2025年GMAT数学专项训练题

2025年GMAT数学专项训练题考试时间：______分钟总分：______分姓名：______1.Ifnisanintegergreaterthan1,whatisthevalueofn?(1)nhasexactlytwopositivedivisors.(2)n-1isaprimenumber.2.Acertaincompanyproducesonlytwoproducts:chairsandtables.Howmanychairsdidthecompanyproducelastyear?(1)Thecompanyproduced3timesasmanytablesaschairslastyear.(2)Thecompanyproducedatotalof90chairsandtableslastyear.3.Ifxandyareintegers,isxdivisibleby3?(1)x+yisdivisibleby3.(2)y-xisdivisibleby3.4.Acertainlistconsistsofseveraldistinctpositiveintegers.Isthemedianofthelistgreaterthan10?(1)Therangeofthelistis20.(2)Theaverage(arithmeticmean)ofthelistis12.5.Whatisthevalueoftheintegerk?(1)kistheproductoftwoconsecutiveoddintegers.(2)kisdivisibleby5.6.Inacertainclass,theaverage(arithmeticmean)scoreofthe10malestudentsis70,andtheaveragescoreofthe5femalestudentsis85.Whatistheaveragescoreofallthestudentsintheclass?(1)Theaveragescoreofthemaleandfemalestudentscombinedis79.(2)Thesumofthescoresofthemalestudentsis140.7.Ifaandbarepositiveintegers,isa^2+b^2greaterthan100?(1)a+b>20(2)a>10andb>108.Inthexy-plane,whatistheslopeofthelinepassingthroughthepoints(1,3)and(4,y)?(1)y=7(2)Thelinepassesthroughthepoint(2,5).9.Aboxcontainsonlyredballs,blueballs,andgreenballs.Ifaballisrandomlyselectedfromthebox,whatistheprobabilitythattheballisnotblue?(1)Theprobabilityofselectingaredballis1/4.(2)Thenumberofblueballsistwicethenumberofredballs.10.Ifxisapositivenumber,isx<1?(1)x^2<x(2)x^3<x^211.Acertainrectanglehasaperimeterof24inches.Whatistheareaoftherectangle?(1)Thelengthoftherectangleistwiceitswidth.(2)Thelengthoftherectangleis6inchesmorethanitswidth.12.Ify=3x+5,whatisthevalueofywhenx=4?(1)3x+5=17(2)y-2x=1313.Acertainclubhas20members.Howmanymembersoftheclubaremale?(1)Exactly3/5ofthemembersarefemale.(2)Thenumberoffemalemembersis12.14.Istheintegerzdivisibleby6?(1)zisdivisibleby3.(2)zisdivisibleby2.15.Ifa,b,andcareconsecutiveintegers,isa+b+ceven?(1)aiseven.(2)bisodd.16.Acertaininvestmentearnsinterestatarateofrpercentperyear.Iftheinvestmentwasmade3yearsago,howmuchinteresthasitearned?(1)Theprincipalamountoftheinvestmentis$1,000.(2)Theinvestmentisnowworth$1,115.17.Inacertainsequence,thetermanisdefinedbytheformulaan=2^n-n.Isa10greaterthana9?(1)nisapositiveinteger.(2)a9ispositive.18.Acertaintankisfilledwithwater.Howmanygallonsofwaterareinthetank?(1)Thecapacityofthetankis300gallons.(2)Thetankiscurrentlyfilledto3/4ofitscapacity.19.Ifxandyarepositiveintegers,isx+ygreaterthan100?(1)x^2+y^2>200(2)x>10andy>1020.Inthexy-plane,whatisthey-interceptofthelineL?(1)TheslopeoflineLis3.(2)ThelineLpassesthroughthepoint(0,5).试卷答案1.D2.B3.D4.E5.E6.B7.E8.A9.C10.B11.A12.B13.A14.E15.A16.E17.D18.C19.E20.B解析1.(1)nhasexactlytwopositivedivisors.Thisimpliesnisaprimenumber.Wecannotdeterminethespecificvalueofaprimenumber.(2)n-1isaprimenumber.Thisimpliesn=primenumber+1.Ifnisprime+1andprime+1isalsoprime,theonlypossibilityisprime=2,son=3.Ifnisprime+1andprime+1iscomposite,wecannotdeterminen.Sincewecannotdeterminenfrom(2)alone,butwecandetermineitfrom(1)alone,theansweris(1).2.(1)Thecompanyproduced3timesasmanytablesaschairslastyear.Letcbethenumberofchairsandtbethenumberoftables.Thent=3c.Thetotalnumberofchairsandtablesisc+t=c+3c=4c.Wedonotknowthevalueofc,sowecannotdeterminethevalueoft.(2)Thecompanyproducedatotalof90chairsandtableslastyear.Letcbethenumberofchairsandtbethenumberoftables.Thenc+t=90.Wedonotknowtheindividualvaluesofcandt.Forexample,c=30,t=60orc=45,t=45.Sincewecannotdeterminethenumberofchairsfrom(2)alone,theansweris(2).3.(1)x+yisdivisibleby3.Ifxis1andyis2,thenx+y=3isdivisibleby3,butxisnotdivisibleby3.Ifxis2andyis1,thenx+y=3isdivisibleby3,butxisnotdivisibleby3.Ifxis3andyis0,thenx+y=3isdivisibleby3,andxisdivisibleby3.Wecannotdetermineifxisdivisibleby3from(1)alone.(2)y-xisdivisibleby3.Thismeansy=x+3kforsomeintegerk.Ifxis1,y=1+3k.Forytobeaninteger,kmustbeaninteger.y=1+3kisdivisibleby3if1+3kisdivisibleby3.Thisistrueforallintegersk.So,ifxis1,ymustbeanoddinteger.Ifxisanoddinteger,y=odd+3kisalsoanoddinteger.Ifxisaneveninteger,y=even+3kisalsoaneveninteger.Inallcases,xandyhavethesameparity.Sincex+yisdivisibleby3(givenin(1))andxandyhavethesameparity,xmustbedivisibleby3.Theansweris(2).4.(1)Therangeofthelistis20.Therangeisthedifferencebetweenthelargestandsmallestelements.Knowingtherangeis20tellsusthatthedifferencebetweenthelargestandsmallestnumbersis20,butwedonotknowtheactualvaluesofthesenumbersorthevaluesoftheothernumbersinthelist.Themediancouldbegreaterthan10,oritcouldbelessthan10.Forexample,thelistcouldbe{1,21}.Themedianis11.Thelistcouldbe{5,25}.Themedianis10.Thelistcouldbe{11,31}.Themedianis21.Sincewecannotdetermineifthemedianisgreaterthan10from(1)alone,theansweris(1).5.(1)kistheproductoftwoconsecutiveoddintegers.Theproductoftwoconsecutiveoddintegersisalwaysodd.Itcouldbe3x5=15,or5x7=35,or7x9=63,etc.Wedonotknowthespecificvalueofk.(2)kisdivisibleby5.kcouldbe5,10,15,20,etc.Sincewecannotdeterminethespecificvalueofkfrom(2)alone,theansweris(2).6.Theaveragescoreofallstudents=(Sumofscoresofmalestudents+Sumofscoresoffemalestudents)/(Totalnumberofstudents)=(10*70+5*85)/(10+5)=(700+425)/15=1125/15=75.Theaveragescoreofallstudentsis75.Thisvalueiscompletelydeterminedbythegiveninformationanddoesnotdependonanyofthestatements.Therefore,neitherstatementisneededtofindtheanswer.TheanswerisD.7.(1)a+b>20.Forexample,ifa=10andb=10,thena+b=20,whichisnotgreaterthan20,buta^2+b^2=100+100=200,whichisnotgreaterthan100.So(1)isnotsufficient.(2)a>10andb>10.Ifa=11andb=11,thena+b=22>20anda^2+b^2=121+121=242>100.So(2)issufficient.Theansweris(2).8.Theslopeofthelinepassingthrough(1,3)and(4,y)is(y-3)/(4-1)=(y-3)/3.(1)y=7.Theslopeis(7-3)/3=4/3.Thisuniquelydeterminestheslope.(2)Thelinepassesthroughthepoint(2,5).Theslopeofthelinepassingthrough(1,3)and(2,5)is(5-3)/(2-1)=2/1=2.Thisuniquelydeterminestheslope.Sincebothstatementsuniquelydeterminetheslope,eitherstatementaloneissufficient.Theansweris(A).9.(1)Theprobabilityofselectingaredballis1/4.Letr,b,gbethenumberofred,blue,greenballs.Totalballs=r+b+g.P(red)=r/(r+b+g)=1/4.Thisgivesr=(1/4)(r+b+g).Weknowr,b,garepositiveintegers,butwedonotknowtheirspecificvaluesorthetotalnumberofballs.WecannotdetermineP(notblue)=(r+g)/(r+b+g)from(1)alone.(2)Thenumberofblueballsistwicethenumberofredballs.b=2r.Wedonotknowthevaluesofr,b,g,orthetotalnumberofballs.WecannotdetermineP(notblue)from(2)alone.(1)and(2)together:r=(1/4)(r+2r+g)=>r=(1/4)(3r+g)=>4r=3r+g=>g=r.So,thenumberofred,blue,greenballsarer,2r,r.Totalballs=4r.P(notblue)=(r+r)/(4r)=2r/4r=1/2.Bothstatementstogetheraresufficient.Theansweris(C).10.(1)x^2<x.Thisisequivalenttox^2-x<0,whichisequivalenttox(x-1)<0.Thisinequalityholdswhen0<x<1.Soxcouldbe1/2,whichislessthan1,orxcouldbe0.6,whichislessthan1.Theanswerto"Isx<1?"isYES.(2)x^3<x^2.Thisisequivalenttox^2(x-1)<0.Sincexisapositivenumber,x^2isalwayspositive.Sotheinequalityholdswhenx-1<0,whichmeansx<1.Theanswerto"Isx<1?"isYES.Bothstatementsalonearesufficient.Theansweris(B).11.(1)Thelengthoftherectangleistwiceitswidth.Letlbethelengthandwbethewidth.Thenl=2w.TheperimeterisP=2(l+w)=2(2w+w)=2(3w)=6w.WearegivenP=24inches.So6w=24=>w=4inches.Thenl=2w=2*4=8inches.TheareaisA=l*w=8*4=32squareinches.Thisuniquelydeterminesthearea.(2)Thelengthoftherectangleis6inchesmorethanitswidth.Letlbethelengthandwbethewidth.Thenl=w+6.TheperimeterisP=2(l+w)=2((w+6)+w)=2(2w+6)=4w+12.WearegivenP=24inches.So4w+12=24=>4w=12=>w=3inches.Thenl=w+6=3+6=9inches.TheareaisA=l*w=9*3=27squareinches.Thisuniquelydeterminesthearea.Sincebothstatementsuniquelydeterminethearea,eitherstatementaloneissufficient.Theansweris(A).12.Theequationisy=3x+5.Weneedtofindthevalueofywhenx=4.Substitutex=4intotheequation:y=3(4)+5=12+5=17.Thevalueofyis17.(1)3x+5=17.Thisequationisidenticaltothegivenequationy=3x+5.If3x+5=17,theny=17.Thisstatementistrueifandonlyify=17.Thisdoesnotgiveusthevalueofy.Ittellsusthaty=17.(2)y-2x=13.Substitutey=3x+5intothisequation:(3x+5)-2x=13.Simplify:x+5=13=>x=8.Wearegivenx=4.Sincex=8contradictsx=4,statement(2)isfalse.Afalsestatementdoesnotprovideanyinformationaboutthevalueofy.Sincewecannotdeterminethevalueofyfrom(1)alone,and(2)isfalse,thecorrectansweris(B).Note:Thisquestionisdesignedsuchthat(1)isactuallysufficienttofindy=17,but(2)isafalsestatementcontradictingthepremisex=4.InarealGMATtest,suchaquestionmightbeconsideredflawedormightbeinterpretedasaskingforsufficiency.However,basedonthestandardtemplatewherethequestionasksforavalueand(1)providesit,theansweris(1).If(2)beingfalseisthekeyissue,theanswerwouldbe(B).Let'sassumethequestionasksforsufficiencytofindy.(1)givesy=17.Thisissufficient.(2)isfalse.Afalsestatementdoesnotprovidesufficiency.So(1)aloneissufficient.Theansweris(1).Ifthequestionasksforthevalueofy,and(2)beingfalsecontradictsthesetup,thenthevaluecannotbedetermined.Butthequestionasks"Whatisthevalueofy...".Thestandardinterpretationisthatthevalueexistsandcanbefound.Therefore,theansweris(1).13.(1)Exactly3/5ofthemembersarefemale.LetTbethetotalnumberofmembers.Thenumberoffemalemembersis(3/5)T.WearegivenT=20.Sothenumberoffemalemembersis(3/5)*20=12.ThenumberofmalemembersisT-(numberoffemalemembers)=20-12=8.Thisuniquelydeterminesthenumberofmalemembers.(2)Thenumberoffemalemembersis12.WearegivenT=20.Sothenumberofmalemembersis20-12=8.Thisuniquelydeterminesthenumberofmalemembers.Bothstatementsalonearesufficient.Theansweris(A).14.(1)zisdivisibleby3.Ifz=3kforsomeintegerk,thenzisdivisibleby3.Butzcouldbe3,whichisdivisibleby3,butzisnotdivisibleby6.Forexample,z=3.So(1)isnotsufficient.(2)zisdivisibleby2.Ifz=2mforsomeintegerm,thenzisdivisibleby2.Butzcouldbe2,whichisdivisibleby2,butzisnotdivisibleby6.Forexample,z=2.So(2)isnotsufficient.(1)and(2)together:zisdivisibleby3andzisdivisibleby2.Thismeanszisdivisiblebytheleastcommonmultipleof2and3,whichis6.Sozmustbedivisibleby6.Forexample,z=6.Bothstatementstogetheraresufficient.Theansweris(C).15.(1)aiseven.Leta=2kforsomeintegerk.Sincea,b,careconsecutiveintegers,b=a+1=2k+1(odd),c=b+1=2k+2(even).Thesuma+b+c=2k+(2k+1)+(2k+2)=6k+3.Since6kiseven,6k+3isodd.Sothesumisodd.Thisuniquelydeterminestheparityofthesum.(2)bisodd.Letb=2m+1forsomeintegerm.Sincea,b,careconsecutiveintegers,a=b-1=(2m+1)-1=2m(even),c=b+1=(2m+1)+1=2m+2(even).Thesuma+b+c=2m+(2m+1)+(2m+2)=6m+3.Since6miseven,6m+3isodd.Sothesumisodd.Thisuniquelydeterminestheparityofthesum.Bothstatementsalonearesufficient.Theansweris(A).16.(1)Theprincipalamountoftheinvestmentis$1,000.Weneedtheinterestearnedover3years.Wealsoneedtheinterestrater.Thisinformationisnotprovided.(2)Theinvestmentisnowworth$1,115.Weneedtheinterestearnedover3years.WealsoneedtheprincipalamountPandtheinterestrater.Thisinformationisnotprovided.(1)and(2)together:WehaveP=$1,000andA=$1,115fort=3years.TheinterestearnedisI=A-P=1115-1000=$115.Theinterestearnedis$115.ThisvalueisdeterminedbyP,A,andt.Theraterisnotneededtocalculatetheinterestearned.Theinterestearnedis$115.Bothstatementstogetheraresufficient.Theansweris(C).17.(1)nisapositiveinteger.Thismeansn=1,2,3,4,...Weneedtocomparea10anda9.a10=2^10-10=1024-10=1014.a9=2^9-9=512-9=503.Since1014>503,a10isgreaterthana9.Thisissufficient.(2)a9ispositive.Ifa9=2^9-9=503ispositive,thennmustbeatleast1.Thecomparisona10>a9holdsforn>=1.Sotheanswerto"Isa10greaterthana9?"isYES.Thisissufficient.Bothstatementsalonearesufficient.Theansweris(D).18.(1)Thecapacityofthetankis300gallons.Wedonotknowhowfullthetankis.Theamountofwaterinthetankcouldbe0,100,200,300,...gallons.Wecannotdeterminetheamountofwater.(2)Thetankiscurrentlyfilledto3/4ofitscapacity.LetCbethecapacity.Theamountofwateris(3/4)C.WearegivenC=300gallons(from(1)).Sotheamountofwateris(3/4)*300=225gallons.Thisuniquelydeterminestheamountofwater.(1)and(2)together:Thecapacityis300gallonsandthetankisfilledto3/4ofitscapacity.Theamountofwateris(3/4)*300=225gallons.Bothstatementstogetheraresufficient.Theansweris(C).19.(1)a^2+b^2>200.Forexample,ifa=15andb=15,thena^2+b^2=225+225=450>200,buta+b=15+15=30,whichisnotgreaterthan100.So(1)isnotsufficient.(2)a>10andb>10.Forexample,ifa=11andb=11,thena+b=11+11=22>100.Sotheanswerto"Isa+bgreaterthan100?"isYES.Forexample,ifa=15andb=15,thena+b=15+15=30>100.SotheanswerisYES.Ifa=12andb=12,thena+b=24>100.SotheanswerisYES.Itseemsthatifa>10andb>10,thena+b>100.Let'sprovethis.Sincea>10,a>=11.Sinceb>10,b>=11.Soa+b>=11+11=22.Since22>100isfalse,thecorrectconclusionisa+b>=22.Weneedtocheckifa+b>100isalwaystruewhena>10andb>10.Let'stesta=10.1andb=10.1.a+b=20.2,whichisnot>100.Sotheconditiona>10andb>10isnotsufficienttoguaranteea+b>100.Forexample,a=10.1,b=10.1=>a+b=20.2.So(2)isnotsufficient.(1)and(2)together:a^2+b^2>200anda>10andb>10.Sincea>10andb>10,a^2>100andb^2>100.Soa^2+b^2>100+100=200.Thisisconsistentwith(1).Let'sseeifthisguaranteesa+b>100.Sincea>10andb>10,a^2>100andb^2>100.a^2+b^2>200.Weknowthat(a+b)^2=a^2+b^2+2ab.Sincea>0andb>0,2ab>0.So(a+b)^2>a^2+b^2>200.Thisimpliesa+b>sqrt(200).sqrt(200)=sqrt(100*2)=10*sqrt(2)approx10*1.414=14.14.Soa+b>14.14.Sincea+bmustbeaninteger(asaandbarepositiveintegers),a+b>=15.Since15>100isfalse,thecorrectconclusionisa