GMAT模拟试题深度钻研及答案公布

GMAT模拟试题深度钻研及答案公布

一、单选题（每题2分，共20分）

1.Ifarectangleslengthisincreasedby20%anditswidthisdecreasedby10%,whatisthepercentagechangeinitsareaA.10%increaseB.10%decreaseC.2%increaseD.2%decreaseE.Nochange【答案】C【解析】Theareaoftherectangleisinitiallylength×width.Ifthelengthisincreasedby20%,itbecomes

1.2timestheoriginallength.Ifthewidthisdecreasedby10%,itbecomes

0.9timestheoriginalwidth.Thenewareais

1.2×

0.9×length×width=

1.08×length×width,whichisan8%increasefromtheoriginalarea.

2.Acertainclubhas50members,andtheratioofmaletofemalemembersis3:

2.If10newmembersareadded,allofwhomarefemale,whatisthenewratioofmaletofemalemembersA.3:4B.4:3C.3:5D.5:3E.4:5【答案】A【解析】Initially,thereare30malemembers3/5of50and20femalemembers2/5of

50.Afteradding10femalemembers,therearestill30malemembersand30femalemembers.Thenewratiois30:30,whichsimplifiesto3:

4.

3.Ifthesumoftwoconsecutiveintegersis47,whatisthelargerintegerA.23B.24C.25D.26E.27【答案】C【解析】Letthetwoconsecutiveintegersbexandx+

1.Theequationisx+x+1=47,whichsimplifiesto2x+1=

47.Solvingforxgivesx=23,sothelargerintegeris

24.

4.Acirclehasaradiusof5cm.WhatistheareaofthecircleA.15πcm²B.20πcm²C.25πcm²D.30πcm²E.50πcm²【答案】C【解析】Theareaofacircleisπr².Witharadiusof5cm,theareaisπ×5²=25πcm².

5.Ifatraintravelsataspeedof60km/h,howfarwillittravelin4hoursA.140kmB.240kmC.360kmD.480kmE.600km【答案】D【解析】Distance=speed×time.Ataspeedof60km/hfor4hours,thedistanceis60×4=240km.

6.Aboxcontains3redballs,4blueballs,and5greenballs.Ifaballisdrawnatrandom,whatistheprobabilityofdrawingablueballA.1/12B.1/4C.1/3D.1/2E.2/3【答案】B【解析】Thetotalnumberofballsis3+4+5=

12.Theprobabilityofdrawingablueballis4/12,whichsimplifiesto1/

3.

7.Iftheslopeofalineis-3/4,whatistheslopeofalineperpendiculartoitA.3/4B.4/3C.-4/3D.-3/4E.1/3【答案】B【解析】Theslopesofperpendicularlinesarenegativereciprocals.Thenegativereciprocalof-3/4is4/

3.

8.Atrianglehasanglesmeasuring45°,45°,and90°.Ifthehypotenuseis10cm,whatisthelengthofoneofthelegsA.5cmB.7cmC.10cmD.7√2cmE.5√2cm【答案】E【解析】Ina45-45-90triangle,thelegsarecongruent,andthehypotenuseis√2timesthelengthofaleg.Therefore,theleglengthis10/√2=5√2cm.

9.Iftheaverageoffivenumbersis27,whatisthesumofthenumbersA.135B.140C.145D.150E.155【答案】A【解析】Theaverageisthesumdividedbythecount.Thesumis27×5=

135.

10.Astoreishavinga25%offsale.Ifashirtoriginallycosts$40,howmuchwillitcostduringthesaleA.$10B.$25C.$30D.$35E.$40【答案】C【解析】Thediscountis25%of$40,whichis$

10.Thesalepriceis$40-$10=$

30.

二、多选题（每题4分，共20分）

1.WhichofthefollowingarepropertiesofaparallelogramA.OppositesidesareparallelB.OppositesidesareequalinlengthC.OppositeanglesareequalD.AdjacentanglesaresupplementaryE.Diagonalsbisecteachother【答案】A、B、C、D、E【解析】Allthegivenpropertiesaretrueforaparallelogram.

2.Inarighttriangle,whichofthefollowingstatementsaretrueA.ThesquareofthehypotenuseisequaltothesumofthesquaresoftheothertwosidesB.Thesumoftheanglesis180°C.Oneangleisalways90°D.Thelengthsofthesidesarealwaysinaratioof3:4:5E.Theareaishalftheproductofthetwolegs【答案】A、B、C、E【解析】ThestatementsaboutthePythagoreantheorem,anglesum,rightangle,andareaaretrue.Theratio3:4:5isspecifictocertainrighttriangles,notall.

3.WhatarethefactorsthataffectthespeedofawaveA.MediumB.FrequencyC.AmplitudeD.WavelengthE.Energy【答案】A、D【解析】Thespeedofawaveisprimarilyaffectedbythemediumthroughwhichittravelsanditswavelength.

4.WhichofthefollowingaretypesofquadrilateralsA.SquareB.RectangleC.RhombusD.TrapezoidE.Triangle【答案】A、B、C、D【解析】Atriangleisnotaquadrilateral;ithasthreesides.

5.Inafrequencydistribution,whichofthefollowingaretrueA.ThemeanisthesumofalldatadividedbythenumberofdatapointsB.ThemedianisthemiddlevaluewhenthedataisarrangedinorderC.ThemodeisthevaluethatappearsmostfrequentlyD.TherangeisthedifferencebetweenthemaximumandminimumvaluesE.Thevariancemeasuresthespreadofthedata【答案】A、B、C、D、E【解析】Allthegivenstatementsaretrueforafrequencydistribution.

三、填空题（每题4分，共20分）

1.Ifa=3andb=4,thena²+b²=______.【答案】25【解析】a²+b²=3²+4²=9+16=

25.

2.Theperimeterofarectanglewithlength10cmandwidth5cmis______cm.【答案】30【解析】Perimeter=2length+width=210+5=30cm.

3.Theslopeofalinepassingthroughthepoints2,3and4,7is______.【答案】2【解析】Slope=y2-y1/x2-x1=7-3/4-2=4/2=

2.

4.Theareaofatrianglewithbase6cmandheight4cmis______cm².【答案】12【解析】Area=1/2×base×height=1/2×6×4=12cm².

5.Iftheprobabilityofdrawingaredcardfromastandarddeckofcardsis1/4,thentheprobabilityofnotdrawingaredcardis______.【答案】3/4【解析】Theprobabilityofnotdrawingaredcardis1-1/4=3/

4.

四、判断题（每题2分，共10分）

1.Thesumoftheinterioranglesofatriangleisalways180°.（）【答案】（√）【解析】Thesumoftheinterioranglesofatriangleisalways180°.

2.Anobtuseangleisgreaterthan90°.（）【答案】（√）【解析】Anobtuseangleisdefinedasananglegreaterthan90°butlessthan180°.

3.Thesquarerootofanegativenumberisnotarealnumber.（）【答案】（√）【解析】Inthesetofrealnumbers,thesquarerootofanegativenumberisnotdefined.

4.Themedianisalwaysequaltothemeaninadataset.（）【答案】（×）【解析】Themedianandmeanarenotnecessarilyequal;theycanbedifferentdependingonthedataset.

5.Acirclecanhavetwocenters.（）【答案】（×）【解析】Acirclehasonlyonecenter.

五、简答题（每题4分，共20分）

1.Explainthedifferencebetweenanacuteangleandanobtuseangle.【答案】Anacuteangleisananglethatmeasureslessthan90°,whileanobtuseangleisananglethatmeasuresmorethan90°butlessthan180°.

2.WhatisthePythagoreantheorem,andwhenisitused【答案】ThePythagoreantheoremstatesthatinarighttriangle,thesquareofthelengthofthehypotenusethesideoppositetherightangleisequaltothesumofthesquaresofthelengthsoftheothertwosides.Itisusedtofindthelengthofonesideofarighttrianglewhenthelengthsoftheothertwosidesareknown.

3.Describethepropertiesofaparallelogram.【答案】Aparallelogramisaquadrilateralwithoppositesidesthatareparallelandequalinlength.Oppositeanglesareequal,andadjacentanglesaresupplementary.Thediagonalsofaparallelogrambisecteachother.

4.Whatisthedifferencebetweenmeanandmedian【答案】Themeanistheaverageofadataset,calculatedbysummingallthevaluesanddividingbythenumberofvalues.Themedianisthemiddlevaluewhenthedataisarrangedinorder.Ifthereisanevennumberofvalues,themedianistheaverageofthetwomiddlevalues.

5.Howdoestheslopeofalinerelatetoitssteepness【答案】Theslopeofalinemeasuresitssteepness.Apositiveslopeindicatesthatthelinerisesasyoumovefromlefttoright,whileanegativeslopeindicatesthatthelinefallsasyoumovefromlefttoright.Theabsolutevalueoftheslopeindicatesthesteepness;alargerabsolutevaluemeansasteeperline.

六、分析题（每题10分，共20分）

1.Arectanglehasaperimeterof30cmandalengthof10cm.Findthewidthoftherectangleandtheareaoftherectangle.【答案】Perimeter=2length+width30=210+width30=20+2width10=2widthwidth=5cmArea=length×widthArea=10×5=50cm²

2.Theaveragescoreof10studentsinatestis

75.Ifonestudentsscoreis60,whatistheaveragescoreoftheremaining9students【答案】Totalsumofscores=average×numberofstudentsTotalsumofscores=75×10=750Sumoftheremaining9studentsscores=totalsum-60Sumoftheremaining9studentsscores=750-60=690Averagescoreoftheremaining9students=sumofscores/numberofstudentsAveragescore=690/9=77

七、综合应用题（每题25分，共50分）

1.AtraintravelsfromCityAtoCityBataspeedof60km/h.ItreturnsfromCityBtoCityAataspeedof40km/h.Ifthetotaltimefortheroundtripis7hours,whatisthedistancebetweenCityAandCityB【答案】LetthedistancebetweenCityAandCityBbedkm.TimefromCityAtoCityB=distance/speed=d/60hoursTimefromCityBtoCityA=distance/speed=d/40hoursTotaltime=timefromCityAtoCityB+timefromCityBtoCityA7=d/60+d/40Tosolveford,findacommondenominator120:7=2d+3d/1207=5d/1207×120=5d840=5dd=840/5d=168kmThedistancebetweenCityAandCityBis168km.

2.Arectanglehasalengththatistwiceitswidth.Iftheperimeteroftherectangleis30cm,findthelengthandwidthoftherectangle,andthencalculatetheareaoftherectangle.【答案】Letthewidthoftherectanglebewcm.Thenthelengthis2wcm.Perimeter=2length+width30=22w+w30=23w30=6ww=30/6w=5cmLength=2w=2×5=10cmArea=length×widthArea=10×5=50cm²Thelengthoftherectangleis10cm,andthewidthis5cm.Theareais50cm².---标准答案

一、单选题

1.C

2.A

3.B

4.C

5.D

6.B

7.B

8.E

9.A

10.C

二、多选题

1.A、B、C、D、E

2.A、B、C、E

3.A、D

4.A、B、C、D

5.A、B、C、D、E

三、填空题

1.

252.

303.

24.

125.3/4

四、判断题

1.（√）

2.（√）

3.（√）

4.（×）

5.（×）

五、简答题

1.Anacuteangleisananglethatmeasureslessthan90°,whileanobtuseangleisananglethatmeasuresmorethan90°butlessthan180°.

2.ThePythagoreantheoremstatesthatinarighttriangle,thesquareofthelengthofthehypotenusethesideoppositetherightangleisequaltothesumofthesquaresofthelengthsoftheothertwosides.Itisusedtofindthelengthofonesideofarighttrianglewhenthelengthsoftheothertwosidesareknown.

3.Aparallelogramisaquadrilateralwithoppositesidesthatareparallelandequalinlength.Oppositeanglesareequal,andadjacentanglesaresupplementary.Thediagonalsofaparallelogrambisecteachother.

4.Themeanistheaverageofadataset,calculatedbysummingallthevaluesanddividingbythenumberofvalues.Themedianisthemiddlevaluewhenthedataisarrangedinorder.Ifthereisanevennumberofvalues,themedianistheaverageofthetwomiddlevalues.

5.Theslopeofalinemeasuresitssteepness.Apositiveslopeindicatesthatthelinerisesasyoumovefromlefttoright,whileanegativeslopeindicatesthatthelinefallsasyoumovefromlefttoright.Theabsolutevalueoftheslopeindicatesthesteepness;alargerabsolutevaluemeansasteeperline.

六、分析题

1.Perimeter=2length+width30=210+width30=20+2width10=2widthwidth=5cmArea=length×widthArea=10×5=50cm²

2.Totalsumofscores=average×numberofstudentsTotalsumofscores=75×10=750Sumoftheremaining9studentsscores=totalsum-60Sumoftheremaining9studentsscores=750-60=690Averagescoreoftheremaining9students=sumofscores/numberofstudentsAveragescore=690/9=77

七、综合应用题

1.LetthedistancebetweenCityAandCityBbedkm.TimefromCityAtoCityB=distance/speed=d/60hoursTimefromCityBtoCityA=distance/speed=d/40hoursTotaltime=timefromCityAtoCityB+timefromCityBtoCityA7=d/60+d/40Tosolveford,findacommondenominator120:7=2d+3d/1207=5d/1207×120=5d840=5dd=840/5d=168kmThedistancebetweenCityAandCityBis168km.

2.Letthewidthoftherectanglebewcm.Thenthelengthis2wcm.Perimeter=2length+width30=22w+w30=23w30=6ww=30/6w=5cmLength=2w=2×5=10cmArea=length×widthArea=10×5=50cm²Thelengthoftherectangleis10cm,andthewidthis5cm.Theareais50cm².。