GMAT（QUANTITATIVE）数学练习试卷1（共231题）

GMAT（QUANTITATIVE）数学练习试

卷1（共9套）

（共231题）

GMAT（QUANTITATIVE）数学练习试

卷第1套

一、单项选择题（本题共30题，每题1.0分，共30

分。）

1、Ifthesmallerof2consecutiveoddintegersisamultipleof5,whichofthefollov/ing

couldNOTbethesumofthese2integers?

A、-8

B、12

C、22

D、52

E、252

标准答案：C

知识点解析:Sincethesmallerofthe2consecutiveoddintegersisamultipleof5,letit

berepresentedbySnforsomeintegern.Thcntheotheroddintegercanberepresentedby

5n+2.ThesumofthesetwointegersislOn+2.Thesumis-8whenn=-1and5n=(5)(-

1)isodd.Thesumis12whenn=1and5n=(5)(1)isodd.Thesumis22whenn=2,but

5n=(5)(2)isnotodd.ThereisnoneedtochecktheDandEbecauseithasbeen

determinedthat22cannoibethesumofthe2consecutiveoddintegers.For

completeness,thesumis52whenn=Sand5n=(5)(5)isodd.Thesumis252whenn=

25and5n=(5)(25)isodd.ThecorrectanswerisC.

2、A8inthefigureabove,iftrianglesABC,ACD,andADEare

isoscelesrighttrianglesandtheareaofAABCis6,thentheareaofAADEis

A、18

B、24

C、36

D、\2yf2

E、24戏36

标准答案：B

知识点解析：BecauseAABCisanisoscelesrighttrianglewithlegs新5d前,itfollows

thatAB=BCandtheareaofAABCis(AB)(BC)/2=(1/2)(AB)2.Itisgiventhatthearea

ofAABCis6,andthus(1/2)(AB-=6,or(AB)~=12,orAB=疝..Applyingthe

PythagoreantheoremtoAABCgives(AC)2=(AB)2+(BC)2,andhence(AC)2=

(何:

12+12=24,orACV24.1.BecauseAACDisanisoscelesrighttriangle

withlegs衣and历.、andAC=日.itfollowsthatAC=CD=424..Applyingthe

777o

PythagoreantheoremtoAACDgives(AD)~=(AC)+(CD),andhence(AD)~=

(衣)+(旧)=24+24=48,orAD=闻..BecauseAADEisanisoscelesrighttriangle

withlegsADandDE,,(jAD=相,，it

an•***•・・,・i-t9followsthatAD=DE=andhencetheareaof

=屈)(屈)=24.加correctanswerisB.

Eachof27white1-centimetercubeswillhaveexactlyoneface

paintedred.Ifthese27cubesarejoinedtogethertoformonelargecube,asshownabove,

whatisthegreatestpossiblefractionofthesurfaceareathatcouldbered?

As11/27

B、13/27

C、1/2

D、5/9

E、19/27

标准答案：B

知识点解析：Allbutoneofthe1-centimetercubes,namelytheI-centimetercubeinthe

center,hasatleastonefacelyingonihesurfaceofthelargecube.Thegreatestpossible

fractionofthesurfaceofthelargecubewillberedwheneachofthese27-1=26non­

center1-centimetercubesisorientedsothatitsredfaceliesonthesurfaceofthelarge

cube.Sincethesurfaceofthelargecubehas6faces,eachconsistingof9facesfromthe

1-centimetercubes,thesurfaceofthelargecubeconsistsofatotalof(6)(9)=54faces

fromthe1-centimetercubes.Therefore,thegreatestpossiblefractionofthesurfacearea

thatcouldberedis26/54=13/27.ThecorrectanswerisB.

4、Thefigureaboveisconstructedbyseparatingacircular

regioninto6equalpartsandrearrangingthepartsasshown.Ifthediameterofthecircle

isd,whatistheperimeterofthefigureabove?

A、兀d

B>27rd

C、兀d+2

D、兀d+d

E、2nd+d

标准答案：D

矢口识点解析：Theperimeterconsistsof6arcsand2segments.Thetotallengthofthe6

arcsisthecircumferenceofthecircle,whichisnd.Eachsegmentisaradiusofthecircle

withlengthd/2.Thereforetheperimeterofthefigureisnd+2(d/2)=nd+d.Thecorrect

answerisD.

5、Onascaledrawingofatriangularpieceofland,thesidesofthetrianglehavelengths

5,12,and13centimeters.IfIcentimeteronthedrawingrepresents3meters,whatisthe

area,insquaremeters,ofthepieceofland?

A、90

B、180

C、240

D、270

E、540

标准答案：D

知识点解析：Since52+122=132,thepieceoflandisintheshapeofarighttriangle.

Thelengthsofthelegsofthepieceofland,inmeters,are(3)(5)=15and(3)(12)=36

since1centimeteronthedrawingrepresents3metersonthepieceofland.Therefore,the

area,insquaremeters,ofthepieceoflandis(1/2)(15)(36)=270squaremeters.The

correctanswerisD.

6、*怪"gurenocd"ssc*Whichofthefollowinggivesallpossiblevaluesofxinthe

figureabove?

A、1<x<4

1<x<7

C>3<x<5

D、4

E、5

标准答案：B

E、4r(n+4)

标准答案：B

知识点解析:Thefigureshowsthatthe(vertical)widthoftheracetrackisequaltothe

diameterofthesemicircles,whichis2r,andthusthe(horizontal)lengthoftheracetrack

is2(2r)=4r.Therefore,theperimeteroftheracetrack,whichconsistsoftwosemicircular

arcsandtwolengthsoftherectangle,is2(兀r)+2(4r)=2i•(兀+4).ThecorrectanswerisB.

Thefigureabove,whichisdividedinto6sectorsofequal

area,containsanarrowrepresentingaspinner.Ifthespinnerisrotated3,840degreesina

clockwisedirectionfromthepositionshown,whichofthefollowingindicatesthesector

(A)△

(B)口

(C)O

(D)

towhichthearrowonthespinnerwillpoint?o

A、

B、

C、

D、

E、

标准答案：B

知识点解析：Thespinnerrotates3840/360=32/3=，03revolutions,whichcanalsobe

seenbyobservingthat3,840degrees-3,600degrees=240degrees=2/3ofarevolution.

Aftermaking10revolutions,thespinnerisbacktothestartingpointandstillneedsto

rotate2/3ofthewayaroundthecircle.Sincerotating2/3ofthewayaroundthecircleis

equivalenttorotatingthrough4ofthe6sectorsofthecircle,thespinnerwillpointtothe

sectorwiththesquare.ThecorrectanswerisB.

11、Whenarectangularvatthatis3feetdeepisfilledto2/3ofitscapacity,itcontains

7I

60gallonsofwaler.If2gallonsofwaleroccupies1cubicfoolofspace,whalisthe

area,insquarefeet,ofthebaseofthevat?

A、4

B、8

C、12

D、150

E、225

标准答案：A

知识点解析:2Whenfilledto2/3capacity,thevatcontains60gallonsofwater(i.e.,

(2/3)(capacity)=60),andsowhenitisfilledtocapacityitcontains(2/3)(60)=90

gallonsofwater,whichoccupies90/7.5=12cubicfeet.IfArepresentstheareaofthe

baseofthevat,insquarefeet,thenthevolumeofthevatis3A=12cubicfeet,andhence

A=4.ThecorrectanswerisA.

12、Thefigureaboverepresentsanantennatowerwithtwoguy

wiresthatextendfrompointQ,40feetabovetheground,topointsPandRasshown.If

thetwowireshaveequallength,approximatelywhatisthetotallength,infeet,ofthetwo

wires?

A、60

B、80

C、100

D、120

E、180

标准答案：C

知识点解析：BecausePQ=QR.itfollowsthatAPQRisisoscelesandtheperpendicular

fromQtoPRbisectsPR•Therefore,eachoftherighttrianglesinthefigurehaslegs

J7()2+A()2

thatare30ftand40ft.BythePythagoreantheorem,PQ=*-ru=50andthe

totallengthofthetwoguywiresis2(50ft)=100ft.ThecorrectanswerisC.

13、Thefiguresaboveshowasealedcontainerthat

isarightcircularcylinderfilledwithliquidto1/2itscapacity.Ifthecontainerisplaced

onitsbase,thedepthoftheliquidinthecontaineris10centimetersandifthecontaineris

placedonitsside,thedepthoftheliquidis20centimeters.Howmanycubiccentimeters

ofliquidareinthecontainer?

A、4,000兀

2,000兀

C>1,000兀

D、400兀

E、200n

标准答案：A

知识点解析:Thefigureontheright,whichshowsthecylinderfilledto1/2itscapacity,

indicatesthattheradiusofthecylinderis20cm.Thefigureontheleftindicatesthatthe

heightoftheliquidis10cmUsingV=7tr2h,whereristheradiusandhistheheightof

theliquidinthecylinder,thevolumeofliquidinthecylindricalcontaineris兀(20)~(10)=

4,000兀cubiccentimeters.ThecorrectanswerisA.

Whatistheradius,inmeters,ofthetabletopwhenallfourleavesareup?

A、1/2

收

B、T

C、1

D、圾

E、2

标准答案：B

知识.点解析/：O-----'Thefigureaboveshowsthecirculartabletopviewedfrom

above.Thediameterofthecircleisthediagonalofthesquare,whichis1meteronaside.

BythePythagoreantheorem,thediagonalis"+0五metersandtheradiusis2

meters.ThecorrectanswerisB.

15>Ifthediameterofacircularskatingrinkis60meters,theareaoftherinkis

approximatelyhowmanysquaremeters?

A、90

B、180

C、900

D、2,800

E、10,800

标准答案：D

知识点解析：Ifthediameterofthecircularskatingrinkis60meters,thentheradiusis

30metersandtheareais兀(30)=900兀squaremeters.Assumingthevalueof兀tobe

slightlygreaterthan3,therinkisapproximately2,800squaremeters.Thecorrectanswer

isD.

16、Whatisthegreatestnumberofblocks8centimetersby6centimetersby9

centimetersthatwillfitintoastoragespacethatis60centimetersby72centimetersby

96centimeters?

A、60

B、840

C、896

D、960

E、1,080

标准答案：D

知识点解析：Thevolumeofthestoragespaceis60x72x96andeachblockis6x8x

9,sothenumberofblocksthatwillfit

is=(60x72x96)/(6x8x9)=60/6x72/9x96/8=10x8x12=960.ThecorrectanswerisD.

17、ClosingPricesofStockXDuringaCertainWeek(indollars)

MondayTuesdayWednesdayThursdayFnday

21192223

-JAcertainfinancialanalystdefinesthe"volatility"

ofastockduringagivenweektobetheresultofthefollowingprocedure:findthe

absolutevalueofthedifferenceinthestock'sclosingpricefbreachpairofconsecutive

daysintheweekandthenfindtheaverage(arithmeticmean)ofthese4values.Whatis

thevolatilityofStockXduringtheweekshownintheTable?

A、2

B、3

C、4

D、6

E、7

标准答案：D

知识点解析：Theeasiestwaytodothisproblemmightbebyjustcountingeverythird

bulbgoingclockwisearoundthecirclestartingalBulb1,whichHashes,skipping2bulbs

andgettingtoBulb4,whichHashes,skipping2bulbsandgettingtoBulb7,which

flashes,skipping2bulbsandgettingtoBulb2,whichflashes,skipping2bulbsand

gettingtoBulb5,whichflashes,skipping2bulbsandgettingtoBulb8,whichflashes,

skipping2bulbsandgettingtoBulb3,whichflashes,andfinallyskipping2bulbsand

gettingtoBulb6,whichflashes.Now,all8bulbshaveflashedonceandthelastoneto

flashwasBulb6.ThecorrectanswerisD.

18、Acertainfinancialanalystdefinesthe"volatility"ofastockduringagivenweekto

betheresultofthefollowingprocedure:findtheabsolutevalueofthedifferenceinthe

stock'sclosingpricefbreachpairofconsecutivedaysintheweekandthenfindthe

average(arithmeticmean)ofthese4values.WhatisthevolatilityofStockXduringthe

weekshowninthetabic?

A、0.50

B、1.80

C、2.00

D、2.25

E、2.50

标准答案：D

知识点解析:ThevolatilityofStockXduringtheweekistheaverageofthe4values

associatedwiththe4pairsofconsecutivedaysduringtheweek.

(Moo&Tue)-»(Ttte&WedH(Wal&cThu)-<-CnMi&Fri)

4

|19-21|+|22-19|+|M5-22|平3-245]

4

_|-2|+|3|+|2.5|+|-L5|2+3+25+1.5_922s

444ThecorrectanswerisD.

13*7

19>Ify=**2-3,forwhatvalueofxwillthevalueofybegreatest?

A、-5

B、-3/5

C、0

D、3/5

E、5/3

标准答案：E

知识点解析：Sincetheabsolutevalueofanyrealnumberisgreaterthanorequalto

zero,itfollowsthat|3x-5|>0.Also,toranyrealnumberxwchavex->0,andhence-

x-<0.Subtracting3frombothsidesofthelastinequalitygives-x~-3<-3.Therefore,

thenumeratoroftheexpressionforyisgreaterthanorequaltozeroandthedenominator

oftheexpressionfbryisnegative.Itfollowsthatthevalueofycannotbegreaterthan0.

However,thevalueofyisequalto0when|3x-5|=0tor3x-5=0,orx=5/3.

Therefore,thevalueofxforwhichthevalueofyisgreatest(i.e.,wheny=0)isx=5/3.

ThecorrectanswerisE.

20>Whatvaluesofxhaveacorrespondingvalueofythatsatisfiesbothxy>0andxy=

x+y?

A、x<-l

B、-1

C、0<x<1

D^x>I

ExAllrealnumbers

标准答案：D

知识点解析:First,usexy=x+ytosolveforyintermsofx.xy=x+ygivenxy-y=x

subtractyfrombothsidesy(x-1)=xfactory=x/(x-l)dividebothsidesbyx-1Note

thatthedivisionbyx-1requiresx/1,andthusx=lneedstobeconsideredseparately.

However,ifx=1,thenxy=x+ybecomesy=1+y,whichisnottrueforanyvalueofy.

Usingy=x/(x-l),itfollowsthattheinequalityxy>0isequivalenttox2/(x-l)>0.Since

x2>0foreachvalueofx,thequotientx2/(x-l)canonlybepositivewhenx/0andx-1

ispositive,orwhenx>1.Alternatively,thecorrectanswercanbefoundbyeliminating

theincorrectanswers,whichcanbeaccomplishedbyconsideringtheendpointsofthe

intervalsgivenintheanswerchoices.Case1:Ifx=-1,thenxy=x+ybecomes-y=-1+

y,ory=1/2.However,inthiscasexy=(-1)(1/2)isnegative,andthusxy>0isnottrue.

Therefore,theanswercannotbeAorE.Case2:Ifx=0,thenxy=0,andthusxy>0is

nottrue.Therefore,theanswercannotbeBorE.Case3:Ifx=1,thenxy=x+vbecomes

y=1+y,whichisnottruefbranyvalueofy.Therefore,theanswercannotbeCorE.

SincetheanswercannotbeA,B,C,orE,itfollowsthattheanswerisD.Thecorrect

answerisD.

21、EmployeeX'sannualsalaryis$12,000morethanhalfofEmployeeY'sannual

salary.EmployeeZ'sannualsalaryis$15,000morethanhalfofEmployeeX'sannual

salary.IfEmployeeX'sannualsalaryis$27,500,whichofthefollowingliststhesethree

peopleinorderofincreasingannualsalary?

A、Y,Z,X

B、Y,X,Z

C、Z,X,Y

D、X,Y,Z

E、X,Z,Y

标准答案：E

知识点解析：Lettingx,y,andzrepresenttheannualsalary,indollars,ofEmployeeX,

EmployeeY,andEmployeeZ,respectively,thefollowinginformationisgiven:(1)x=

12,000+y/2(2)z=15,000+x/2(3)x=27,500From(1)and(3),itfollowsthat27,500

=12,000+y/2ory=2(27,500-12,000)=31,000.From(2)and(3),itfollowsthatz=

15,000+27500/2=28,750.Therefore,x<z<y.ThecorrectanswerisE.

C/0.10s,ifss60.000

22、-10.10"0.MAeo,ooo)/Sn60.000TheformulaabovegivesthecontributionC,in

dollars,toacertainprofit-sharingplanforaparticipantwithasalaryofsdollars.How

manymoredollarsisthecontributionforaparticipantwithasalaryof$70,000thanfora

participantwithasalaryof$50,000?

A、$800

B、$1,400

C、$2,000

D、$2,400

E、$2,800

标准答案：D

知识点解析:Foraparticipantwithasalaryof$70,000,C=0.1(S70,000)+

0.04($70,000-$60,000)=$7,000+$400=$7,400.Foraparticipantwithasalaryof

$50,000,C=0.1($50.0001=$5,000.Thedifferenceis$7,400-$5,000=$2,400.The

correctanswerisD.

23、Nextmonth,RonandCathywilleachbeginworkingpart-timeat3/5oftheir

respectivecurrentsalaries.IfthesumoftheirreducedsalarieswillbeequaltoCathy's

currentsalary,thenRon'scurrentsalaryiswhatfractionofCathy'scurrentsalary?

A、1/3

B、2/5

C、1/2

D、3/5

E、2/3

标准答案：E

知识点解析:LettingRandC,respectively,representRon'sandCathy'scurrent

salaries,itisgiventhat3R/5+3C/5=C.Itfollowsthat3R/5=2C/5andR=3'5'3

ThecorrectanswerisE.

24、DavidandRonareorderingfoodforabusinesslunch.Davidthinksthatthere

shouldbetwiceasmanysandwichesastherearepastries,butRonthinksthenumberof

pastriesshouldbe12morethanone-fourthofthenumberofsandwiches.Howmany

sandwichesshouldbeorderedsothatDavidandRoncanagreeonthenumberofpastries

toorder?

A、12

B、16

C、20

D、24

E、48

标准答案：E

知识点解析：LetSbethenumberofsandwichesthatshoulcbeorderedandletPbethe

numberofpastriesthatshouldbeordered.ThenDaviddesiresS=2PandRondesiresP=

12+S/4.S=2PgivenS=2(12+S/4)P=12+S/4S=24+S/2distributivelawS/2=24

subtractS/2frombothsidesS=48multiplybothsidesby2ThecorrectanswerisE.

25、Thecostofpurchasingeachboxofcandyfromacertainmailordercatalogisv

dollarsperpoundofcandy,plusashippingchargeofhdollars.Howmanydollarsdoesit

costtopurchase2boxesofcandy,onecontainingspoundsofcandyandtheother

containingtpoundsofcandy,fromthiscatalog?

A、h+stv

B、2h+srv

C>2hstv

D、2h+s+t+v

E、2h+v(s+t)

标准答案：E

知识点解析：Thecost,indollars,topurchasethe2boxesofcandyisthesumof2

shippingchargesandthecostofs+tpoundsofcandy,cost=(2shippingcharges)+(v)(s

+/)cost=2(h)+(v)(s+t)cost=2h+v(s+i)ThecorrectanswerisE.

6/♦31-8x-4

26、Ifxrl/2,then―2K.i

A、3X2+3X/2-8

B、3X2+3X/2-4

C、3x2-4

D、3x-4

E、3x+4

标准答案：C

6*'-8*-4=(6y'<-)—(8JT-»4)

2*+1=2x+lgroup

£七*+1)-42"1)

taclor

2x*l

(3-T3+1)

factor

cancdsince

知识点解析:Alternatively,sometimesitis

easierorquickertotestone-variableexpressionsforequalitybysubstitutingaconvenient

valueforthevariableandeliminatinganswerchoicesfbrwhichthevalueofthe

expressioninthatanswerchoicedoesnotequalthevalueofthegivenexpression.For

example,choosex=0,sincecalculationsforx=0areminimal.Then,asshowninthe

tablebelow,2x+11"but3x-+3x/2-8=-8and3x+4=4,neitherofwhich

equals-4,soanswerchoicesAandEcanbeeliminated.Anotherconvenientvalueto

choosefbrxisI.ThereisnoneedtoevaluateanswerchoicesAandEat1sincethey

+3*i_8jr_4.一］、

havealreadybeeneliminated.Asshown,whenx=I,A+i-'but3x~+3x/2-

4=l/2^-l,soanswerchoiceBcanbeeliminated.Athirdconvenientvalueforxis-1.

ThereisnoneedtoevaluateanswerchoicesA,B,andEat-1sincetheyhavealready

6x'♦.........-...8..x-4a.

beenclimiiialcd.Asshuwn,whenx=-l,but3x-4=-7/-1,soanswer

choiceDcanbeeliminated.Notethat,ifx=-1hadbeenchoseninitially,A,B,D,andE

wouldhavebeeneliminatedimmediatelysince3x2+3x/2-8=62,3x2+3x/2-4=

zx-0x-1

+3/-8x-4T-1-1

2x>l

A-8

1

B短哮-4-4

2

C3x2~4-4-1-i

D3*-4-4-1-7

244

2±-\,3x-4=-7丰-1,and3x+4=1/-I.回_____/The

correctanswerisC.

27、Ifx2+bx+5=(x|内ballnumbersx,wherebandcarepositiveconstants,

⑻而

(C)275

(DI2而

(E)10

whatisthevalueofb?

A、

B、

C、

D、

E、

标准答案：C

知识点解析：Giventhatx2+bx+5=(x+c)2,since(x+c)2=x2+2cx+c2,itfollows

that5=c2andb=2c.ThepossiblevaluesofcareYmd7s,butsincecispositive,c二6

andb=2c=26..ThecorrectanswerisC.

28、LastyearShannonlistenedtoacertainpublicradiostation10hoursperweekand

contributed$35tothestation.Ofthefollowing,whichisclosesttoShannon's

contributionperminuteoflisteningtimelastyear?

A、$0.001

B、$0.010

C、$0.025

D、$0.058

E、$0.067

标准答案：A

知识点解析:Sincethereare52weeksin1yearand60minutesin1hour,10hoursper

weekisequivalentto(10)(52)(60)=31,200minutesperyear.Shannon's35$35

contributionisthen35/31200dollarsperminute,whichisclosestto$0,001perminute.

ThecorrectanswerisA.

29、Eachofthe20employeesatCompanyJistoreceiveancnd-of-ycarbonusthisyear.

Agneswillreceivealargerbonusthananyotheremployee,butonly$500morethan

Cherylwillreceive.NoneoftheemployeeswillreceiveasmallerbonusthanCheryl.If

theamountofmoneytobedistributedinbonusesatCompanyJthisyeartotals$60,000,

whatisthelargestbonusAgnescanreceive?

A、$3,250

B、$3,325

C、$3,400

D、$3,475

E、$3,500

标准答案：D

知识点解析：Sincethetotalamountofthebonusesisfixed,thelargestpossiblebonus

thatAgnescanreceivewilloccurwhenthetotalamountreceivedbythe19employees

otherthanAgnesisthesmallestpossible.LetAbethebonus,indollars,thatAgnes

receives.Then,indollars,Cherylwillreceive(A-500),andeachoftheremaining18

employeeswillreceivebetween(A-500)andA.Therefore,thetotalamountreceivedby

the19employeesotherthanAgnesissmallestwheneachofthese19employeesreceives

(A-500)dollars.19(A-500)+A=60,000totalof20bonusesis$60,00019A-9,500+A=

60,000distributivelaw20A-9,500=60,000combineliketerms20A=69,500add9.500

tobothsidesA=3,475dividebothsidesby20ThecorrectanswerisD.

30、Beth,Naomi,andJuanraisedatotalof$55forcharity.Naomiraised$5lessthan

Juan,andJuanraisedtwiceasmuchasBeth.HowmuchdidBethraise?

A、$9

B、$10

C、$12

D、$13

E、$15

标准答案：C

知识点解析:LetB,N,andJbetheamountsraised,respectivelyandindollars,byBeth,

Naomi,andJuan.B+N+J=55givenN=J-5givenJ=2BgivenJ=55-B-NsubtractB

+NfrombothsidesoffirstequationJ=55-B-(J-5)N=J-52B=55-B-(2B-5)J=2BB=

12solveforBThecorrectanswerisC.

GMAT(QUANTITATIVE)数学练习试

卷第2套

一、单项选择题(本题共30题，每题7.0分，共30

分。)

1、Howmanyhourswerebudgetedforacertainjob?(1)Thenumberofhoursbudgeted

forthejobplustheactualnumberofhoursusedforthejobwas140.(2)Theactual

numberofhoursusedforthejobminusthenumberofhourbudgetedforthejobwas8.

A、Statement(1)ALONEissufficient,butstatement(4)aloneisnotsufficienttoanswer

thequestionasked.

B、Statement(2)ALONEissufficient,butstatement(3)aloneisnotsufficienttoanswer

thequestionasked.

C^BOTHstatement(I)and(4)TOGETHERaresufficienttoanswerthequestion

asked,butNEITHERstatementALONEissufficient.

D、EACHstatementALONEissufficienttoanswerthequestionasked.

E、Statement(1)and(4)TOGETHERareNOTsufficienttoanswerthequestionasked,

andadditionaldataspecifictotheproblemareneeded.

标准答案：C

知识点解析：假设Thenumberofhoursbudgetedforthejob为x,theactualnumber

ofhoursusedforthejob为y,那么得到：单独⑴x+y=140,一个方程两个未知数有

无数解；单独(2)y-x=8,一个方程两个未知数有无数解；把⑴和⑵结合起来考

虑，两个未知数，两个方程，可以求解，所以答案为C。

2、Isthepositiveintegermequaltothecubeofaninteger?(1)Foreveryprimenumber

q,ifqisafactorofm,thenq’isalsoadivisorofm.(2)以isaninteger.

A、Statement(1)ALONEissufficient,butstatement(12)aloneisnotsufficientto

answerthequestionasked.

B、Statement(2)ALONEissufficient,butstatement(11)aloneisnotsufficientto

answerthequestionasked.

C、BOTHstatement(1)and(12)TOGETHERarcsufficienttoanswerthequestion

asked,butNEITHERstatementALONEissufficient.

D、EACHstatementALONEissufficienttoanswerthequestionasked.

E、Statement(1)and(12)T0GETHERareNOTsufficienttoanswerthequestionasked,

andadditionaldataspecifictotheproblemareneeded.

标准答案：B

知识点解析：单独(1),q,q3是m的因子，m不一定是完全立方数，比如m=q4同

样能满足q,q3是m的因子。单独(2),而是整数，满足完全立方数的定义，所以

选择Bo

3、Whatistheunitsdigitofpositiveintegerx?(l)xdividedby9hasaremainderof5.

(2)xdividedby3hasaremainderof2.

A、Statement(1)ALONEissufficient,butstatement(20)aloneisnotsufficientto

answerthequestionasked.

B、Statement(2)ALONEissufficient,butstatement(19)aloneisnotsufficientto

answerthequestionasked.

C、BOTHstatement(1)and(20)TOGETHERarcsufficienttoanswerthequestion

asked,butNEITHERstatementALONEissufficient.

D、EACHstatementALONEissufficienttoanswerthequestionasked.

E>Statement(1)and(20)TOGETHERareNOTsufficienttoanswerthequestionasked,

andadditionaldataspecifictotheproblemareneeded.

标准答案：E

知识点解析：Statement⑴中x=9n+5,随着n的不同，x的个位数也不同，所以单

独(I)无法回答问题。Statement(2)^x=3m+2,随着m的不同,x的个位数也不

同，单独(2)也无法回答问题。把(1)和(2)结合起来，x=9n+5,除以3余2,所以结

合起来的性质仍然等同于(1),无法回答问题，所以E为正确答案。

4、Theaverage(arithmeticmean)ofMconsecutiveoddintegersis10.Whatisthe

smallestnumberinthesequence?(I)ThcrangeoftheMconsecutiveoddintegersis14.

(2)ThegreatestnumberoftheMconsecutiveoddintegersis15.

A、Statement(1)ALONEissufficient,butstatement(28)aloneisnotsufficientto

answerthequestionasked.

Statement(2)ALONEissufficient,butstatement(27)aloneisnotsufficientto

answerthequestionasked.

C、BOTHstatement(1)and(28)TOGETHERaresufficienttoanswerthequestion

asked,butNEITHERstatementALONEissufficient.

D、EACHstatementALONEissufficienttoanswerthequestionasked.

E^Statement(1)and(28iTOGETHERareNOTsufficienttoanswerthequestionasked,

andadditionaldataspecifictotheproblemarcneeded.

标准答案：D

知识点解析：设最小的奇数为ai，M个连续奇数是一个等差数列，公差为2,它们

的平均数为10,那么它们的和为10M,在Statement⑴中,am-ai=14,那么

M=7,知道了和、项数、公差，首项当然可以求得，所以单独(1)可以回答问题。

在Statement⑵中，设am为原数列中最大的奇数,则am=15,那么

S=10M=(ai+15)/215=ai+(M・l)x2从方程组里面能够求得ai，也就是数列中的最小

值，所以单独(2)也可以回答问题。因此D为正确答案。

5、Ifrs=s,whatisthevalueofr+s?(1)r=4(2)5=0

A、Statement(1)ALONEissufficient,butstatemem(36)aloneisnotsufficientto

answerthequestionasked.

Statement(2)ALONEissufficient,butstatement(35)aloneisnotsufficientto

answerthequestionasked.

C、BOTHstatement(1)and(36)TOGETHERaresufficienttoanswerthequestion

asked,butNEITHERstatementALONEissufficient.

D、EACHstatementALONEissufficienttoanswerthequestionasked.

E、Statement(1)and(36)TOGETHERareNOTsufficienttoanswerthequestionasked,

andadditionaldataspecifictotheproblemarcneeded.

标准答案：A

知识点解析：对于Statement(1),r=4,要满足4s=S,s必然为0,可以求得r+s。

对于Statement(2),s=0,那么「可以为任意值，所以r+s不确定，因此答案为A。

6、DoesthelineLpasscuadranlIV?(1)TheslopeofLisnegative.(2)y-inter