?A、0.5B、0.6C、0.7D、0.8E、0.9标准答案：C知识点解析：Theprobabilitythatneitherofthemembersselectedwillbealawyerisequaltothefractionthenumberofways2memberswhoarenotlawyerscanbeselectedthenumberofways2memberscanbeselectedwheretheorderofselection