GMAT（QUANTITATIVE）数学模拟试卷1（共295题）

GMAT（QUANTITATIVE）数学模拟试卷1（共9套）（共295题）GMAT（QUANTITATIVE）数学模拟试卷第1套一、单项选择题(本题共37题，每题1.0分，共37分。)Solvetheproblemandindicatethebestoftheanswerchoicesgiven.NUMBERS:Allnumbersusedarerealnumbers.FIGURES:Afigureaccompanyingaproblem-solvingquestionisintendedtoprovideinformationusefulinsolvingtheproblem.FiguresaredrawnasaccuratelyaspossibleEXCEPTwhenitisstatedinaspecificproblemthatitsfigureisnotdrawntoscale.Straightlinesmaysometimesappearjagged.Allfigureslieinaplaneunlessotherwiseindicated.Thefollowingdatasufficiencyproblemsconsistofaquestionandtwostatements,labeled(1)and(2),inwhichcertaindataaregiven.Youhavetodecidewhetherthedatagiveninthestatementsaresufficientforansweringthequestion.Usingthedatagiveninthestatementsplusyourknowledgeofmathematicsandeverydayfacts(suchasthenumberofdaysinJulyorthemeaningofcounterclockwise),youmustindicatewhetherＡ.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.Ｂ.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.Ｃ.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.Ｄ.EACHstatementALONEissufficient.Ｅ.Statements(1)and(2)TOGETHERareNOTsufficient.1、Ifxisaninteger,isaninteger?(1)18＜x＜54(2)xisamultipleof18标准答案：C知识点解析：aloneisinsufficient,becauseifx=36,thentheansweris"yes,"butifx=37,thentheansweris"no."(2)aloneisinsufficient,becauseifx=36,thentheansweris"yes,"butifx=180,thentheansweris"no."Ifthestatementsarecombined,however,thentheonlyvalueofxthatmeetsalltheconditionsis36,forwhichtheansweris"yes."2、Ifa＞0andb＞0,is(1)a=b-2(2)标准答案：D知识点解析：aloneissufficientbecauseittellsusthatbisalargernumberthana,whichmeansthattheanswertothequestionmustbe"no."(2)aloneissufficient;thestatementcanbesimplifiedto5a=4b,whichmeansthatbislargerthana,sotheanswertothequestionmustbe"no."3、Thefigureaboveshowstheshapeofaflowerbed.IfarcsWZandXYaresemicirclesandWXYZisasquare,whatistheareaoftheflowerbed?(1)TheperimeterofsquareWXYZis24.(2)Thediagonal标准答案：D知识点解析：aloneissufficient;iftheperimeterofthesquareis24,thenthelengthofeachsideis24/4=6,andtheradiusofeachofthesemicirclesis6/2=3.Theareaofthesquareis6×6=36,andsincetheformulafortheareaofacircleisπr2,theareaofthesemicirclesis2×1/2[π(3×3)]=9π;36+9πistheareaoftheflowerbed.(2)aloneissufficient;thesideofasquareisthediagonaldividedby(thisisderivedfromthePythagoreantheorem),sothesidesareequalto6;byfollowingthesameprocessusedwithstatement(1),wecandeterminetheareaoftheflowerbed.4、Atotalof72passengersareonaship,andtheygooutonanexcursioninboatsRandQ.Howmanyoftheship’spassengersarefemale?(1)Thereare13femalesonboatQ.(2)ThereareequalnumbersofwomenonboatsRandQ.标准答案：C知识点解析：aloneisinsufficientbecauseitgivesnoinformationaboutthenumberoffemalesonboatR.(2)aloneisinsufficientbecauseitdoesnotgivethenumberofwomenoneitherboat.Ifthestatementsarecombined,weseethatthereare13womenoneachboat,or26inall.5、Inthexyplane,isthepoint(4,-2)onthelinel?(1)Point(1,1)isonlinel.(2)Theequationx=2-ydescribeslinel.标准答案：B知识点解析：aloneisinsufficientbecauseitoffersinformationaboutonlyonepointontheline.(2)aloneissufficient,becausethelineitdescribesincludesthepoint(4,-2).6、Atypeofextra-largeSUVaverages12.2milespergallon(mpg)onthehighway,butonly7.6mpginthecity.Whatisthemaximumdistance,inmiles,thatthisSUVcouldbedrivenon25gallonsofgasoline?A、190B、284.6C、300D、305E、312标准答案：D知识点解析：TheSUVwillreachitsmaximumdistanceonlyifdrivenonlyonthehighway;25×12.2=305.7、Theratioof2quantifiesis5to6.Ifeachofthequantitiesisincreasedby15,whatistheratioofthesetwonewquantifies?A、5:6B、25:27C、15:16D、20:21E、Itcannotbedeterminedfromtheinformationgiven.标准答案：E知识点解析：Withnoideaofwhatthequantifiesactuallyare,thereisnowaytotellhowadding15toeachofthemwillaffecttheirratio;forexample,ifthequantitieswere5and6,thenewratiowouldbe20:21,butifthequantitieswere10and12,theratiowouldbe25:27.8、A、B、8C、9D、10E、标准答案：C知识点解析：9、Inananimalbehaviorexperiment,50taggedwhitepigeonsand200taggedgraypigeonswerereleasedfromalaboratory.Withinoneweek,88percentofthewhitepigeonsand80.5percentofthegraypigeonshadreturnedtothelaboratory.Whatpercentofthetotalnumberofpigeonsreturnedtothelaboratory?A、80.5B、82C、82.5D、85E、86.5标准答案：B知识点解析：88%of50is44,and80.5%of200is161.44+161=205.205/250totalpigeons=0.82=82%.10、Inthecircularregionshownabove,sectionsAandBrepresent3/8and5/11,respectively,oftheareaofthecircularregion.SectionCrepresentswhatfractionalpartoftheareaofthecircularregion?A、

B、

C、

D、

E、

标准答案：A知识点解析：SectionCisequalto1-(3/8+5/11)=1-(33/88+40/88)=15/88.11、Atthewholesalestoreyoucanbuyan8-packofhotdogsfor$1.55,a20-packfor$3.05,anda250-packfor$22.95.Whatisthegreatestnumberofhotdogsyoucanbuyatthisstorewith$200?A、1,108B、2,100C、2,108D、2,124E、2,256标准答案：B知识点解析：Youshouldstartwiththe250-packs,becausethatisthebestvalue,witheachhotdogcostinglessthan10cents.Rounding22.95to23forsimplicity,youcandeterminethatyoucanafford8ofthe250-packs,foratotalof$183.60.The20-packsarethenextbestvalueataround15centsperhotdog,sowiththeremaining$16.40youcanbuy5ofthe20-packsfor$15.25,leaving$1.15.$1.15isn’tenoughforan8-pack,sothetotalnumberofhotdogsis8×250+5×20=2,100.Thefollowingdatasufficiencyproblemsconsistofaquestionandtwostatements,labeled(1)and(2),inwhichcertaindataaregiven.Youhavetodecidewhetherthedatagiveninthestatementsaresufficientforansweringthequestion.Usingthedatagiveninthestatementsplusyourknowledgeofmathematicsandeverydayfacts(suchasthenumberofdaysinJulyorthemeaningofcounterclockwise),youmustindicatewhetherＡ.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.Ｂ.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.Ｃ.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.Ｄ.EACHstatementALONEissufficient.Ｅ.Statements(1)and(2)TOGETHERareNOTsufficient.12、WhatwasthepercentdecreaseinthepriceofMegaTek(MGTK)stockduringthemarketdeclineofMarch1,2001,toMarch1,2002?(1)ThepriceofMGTKwas$56.20onMarch1,2001.(2)ThepriceofthestockonJanuary1,2002,wasonlyone-quarterofitspriceasofMarch1,2001.标准答案：E知识点解析：aloneisinsufficientbecauseitgivesonlythevalueatthestartingpointoftheperiodinquestion.(2)aloneisinsufficientbecausethepriceasofJanuary1,2002,isirrelevanttothequestion.Combiningthetwostatementsyieldsnonewinsights.13、Greg’slong-distancetelephoneplanchargeshim$0.50forthefirst4minutesofacall,and$0.07perminuteforeachsubsequentminute.GregmadeacalltoCarrieforxminutes,wherexisaninteger.HowmanyminuteslongwasGreg’scall?(1)Thelast7minutesofGreg’scallcost$0.22lessthanthefirst7minutesofthecall.(2)Thecalldidnotcostmorethan$1.05.标准答案：C知识点解析：aloneisinsufficient;weknowthatthefirst7minutescost$0.50+3×$0.07=$0.71;theleastthelast7minutescouldcostis7×$0.07=$0.49,whichisexactly$0.22lessthanthefirst7minutes,soweknowthatthelast7minutesdidnotincludethefirst4minutes,butthatisallwecantell.(2)aloneisinsufficient,becausethecallcouldhavelastedanylengthoftimeunder12minutes(12minutes=$1.06,11minutes=$0.99).Ifthetwoarecombined,theonlyvaluethatmeetsalltheconditionsis11minutes.14、Ifxandyarebothpositivenumbers,isxgreaterthan75%ofy?(1)5x＞4y+1(2)x=6标准答案：A知识点解析：statesthatxisgreaterthan80percentofy(theeasiestwaytoconfirmthisistopluginnumbers),sothequestionisansweredintheaffirmativeand(1)aloneissufficient.(2)isinsufficientwithoutprovidinganyinformationabouttherelativevalueofy,sotheanswerisA.15、Isxyz=1?(1)x(yz)=1(2)5z=0标准答案：B知识点解析：aloneisinsufficient,becausex,y,andzcouldbe(1,1,1)or(1,1,0)orothervalues,whichgivedifferentanswerstothequestion.(2)aloneissufficient,becauseifz=0,itdoesnotmatterwhatthevaluesareforxandy;xyz=0≠1.16、Whatistheaverage(arithmeticmean)ofxandy?(1)Theaverageofx+3andy+5is14.(2)Theaverageofx,y,and16is12.标准答案：D知识点解析：aloneissufficient;thestatementcouldberestatedtosaythatx+y+3+5=14×2,orx+y=20;therefore,theaverageofxandyis10.(2)aloneissufficient;thestatementcouldberestatedasx+y+16=12×3,orx+y=20;therefore,theaverageofxandyis10.17、Onedayacarrentalagencyrented2/3ofitscars,including3/5ofitscarswithCDplayers.If3/4ofitscarshaveCDplayers,whatpercentofthecarsthatwerenotrentedhadCDplayers?A、10%B、35%C、45%D、66.7%E、90%标准答案：E知识点解析：Onewaytoapproachthisproblemistothinkofthefractionsasactualcars.Sincethegivendenominatorsare3,4,and5,imaginethatthereare60cars.Inthiscase,theagencyrented40cars(2/3),45ofthetotalcarshaveCDplayers(3/4),and27ofitscarswithCDplayerswererented(3/5of3/4).Fromthesenumbers,wecandeterminethat20carsintotalwerenotrented,and18carswithCDplayerswerenotrented.18outof20is90percent.18、Ifxis20percentgreaterthan88,thenx=A、68B、70.4C、86D、105.6E、108标准答案：D知识点解析：20percentof88is17.6.88+17.6=105.6.19、Afarmerwith1,350acresoflandhadplantedhisfieldswithcorn,sugarcane,andtobaccointheratioof5:3:1,respectively,buthewantedtomakemoremoney,soheshiftedtheratioto2:4:3,respectively.Howmanymoreacresoflandwereplantedwithtobaccounderthenewsystem?A、90B、150C、270D、300E、450标准答案：D知识点解析：Thenumbersinbothsetsofratiosaddupto9,soyoucanlookateachoftheratiosintermsofninthsof1,350.Intheoriginalplantingsystem,tobaccoaccountedfor1/9ofthetotal,so1,350/9=150.Inthenewsystem,tobaccoaccountsfor3/9,or450.450-150=300.20、A、18B、33C、36D、42E、45标准答案：E知识点解析：Thestatementcanberestatedas12+15+18=45.21、Whatistheperimeterofasquarewitharea?A、

B、

C、

D、

E、

标准答案：C知识点解析：Theareaofasquareisthesquareofitssides,sooneofthesidesofthissquareis.Theperimeterofasquareisitssidetimes4,sotheperimeteris3P.22、Ifathree-digitnumberisselectedatrandomfromtheintegers100to999,inclusive,whatistheprobabilitythatthefirstdigitandthelastdigitoftheintegerwillbothbeexactlytwolessthanthemiddledigit?A、1:900B、7:900C、9:1,000D、1:100E、7:100标准答案：B知识点解析：Thereareexactly7digitsoutofthe900forwhichthisstatementistrue:131,242,353,464,575,686,797;thatequalsaprobabilityof7outof900.23、Whichofthefollowinginequalitiesisequivalentto-4＜x＜8?A、|x-1|＜7B、|x+2|＜6C、|x+3|＜5D、|x-2|＜6E、Noneoftheabove标准答案：D知识点解析：|x-2|＜6alsorepresentsallofthevaluesforxbetween-4and8.Aisequivalentto-6＜x＜8,Bisequivalentto-8＜x＜4,andCisequivalentto-8＜x＜2.24、A、416B、224C、188D、104E、56标准答案：B知识点解析：Thestatementisequivalentto4[80-6(4)]=4(56)=224.25、ThreedifferentlumberjackscanchopWamountofwoodin30minutes,45minutes,and50minutesaccordingtotheirdifferentlevelsofskillwiththeaxe.Howmuchwood,intermsofW,couldthetwofastestlumberjackschopin2hours?A、

B、

C、

D、

E、

标准答案：A知识点解析：ThefastestlumberjackcanchopWin30minutes,soin2hours=120minutes,hewillchop4W.ThenextfastestcanchopWin45minutes,sohewillbeabletochopThefollowingdatasufficiencyproblemsconsistofaquestionandtwostatements,labeled(1)and(2),inwhichcertaindataaregiven.Youhavetodecidewhetherthedatagiveninthestatementsaresufficientforansweringthequestion.Usingthedatagiveninthestatementsplusyourknowledgeofmathematicsandeverydayfacts(suchasthenumberofdaysinJulyorthemeaningofcounterclockwise),youmustindicatewhetherＡ.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.Ｂ.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.Ｃ.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.Ｄ.EACHstatementALONEissufficient.Ｅ.Statements(1)and(2)TOGETHERareNOTsufficient.26、InwhatyearwasEdwardborn?(1)In1988,Edwardturned17yearsold.(2)Edward’ssisterLisa,whois14monthsolderthanEdward,wasbornin1970.标准答案：A知识点解析：aloneissufficientbecauseitgives1971astheonlyanswer.(2)aloneisinsufficient,becausetheconditionsstatedcouldapplytoeither1971or1972.27、Isrs=rx-2?(1)risanoddnumber(2)x=s+2标准答案：B知识点解析：alonecanneitherprovenordisprovetheequationabovebecausethereareinfinitevaluesofr,s,andxforwhichtheequationcouldbetrueorfalse.(2)issufficienttoprovethattheequationistrue;restatetheequationasrs=rs+2r-2;therefore,2=2r,andr=1.Ifr=1,thentheequationabovecanbesimplifiedtos=x-2,whichisthesamestatementas(2),whichweknowtobetrue.So(2)issufficient.28、ACEOisbuildinganextra-widegarageinwhichtoparkhislimousines.Thegarageisxfeetwide,andatleast2feetofspaceisrequiredbetweeneachtwocarsandbetweenthecarsandthewalls.Willall9limousinesfitinthegarage?(1)Theaveragewidthofthelimousinesisthesquarerootofx.(2)x=100.标准答案：C知识点解析：aloneisinsufficientbecauseitgivesusnoactualmeasurements.(2)aloneisinsufficientbecauseitgivesusthewidthofthegarage,butnotthewidthofthecars.Ifthetwoarecombined,weseethatthecarscannotfitinthegarage.Thesquarerootof100=10,sothe9carswillrequire90feetofspace,buttheadditionalspacerequiredbetweenandaroundthecarswillbeanother18feet,sothecarsnotfitinthegarage.29、Ifq+r+s=45,whatisthevalueofqr?(1)q=r=s(2)q-r-s=-15标准答案：A知识点解析：aloneissufficient,becausetheonlyvalueforq,r,andsthatmeetstheconditionsofthequestionandthestatementis15;thus,wecandeterminethevalueofqr.(2)aloneisnotsufficient;althoughitwouldworkforthevalues(q,r,s)=(15,15,15),itwouldalsoworkfor(q,r,s)=(15,14,16).30、Isthetriangledepictedaboveisosceles?(Figurenotnecessarilydrawntoscale.)(1)180°-(a+c)=60°(2)a=2b-c标准答案：E知识点解析：Atriangleisisoscelesiftwoofitsanglesareequal.(1)tellsusthat(a+c)=120°,whichisnotsufficienttoprovewhetherornotthetriangleisisosceles.(2)canbealteredto(a+c)=2b,whichisnotsufficienttoprovewhetherornotthetriangleisisosceles.Ifthetwoarecombined,wehave2b=120°,andthereforeb=60°.Knowingthemeasureofoneangleisstillinsufficient,sinceacouldequal59°andccouldequal61°,sothequestionremainsunresolved.31、LastyearJackiesaved5%ofherannualsalary.Thisyear,shemade10%moremoneythanlastyear,andshesaved8%ofhersalary.Theamountsavedthisyearwaswhatpercentoftheamountshesavedlastyear?A、56%B、76%C、158%D、176%E、188%标准答案：D知识点解析：Forsimplicity,assumethatsheearned$100lastyearandsaved$5.Thisyearsheearned$110andsaved$110×0.08=$8.80.8.80/5=1.76.32、Thetableaboveshowstheone-waydrivingdistance,inmiles,betweenfourcities:P,Q,R,andS.Forexample,thedistancebetweenPandQis144miles.IftheroundtripbetweenSandQis16milesfurtherthantheroundtripbetweenSandR,andtheroundtripbetweenSandRis24mileslessthantheroundtripbetweenSandP,whatisthevalueofX?A、174B、182C、186D、348E、364标准答案：B知识点解析：TofindX,thedistancebetweenSandQ,startwithanumberyouknow;thedistancebetweenSandPis186miles,andtheroundtripthereforeis372miles;372=theSRroundtrip+24miles,soSRroundtrip=348miles;SQroundtrip=SRroundtrip-16miles,soSQroundtrip=364.Xistheone-waySQdistance,so364/2=182.33、If35percentof400is20percentofx,thenx=A、200B、350C、700D、900E、1,400标准答案：C知识点解析：First,35%of400=140.If140=0.2x,thenx=140/0.2=700.34、(23-1)(23+1)(26+1)(212+1)=A、(224-1)B、(224-1)C、(248-1)D、(296+1)E、26(212-1)标准答案：A知识点解析：isequalto(212-1)(212+1),whichisequalto(212+1)(26+1)(26-1),whichisequalto(212+1)(26+1)(23-1)(23+1).35、Tobeconsideredfor"movieoftheyear,"afilmmustappearinatleast1/4ofthetop-10-movieslistssubmittedbytheCinematicAcademy’s765members.Whatisthesmallestnumberoftop-10listsafilmcanappearonandstillbeconsideredfor"movieoftheyear?"A、191B、192C、193D、212E、213标准答案：B知识点解析：765times1/4equals191.25,butthequestionstates"atleast1/4,"sothemoviemustappearon192lists.36、Inasampleofassociatesatalawfirm,30percentaresecond-yearassociates,and60percentarenotfirst-yearassociates.Whatpercentageoftheassociatesatthelawfirmhavebeenthereformorethantwoyears?A、10B、20C、30D、40E、50标准答案：C知识点解析：Theanswermustbeasubsetofthe60percentofassociatesthatarenotfirst-yearassociates.Ofthese,youmustsubtractthe30percentthataresecond-yearassociates,leavingonly30percent,sotheanswerisC.37、Whichofthefollowingfractionshasthegreatestvalue?A、

B、

C、

D、

E、

标准答案：A知识点解析：Thisproblembecomesmucheasierifyourecognizethatallofthefractionsinclude;forpurposesofcomparison,youcanmultiplyeachofthefractionsby(23)(32)tosimplifythings.Thisleavesyouwiththefollowingvalues:A=12,B=2,C=6,D=8,andE=3;Aisthegreatestvalue.GMAT（QUANTITATIVE）数学模拟试卷第2套一、单项选择题(本题共37题，每题1.0分，共37分。)1、Jim’sTaxiServicechargesaninitialfeeof$2.25atthebeginningofatripandanadditionalchargeof$0.35foreach2/5ofamiletraveled.Whatisthetotalchargeforatripof3.6miles?A、$3.15B、$4.45C、$4.80D、$5.O5E、$5.4O标准答案：E知识点解析：6milesdividedby2/5equals9,sothetotalchargeis$2.25+(9×$0.35)=$5.40.2、Iftheareaofasquarewithsidesoflength8centimetersisequaltotheareaofarectanglewithawidthof4centimeters,whatisthelengthoftherectangle,incentimeters?A、4B、8C、12D、16E、18标准答案：D知识点解析：Thesquarehasanareaof8×8=64,sothelengthoftherectangleis64/4=16(theareaofarectangleisitswidthtimesitslength).3、Acertainlabexperimentswithwhiteandbrownmiceonly.Inoneexperiment,2/3ofthemicearewhite.Ifthereare13brownmiceintheexperiment,howmanymiceintotalareintheexperiment?A、39B、33C、26D、21E、10标准答案：A知识点解析：Brownmicemakeup1/3ofthemiceintheexperiment,sothetotalnumberofmiceis13×3=39.4、If,wherea,b,andcareeachequalto0or1,thenxcouldbeeachofthefollowingEXCEPT:A、

B、

C、

D、

E、

标准答案：D知识点解析：Themostdirectwaytoaddressthisproblem,sincethereareonlyeightpossiblevaluesforx,istodetermineallthepossiblevaluesandthencheckthemagainstthepossibleanswers,xcouldequal0,1/27,3/27(=1/9),4/27,9/27(=1/3),10/27,12/27(=4/9),or13/27.TheonlyanswernotamongthesechoicesisD,2/9.5、Fiftyapplicantsforajobweregivenscoresfrom1to5ontheirinterviewperformance.Theirscoresareshowninthetableabove.Whatwastheaveragescoreforthegroup?A、2.79B、2.86C、2.91D、2.99E、3.03标准答案：B知识点解析：YoucancalculatethisaveragescoreexactlythesamewayyouwouldcalculateaGPA--multiplyeachofthescoresbythenumberofapplicantswiththatscore,addthemallup,anddividethesumby50.10+48+63+14+8=143;143/50=2.86.Thefollowingdatasufficiencyproblemsconsistofaquestionandtwostatements,labeled(1)and(2),inwhichcertaindataaregiven.Youhavetodecidewhetherthedatagiveninthestatementsaresufficientforansweringthequestion.Usingthedatagiveninthestatementsplusyourknowledgeofmathematicsandeverydayfacts(suchasthenumberofdaysinJulyorthemeaningofcounterclockwise),youmustindicatewhetherＡ.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.Ｂ.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.Ｃ.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.Ｄ.EACHstatementALONEissufficient.Ｅ.Statements(1)and(2)TOGETHERareNOTsufficient.6、Carrie,Lisa,andBettyallmakepurchasesatamusicstorethatsellsallrecordsforacertainpriceandallCDsforacertainprice.HowmuchdoesCarriepayfor1recordand2CDs?(1)Lisabought3recordsfor$22.50.(2)Bettybought2recordsand4CDsfor$55.00.标准答案：B知识点解析：aloneisinsufficientbecauseittellsyouonlythepriceperrecord,anddoesnotgivethepriceofCDs.(2)aloneissufficient,becausethequantityofitemsistwicethatofCarrie’spurchase,sothepurchasepriceisthereforehalfofwhatBettypaid--$27.50.7、NandParepointsonthenumberlinebelow20.IsPcloserto10thanNis?(1)Pisgreaterthantheaverageof10andN.(2)标准答案：E知识点解析：Bothstatementsaloneandcombinedareinsufficient,because,forexample,thevalues(9,3)for(P,N)meetalltheconditionsandyieldananswerof"yes,"whilethevalues(18,6)meetalltheconditionsandyielda"no."8、WhatistheareaoftherectangularregiondepictedabovewithsidesAandBanddiagonalC?(1)C2=9+A2(2)A+B=7标准答案：C知识点解析：YouneedtoknowtheproductofAandBtosolvethisquestion.(1)aloneisinsufficientbecauseitdoesnotgivethevalueforA,althoughyoucaninferfromthePythagoreantheoremthatB=3.(2)aloneisinsufficientbecause(A,B)couldbe(1,6)oritcouldbe(3,4),thereisnowaytotell.Ifthestatementsarecombined,youcantakethevaluethatB=3anddeterminefromtheequationinstatement(2)thatA=4;therefore,theareaoftherectangleis12.9、Doatleast20percentofthepeopleincountryXwhoareovertheageof25possessacollegediploma?(1)IncountryX,amongthepopulationovertheageof25,26percentofthemalepopulationand16percentofthefemalepopulationpossesscollegediplomas.(2)IncountryX,womenaccountfor55percentofthetotalpopulation.标准答案：E知识点解析：isinsufficientbecauseitdoesnottellwhatpercentageofthepopulationover25isfemale;ifthegendersplitis50/50,thentheanswertothequestionis"yes,"ifthegendersplitis25/75withmorefemales,thentheansweris"no."(2)aloneisinsufficient,andalthoughitappearstoaddresstheinsufficiencyinstatement(1),itactuallydoesnot,becausewecannotinferthatthegendersplitforthetotalpopulationisthesameasthegendersplitforthepopulationover25.10、Ifands≠0,whatisthevalueofC?(1)r=4s(2)标准答案：A知识点解析：Inordertoanswerthisquestion,youneedtoremovebothvariablessothatanumericalanswerisleft.(1)issufficientbecauseitallowsyoutorestatetheequationas.(2)isinsufficient,becauseavariableremainsintheequation.11、If8a=9bandab≠0,whatistheratioof?A、

B、

C、

D、

E、

标准答案：C知识点解析：Theratioofthesenumbersis(a/9)/(b/8);youcansubstituteintheratiosfromthequestion,soa=9b/8;theratiothenis(9b/72)/(b/8);dividebfrombothsidesoftheratio,andmultiply8timesbothsidesoftheratio,andyouwindupwith72/72=1.12、Twohundredmultiplesofsevenarechosenatrandom,and300multiplesofeightarechosenatrandom.Approximatelywhatpercentageofthe500selectednumbersareodd?A、20%B、25%C、40%D、5O%E、80%标准答案：A知识点解析：Allmultiplesof8areeven,andhalfofthemultiplesof7areodd;themultiplesof7makeup2/5ofthetotal,soif1/2ofthosemultiplesof7areodd,then1/5ofthetotalwillbeodd,or20%.13、IntriangleABCabove,if∠BADand∠ADBhavemeasuresof4n,∠ACBhasameasureofn,and∠DBChasameasureof45°,whatisthemeasureof∠ABC?(Figurenotnecessarilydrawntoscale.)A、45°B、60°C、90°D、105°E、120°标准答案：D知识点解析：Theprincipletorememberhereisthatanexteriorangleofatriangle--suchas∠ADB--isequaltothesumoftheremoteinterioranglesofthetriangle,inthiscase∠DBCand∠DCB(=∠ACB)oftriangleBDC.Thus,∠DCB+∠DBC=4n,or∠DBC=3n=45°,andthereforen=15°and4n=60°.Thethreeanglesofatrianglemustequal180°,so∠ABC=180°-60°-15°=105°.14、AcoedsoccerteamhasWwomenandMmenontheteam.If4womenand2menareaddedtotheteamroster,andifonepersonontheteamisselectedatrandomtoserveasteamcaptain,thentheprobabilitythattheteamcaptainwillbeawomancanberepresentedasA、

B、

C、

D、

E、

标准答案：A知识点解析：Theprobabilityisequaltothenewnumberofwomen,i.e.,W+4,dividedbythenewtotal,whichisW+M+6.Theanswer,therefore,is.15、Whatisthetwenty-thirddecimaltotherightinthefraction?A、1B、2C、3D、4E、5标准答案：C知识点解析：Thiswouldbeanunreasonablydifficultquestionexceptthatthefractioninquestionisthenonterminatingdecimal,sothenumbertotherightofanythingafterthethirddecimalis3.16、IfScotthasearnedxdollarsbyworking3daysaweekataconstantdailyrateforWweeks,whichofthefollowingrepresentshisdailywage?A、

B、

C、

D、

E、

标准答案：E知识点解析：Hisdailywagecanbedeterminedbydividinghistotalincomebythetotalnumberofdayshehasworked,xishisincome,and3wisthetotalnumberofdayshehasworked,sox/3wishisdailywage.17、A、

B、

C、

D、

E、

标准答案：A知识点解析：Thestatementequals.18、Inacertainconservativemutualfund,70percentofthemoneyisinvestedinbonds,andofthatportion,40percentisinvestedinhighlyratedcorporatebonds.Ifatleast$1.4millioninthisfundisinvestedinhighlyratedcorporatebonds,whatisthesmallestpossibletotalvalueforthemutualfund?A、$4millionB、$5millionC、$6millionD、$7millionE、$8million标准答案：B知识点解析：If40percentoftheamountinvestedinbondsisinvestedinhighlyratedcorporatebonds,thenthetotalamountinvestedinbondsis$1.4milliontimes10/4=$3.5million.$3.5millioninbondsis70percentofthetotalfund,sothetotalfundis$3.5milliontimes10/7=$5million.19、Ifthediameterofacircleis14,thentheareaofthecircleisA、7πB、14πC、28πD、49πE、196π标准答案：D知识点解析：Thediameterofacircleistwiceitsradius,soifthediameteris14,thentheradiusis7.Theformulafortheareaofacircleisπr2,sotheareaofthis