2026年GMAT《定量推理》考试试题及答案

2026年GMAT《定量推理》考试试题及答案Question1ProblemSolvingIfthesumofthefirstntermsofasequenceisgivenbytheformula=+A.42B.43C.44D.45E.46Answer:BAnalysis:Tofindthe20thterm(),weneedtounderstandtherelationshipbetweenthesumofthefirstnterms()andthesumofthefirstn−1terms().Then-thtermisdefinedasthedifferencebetweenthesumofthefirstntermsandthesumofthefirstn−=Given=+3n=Next,wecalculate:=Now,findthe20thterm:=Wait,letmere-checkthecalculation.=400.3=361.3460418Let'schecktheoptions.OptionAis42.However,let'sdoublechecktheformulaapplication.Alternatively,=====Forn==2ThecorrectanswerisA.Question2DataSufficiencyIfxandyarepositiveintegers,isxamultipleofy?(1)xisamultipleofy+(2)yisamultipleofx+A.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:BAnalysis:Weneedtodetermineifxisdivisiblebyy(i.e.,x=kyStatement(1):xisamultipleofy+Thismeansx=Doesthisimplyxisamultipleofy?Notnecessarily.Example1:Lety=2.Theny+1=3.IfExample2:Lety=2.Theny+1=3.IfSincewecangetbothYesandNo,Statement(1)isinsufficient.Statement(2):yisamultipleofx+Thismeansy=Sincexandyarepositiveintegers,x+Therefore,yisamultipleofanumberstrictlylargerthanx.Thisimpliesy>x(sincethemultiplemustbeatleastIfy>xandbotharepositiveintegers,xcannotbeamultipleofy(unlessx=Thus,theanswerisdefinitivelyNo.Statement(2)issufficient.Question3ProblemSolvingAcertainbookstoresellstwotypesofnotebooks:TypeAandTypeB.TherevenuefromthesaleofTypeAnotebooksin2025wasppercentofthebookstore'stotalrevenuefromnotebooks.In2026,therevenuefromTypeAnotebooksincreasedby20percentandtherevenuefromTypeBnotebooksincreasedby30percent.Ifthetotalrevenuefromnotebooksincreasedby25percentfrom2025to2026,whatisthevalueofp?A.40B.45C.50D.55E.60Answer:CAnalysis:LettherevenuefromTypeAin2025beAandrevenuefromTypeBin2025beB.Totalrevenuein2025=A+WearegivenA=In2026:RevenuefromTypeA=1.2ARevenuefromTypeB=1.3BTotalrevenuein2026=1.2AWearealsogiventhatthetotalrevenueincreasedby25%.So,Totalrevenuein2026=1.25(Equatingthetwoexpressionsfor2026revenue:1.21.2RearrangingtermstosolvefortherelationshipbetweenAandB:1.30.05BSinceB=A,thetotalrevenueWeneedtofindp,whereAispoftotalrevenue.pppThecorrectanswerisC.Question4DataSufficiencyInthexy-plane,doesthelinewithequationy=m(1)m(2)mA.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:EAnalysis:Thecircle+=Thelineintersectsthecircleifthedistancefromthecenter(0,0)tothelinemxThedistancedfrom(0,0dIntersectionoccursif,whichsimplifiesto≤+1Since+1isalwayspositive,thisisalmostalwaystrueunless|b|Specifically,since≥0,≥1.SoIf|b|≤If|b|>Let'stestthestatements.Statement(1):m>Case1:m=0,Line:y=Case2:m=0,Line:y=Statement(1)isinsufficient.Statement(2):m+Case1:m=10,Line:y=Case2:m=0,Line:y=Statement(2)isinsufficient.Together:m>bandFromCase2ofStatement2analysis(m=Doesitsatisfy(1)?0>Let'strytofindacasewherebotharetruebutnointersection.Weneed|b|>Weneed4>Wealsoneedm>Butmcannotbeboth<1.732and>2.SoLet'stryb=Conditionfornointersection:2.25>Condition(1):m>Condition(2):m+Ifm>1.5,thenCheckdistance:.Since>2.25,>Sodistance<<Thissuggeststheyalwaysintersect?Let'scheckm=(1)1.1>(2)1.1+Distance:.Intersects.Let'strytoprovetheyalwaysintersect.Wewanttoknowif≤+1isalwaystruegivenm>Suppose>+1.ThenSincem>b,ifbispositive,thenSom>Squarebothsides(sincepositive):>>Thisimplies>+1,whichisimpossible(Soifb>Whatifb≤Ifb≤0,thenWait,ifb=−5,|b|=5Checkconditionsform=(1)0>(2)0+Sobcannotbeverynegative.Wehavem+b>Summingthem:2mIfbisnegative,sayb=−km>−kAlsom>bimpliesSomispositiveifk<1.Ifk≥However,weestablishedthatifb>Ifb≤Weneedtocheckif≤+Ifb≤0,thenm+b>1impliesSom>Wealsohavem>b,whichisautomaticallytruesincem>Soconditionsreduceto:m>1andb≤Weneedtocheckif>+>+Sincem>1,Example:b=−2Weneed+1Alsoneedm>Soweneed3<Example:b=−1Need+1Example:b=−0.5Need+1Itseemsthatwithm>1andm>Let'sverify.Weneed>+Sincem>1−Substitutethisintotheinequality:>>02b>Butweareinthecaseb≤Thus,itisimpossibleforthelineNOTtointersectthecircle.TheanswerisalwaysYes.Bothstatementstogetheraresufficient.Question5ProblemSolvingAcylindricaltankhasaradiusof5feetandaheightof10feet.Ifwaterisdrainingfromthetankataconstantrateof2cubicfeetperminute,howmanyminuteswillittaketoreducethewaterlevelbyhalf?A.19.6B.39.25C.62.8D.125.6E.196.25Answer:DAnalysis:First,calculatethetotalvolumeofthecylindricaltank.Formulaforvolumeofacylinder:V=Given:Radiusr=Heighth=TotalVolume=πWewanttoreducethewaterlevelbyhalf.Thismeansweneedtodrainhalfofthetotalvolume.Volumetodrain==Thedrainrateis2cubicfeetperminute.Timet=t=Usingtheapproximationπ≈t≈Calculation:62.562.5187.5+Wait,letmere-readtheoptions.A.19.6B.39.25C.62.8D.125.6E.196.25Mycalculationleadsto196.25.Letmere-readthequestion."reducethewaterlevelbyhalf".Does"waterlevel"refertoheightorvolume?Usually"waterlevel"meansheight.Iftheheightisreducedbyhalf,thenewheightis5feet.Thevolumeremovedcorrespondstoacylinderofheight5.Sothevolumeremovedisindeedhalfthetotalvolume.So62.5π62.5×Letmechecktheoptionsagain.Eis196.25.Isitpossibletherateisdifferentordimensions?No.MaybeIshouldcalculateexactly.62.5×TheanswerisE.Question6DataSufficiencyIs>?(1)x(2)yA.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:CAnalysis:Inequality:>.Rearranging:>0Statement(1):x>Wedon'tknowthesignsorvaluesofyandz.Ifx=1,Ifx=1,Statement(1)isinsufficient.Statement(2):y>Thisimpliesyandzarepositive,soyzAlsozySothetermisnegative.Theinequalitybecomesx×Thisistrueifx<0andfalseifWedon'tknowthesignofx.Statement(2)isinsufficient.Together:From(1),x>From(2),thetermisnegative.Sox(PositivetimesNegativeisNegative.SoNeTheanswerisdefinitivelyNo.Bothstatementstogetheraresufficient.Question7ProblemSolvingIf|x3|A.6B.8C.10D.12E.14Answer:AAnalysis:Theequation|xCase1:xxCase2:xxThepossiblevaluesofxare8and-2.Thesumofthesevaluesis8+Alternatively,for|xa|=b,thesolutionsareaHerea=3,sothesumisThecorrectanswerisA.Question8DataSufficiencyWhatisthevalueofthetwo-digitintegerN?(1)Thesumofthedigitsis12.(2)Thetensdigitis2morethantheunitsdigit.A.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:CAnalysis:Letthetensdigitbetandtheunitsdigitbeu.N=Constraints:t∈1,Statement(1):t+Manypairssatisfythis:(3,9),(4,8),(5,7),(6,6),(7,5),(8,4),(9,3).Statement(1)isinsufficient.Statement(2):t=Manypairssatisfythis:(2,0),(3,1),...,(9,7).Statement(2)isinsufficient.Together:Substitute(2)into(1):(22uThent=Thenumberis75.Bothstatementstogetheraresufficient.Question9ProblemSolvingAcommitteeof3peopleistobechosenfrom4marriedcouples.Whatistheprobabilitythatthecommitteecontainsnomarriedcouples?A.B.C.D.E.Answer:CAnalysis:Totalnumberofpeople:4×Weneedtochooseacommitteeof3people.Totalnumberofwaystochoose3peoplefrom8isC(CWewantthenumberofwaystochoose3peoplesuchthatnotwoareamarriedcouple.Thismeanswemustselect3peoplefrom3distinctcouples.Step1:Choose3couplesfromthe4availablecouples.Numberofways:C(Step2:Fromeachofthe3chosencouples,select1person(eitherhusbandorwife).Foreachcouple,thereare2choices.Totalchoicesforpeople:2×Totalfavorableoutcomes=(Waystochoosecouples)×(Waystochoosepeople)4×ProbabilityP=Simplifythefraction:Dividenumeratoranddenominatorby8:=.ThecorrectanswerisC.Question10DataSufficiencyIfxisaninteger,isxdivisibleby6?(1)xisodd.(2)xisamultipleof3.A.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:DAnalysis:Theexpressionisx=Thisistheproductoftwoconsecutiveintegers.Theproductoftwoconsecutiveintegersisalwaysdivisibleby2(sinceoneofthemmustbeeven).So,x(Forittobedivisibleby6,itmustbedivisibleby2AND3.Sinceitisalwaysdivisibleby2,wejustneedtocheckifitisdivisibleby3.Anyproductof3consecutiveintegersisdivisibleby3.Herewehavex(x−1)Statement(1):xisodd.Ifxisodd,x−Weneedtocheckdivisibilityby3.Example:x=1.Example:x=3.Example:x=5.Statement(1)isinsufficient.Statement(2):xisamultipleof3.Ifxisamultipleof3,thenx(Asestablished,x(Sinceitisdivisiblebyboth2and3,itisdivisibleby6.Statement(2)issufficient.Wait,letmere-evaluateStatement(1).IsthereapropertyImissed?Productoftwoconsecutiveintegersisdivisibleby2.Weneeddivisibilityby3.Ifxisodd,sayx=Expression:(2Weneed(2Ifk=1(Ifk=2(So(1)isindeedinsufficient.SotheanswershouldbeB.Letmechecktheoptionsprovidedinthequestionstructure.A.Statement(1)ALONE...B.Statement(2)ALONE...C.BOTH...D.EACH...E.NOTsufficient.MyanalysissaysB.Letmedoublechecktheprompt'soptionsormylogic.Is−xalwaysdivisibleby6ifxIs−xalwaysdivisibleby6ifxIfx=3kCorrectanswerisB.Question11ProblemSolvingIf+=,whatisthevalueofzintermsofxandyA.B.C.D.xE.xAnswer:AAnalysis:Givenequation:+=Combinetheleftside:=.Cross-multiplytosolveforz:z(Dividebyx+z=ThecorrectanswerisA.Question12DataSufficiencyArectangulargardenistobebuiltnexttoahouse,sothatthehouseservesasonesideofthegarden.Thegardenerhas60feetoffencingfortheotherthreesides.Whatistheareaofthegarden?(1)Thelengthofthesideparalleltothehouseis20feet.(2)Thelengthofthesideperpendiculartothehouseis15feet.A.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:DAnalysis:LetLbethelengthofthesideparalleltothehouse.LetWbethelengthofthetwosidesperpendiculartothehouse.Totalfencing=L+WewanttofindtheAreaA=Statement(1):L=Substituteintothefencingequation:202W=AreaA=Statement(1)issufficient.Statement(2):W=Substituteintothefencingequation:LLL=AreaA=Statement(2)issufficient.Eachstatementaloneissufficient.Question13ProblemSolvingAstorediscountedatelevisionsetby20%forasale.Ifthecustomerhasacouponthatgivesanadditional15%offthesaleprice,whatisthetotalpercentagediscountfromtheoriginalprice?A.32%B.35%C.36.8%D.40%E.68%Answer:AAnalysis:LettheoriginalpricebeP.Firstdiscount(20%):SalePriceS=Seconddiscount(15%offthesaleprice):FinalPriceF=SubstituteS:F=Thefinalpriceis68%oftheoriginalprice.Totaldiscount=100.ThecorrectanswerisA.Question14DataSufficiencyIstheintegerndivisibleby15?(1)nisdivisibleby3.(2)nisdivisibleby5.A.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:CAnalysis:Weneedtodetermineifnisdivisibleby15.Since15=3×Statement(1):nisdivisibleby3.Thisdoesnotguaranteedivisibilityby5.Example:n=3(No).Insufficient.Statement(2):nisdivisibleby5.Thisdoesnotguaranteedivisibilityby3.Example:n=5(No).Insufficient.Together:nisdivisibleby3andnisdivisibleby5.Since3and5arecoprime,nmustbedivisibleby3×Sufficient.Question15ProblemSolvingIf=,whatisxintermsofy?A.2B.2C.2D.3E.3Answer:CAnalysis:Equation:=.Express9asapowerof3:9=So,=(Nowequatetheexponents:x+Solveforx:xx=ThecorrectanswerisC.Question16DataSufficiencyPointsA,B,C,andDlieonalineinthatorder.IfA(1)BC(2)ADA.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:DAnalysis:Orderonline:A--B--C--D.Segments:ABGiven:ACBDWeneedABStatement(1):BCFromAC=10ABStatement(1)issufficient.Statement(2):ADADWehavethesystem:1)A2)B3)ASubstitute(2)into(3):ABStatement(2)issufficient.Question17ProblemSolvingAmachineproduces100toysevery5minutes.Atthisrate,howmanyminuteswillittaketoproduce3000toys?A.120B.150C.180D.200E.240Answer:BAnalysis:Rateofproduction:toysperminute.Timerequired=.Time==150Alternatively,usingproportions:=.100xx=ThecorrectanswerisB.Question18DataSufficiencyIfxandyareintegers,is+odd?(1)xisodd.(2)yiseven.A.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:CAnalysis:Weanalyzetheparityof+.Recall:Od=OOdEvOdSo+isoddonlyifoneofx,Statement(1):xisodd.Wedon'tknowy.Ifyisodd,sumisEven.Ifyiseven,sumisOdd.Insufficient.Statement(2):yiseven.Wedon'tknowx.Ifxisodd,sumisOdd.Ifxiseven,sumisEven.Insufficient.Together:xisodd,yiseven.SumisOdd+Even=Odd.Sufficient.Question19ProblemSolvingWhatisthegreatestcommonfactor(GCF)of60and84?A.6B.12C.14D.24E.36Answer:BAnalysis:Primefactorizationof60:60=Primefactorizationof84:84=TheGCFistheproductofthelowestpowersofcommonprimefactors.Commonprimes:2and3.For2:minpowerismin(For3:minpowerismin(GCThecorrectanswerisB.Question20DataSufficiencyAtaxicompanychargesabasefareplusaper-milecharge.Ifa5-mileridecosts\10a(1)Theper-milechargeis\$1.60.(2)A2-mileridecosts\$5.20.A.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:DAnalysis:LetBbethebasefareandMbetheper-milecharge.CostC=Fromtheproblemstem:1)B2)BSubtract(1)from(2):5MSubstituteMbackinto(1):B+ThequestionstemactuallyprovidesenoughinformationtosolveforBdirectly.Wait,usuallyDataSufficiencyquestionsdon'tprovideenoughinfointhestem.Letmere-readcarefully."Ifa5-mileridecosts\10aYes,thestemissufficient.10M=8→M=0.8(Wait,18B=Sotechnically,theanswerisDwithoutlookingatstatements,implyingthestatementsareredundantorthequestionimplieswemightneedthem?Actually,ifthestemissufficient,thentheanswerisD(EACHstatementALONEissufficient)becausethestatementsareindividuallysufficient(sincetheproblemisalreadysolved).Orisitatrick?Usually,thismeansthestatementsarejustextraconfirmations.Statement(1):M=Statement(2):2-mileridecosts5.20.Checkconsistency:B+SoDisthecorrectchoice.Question21ProblemSolvingInacoordinateplane,thepoints(2,1),(4A.2B.3C.4D.5E.6Answer:BAnalysis:Sincethepointsarecollinear,theslopebetweenanytwopairsmustbeequal.Slopem=Usingpoints(2,1m=Nowusepoints(2,1Slopemustbe2.=2=2Multiplybothsidesbyk22=Divideby2:1=k=ThecorrectanswerisB.Question22DataSufficiencyWhatisthemedianofthesetofnumbersx,(1)x<(2)Therangeofthesetis20.A.Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.B.Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.C.BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.D.EACHstatementALONEissufficient.E.Statements(1)and(2)TOGETHERareNOTsufficient.Answer:AAnalysis:Thesethas5numbers.Themedianisthe3rdnumberwhensortedinascendingorder.Statement(1):x<Weknowthefixednumbersare10and15.Sotheorderisx,Themedian(3rdnumber)isz.However,wedon'tknowthevalueofz,justitsposition.Wait,isthequestionaskingforthevalueorjustidentifyingit?"Whatisthemedian?"impliesthevalue.Soweknowthemedianisz,butwedon'tknowwhatzis.SoStatement(1)isinsufficient.Statement(2):Therangeis20.Range=MaxMin=20.Wehave10and15intheset.Possiblescenarios:Case1:Maxis15.Then15MSooneofx,Case2:Minis10.ThenMaSooneofx,Case3:Maxisoneofx,y,Wecannotdeterminetheorderorthespecificvalueofthemedian.Statement(2)isinsufficient.Together:From(1),orderisx,Maxis15.Minisx.From(2),Range=20.15xSoweknowx=Thesetis−5,yThemedianisstillz.Westilldon'tknowthevalueofz.Itcouldbe0,5,9,etc.Soeventogether,wecannotfindthevalueofthemedian.Answer