GMAT（QUANTITATIVE）數(shù)學(xué)練習(xí)試卷3（共238題）

GMAT（QUANTITATIVE）數(shù)學(xué)練習(xí)試

卷3（共9套）

（共238題）

GMAT（QUANTITATIVE）數(shù)學(xué)練習(xí)試

卷第1套

一、單項選擇題（本題共30題，每題1.0分，共30

分。）

1、Thetableshowsthenumberofpeoplewhoresponded

"yes"or"no"or"don'tknow"whenaskedwhethertheircitycouncilshouldimplement

environmentalprogramsXandY.Ifatotalof1,000peoplerespondedtothequestion

aboutbothprograms,whatwasthenumberofpeoplewhodidnotrespond"yes"to

implementingeitherofthetwoprograms?(1)Thenumberofpeoplewhoresponded

"yes"toimplementingonlyProgramXwas300.(2)Thenumberofpeoplewho

responded"no"toimplementingProgramXand"no"toimplementingProgramYwas

100.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

CNBOTHstatementsTOGETHERarcsufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：A

知識點解析：(1)Giventhat300peopleresponded"yes"toimplementingonlyProgram

X,andbecause400peoplealtogetherresponded"yes"toimplementingProgramX,it

followsthat400-300=100peopleresponded"yes"toimplementingbothProgramX

andProgramY.Therefore,because300peoplealtogetherresponded"yes"to

implementingProgramY,300-100=200peopleresponded"yes"toimplementingonly

.16—?

ProgramY.TheseresultsareshownintheVenndiagrambelow.4SincetheVenn

diagramaboverepresentsatotalof1,000people,itfollowsthatthenumberofpeople

whodidnotrespond"yes"toimplementingeitherProgramXorProgramYis1,000-

(300+100+200)=400;SUFFICIENT.(2)Giventhat100peopleresponded"no"both

toimplementingProgramXandtoimplementingProgramY,thetablebelowshowsa

possibilitywherebythenumberofpeoplewhodidnotrespond"yes"toimplementing

eitherProgramXorProgramYcouldbe400.Notethatforeachofthecolumnheadings

"Yes,""No,"and"Don'tKnow,"thenumbersunderthatcolumnheadingsatisfy(X

answered)+(Yanswered)-(bothanswered)+(neitheranswered)=1,000.Indeed,fbr

eachofthesethreecolumnsaVenndiagramcanbegiventhatrepresentsthenumbersin

Therefore,amongotherpossibilities,thenumberofpeoplewhodidnotrespond"yes"to

implementingeitherProgramXorProgramYcouldbe400,andthisnumbercouldalso

be500;NOTsufficient.ThecorrectanswerisA;statement1aloneissufficient.

2、Anestimateofanactualdatavaluehasanerrorofppercentifp=100|e-a|/a,wheree

istheestimatedvalueandaistheactualvalue.Emma'sestimatefbrhertotalincomelast

yearhadanerroroflessthan20percent.Emma'sestimateofherincomefromtutoring

lastyearalsohadanerroroflessthan20percent.WasEmma'sactualincomefrom

tutoringlastyearatmost45percentofheractualtotalincomelastyear?(1)Emma's

estimatedincomelastyearfromtutoringwas30percentofherestimatedtotalincome

lastyear.(2)Emma'sestimatedtotalincomelastyearwas$40,000.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

C、BOTHstatementsTOGETHERarcsufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：A

知識點解析：GiventhatEmma'sestimatesfbrbothhertotalincomeandherincome

fromtutoringlastyear,E]andET,respectively,werewithin20percentofheractualtotal

incomeandheractualincomefromtutoring,AjandAT,respectively,itfollowsthat

0.8Ej<Aj<1.2Eiand0.8ET<AT<1.2E「DeterminewhetherEmma'sactualincome

fromtutoringwasatmost45percentofheractualtotalincomeorifAT/AI<0,45.(1)

GiventhatET=0.3Ebitfollowsfrom0.8ETT<1.2ETthat0.24Ei<Ai<0.36E1.Then,

1-1,1

sinceO.8E1<Ai<1.2Eiitfollowsthat4Multiplyingtheinequalities

02g<±L<0.36—

gives(。.犯cr0.2<AT/AI<0.45；SUFFICIENT.⑵GiventhatEmma's

estimatedtotalincomelastyearwas$40,000,itisimpossibletodeterminewhetherher

actualincomefromtutoringwasatmost45percentofheractualtotalincomebecauseno

informationisgivenaboutheractualincomefromtutoringotherthanitwaswithin20

percentofherestimatedincomefromtutoring.Andthereisnoinformationfromwhich

herestimatedincomefromtutoringcanbedetermined;NOTsufficient.Thecorrect

answerisA;statement1aloneissufficient.

3、WasStoreK'sprofitlastmonthatleast10percentgreaterthanitsprofittheprevious

month?(1)StoreK'sexpenseslastmonthwere5percentgreaterthanitsexpensesthe

previousmonth.(2)StoreK'srevenueslastmonthwere10percentgreaterthanits

revenuesthepreviousmonth.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：C

知識點解析：LetPiast,Elast,andR|astbe,respectively,theprofit,expenses,andrevenues

forlastmonth.Also,letPpreviousEprevious,andRpreviousbe,respectively,theprofit,

expenses,andrevenuesfbrthepreviousmonth.ThenwehavePiast=Riast-Eiastana

=

PpreviousRprevious-Epre\ious.DeterminewhetherP|as(>LIPpreviousistrue,or

equivalently,determinewhetherRiast-Elast^llRprevious-1?1Epreviousistrue.(1)Giventhat

Elast=105Eprevious,itfollowsthattheinequalityRiast?ElastN1.1Rprevious1?1Rpreviousis

equivalenttoRiast-1.1Rprevious^-0.05EprCvious,Itisclearthat,forsuitableValuesof

RlasuRprevious,andEprevious，thislastinequalitycouldbetrucandthislastinequality

couldbefalse;NOTsufficient.(2)GiventhatR|ast=1JRprevious，itfollowsthatthe

inequalityRiast-Elast>1.1^previous-EpreviousisequivalenttoEjastS1.1Eprevious*Itis

clearthat,fbrsuitablevaluesofE|astandEprevious,thislastinequalitycouldbetrucand

thislastinequalitycouldbefalse;NOTsufficient.Taking(1)and(2)together,the

followingshowsthatPlasl^l.lPprcviousistrue.Pprcvious=Rlast-Elast=1.1Rprevious-

certainrange)linekintersectsanotherline(thex-axis),Althoughalinewithonlyasingle

x-interceptwouldnotbehorizontal,thelinekcouldhaveanynon-horizontalslope.

Likewiseinthecaseofline1.Forexample,theslopeofkcouldbepositiveandtheslope

of1negative,orviceversa;NOTsufficient.(2)GiventhatkandIintersectonthe

positivey-axis,wecannotdeterminewhethertheslopeofkislessthantheslopeof1.The

pointhereisthesameasthepointwithstatement1.Withstatement2,wehaveonlybeen

given,foreachoflineskand1,aconditiononwherethetwolinesintersect.And,given

onlythatalinepassesthroughaparticularpoint(andregardlessofwhetheranotherline

happenstopassthroughthispoint),thelinecouldhaveanyslope.Forexample,again,

theslopeofkcouldbepositiveandtheslopeof1negative,orviceversa;NOTsufficient.

Consideringstatements1and2together,wehave,loreachoflineskand1,acondition

ontwoofthepointsthat(helinepassesthrough.Asillustratedinthediagram,thetwo

conditionstogetheraresufficientfordeterminingtherelationshipinquestion.

negativex-axisandthepositivey-axis,itsslopemustbeupward(positive).Theslopeof

kisthereforelessthantheslopeof1.ThecorrectanswerisC;bothstatementstogether

aresufficient.

6、Isnlessthan1?(1)nislessthan0.01percentof10,000.(2)nislessthan0.1percent

of1,200.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and⑵TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：A

知識點解析：Determinewhethernislessthan1.(1)Giventhatnislessthan0.01%of

10,000,itfollowsthatn<0.0001(10,000)orn<1;SUFFICIENT.(2)Giventhatnisless

than0.1%of1,200,itfollowsthatn<0.001(1,200)orn<1.2,soncouldbe0,inwhich

casen<l.Ontheotherhand,ncouldbe1.1,inwhichcasen>1;NOTsufficient.The

correctanswerisA;statement1aloneissufficient.

7、Grossprofitisequaltosellingpriceminuscost.Acardealer'sgrossprofitonthesale

ofacertaincarwaswhatpercentofthecostofthecar?(1)Thesellingpriceofthecar

was11/10ofthecostofthecar.(2)Thecostofthecarwas$14,500.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：A

知識點解析：

Determinethegrossprofit,P,onthesaleofacarasape。r9centofthecost,

11cp.11c■c工I.c

C,ofthecar.(1)Giventhatthesellingpriceofthecarwasio"*io-"ioThus,the

profitwas10%ofthecostofthecar;SUFFICIENT.⑵Giventhatthecostofthecar

was$14,500,itisimpossibletodeterminetheprofitbecausethesellingpriceisnot

knownnoristhereenoughinformationtodetermineit;NOTsufficient.Thecorrect

answerisA;statementIaloneissufficient.

8、Whenthewindspeedis9milesperhour,thewind-chillfactorwisgivenbyw=-

17.366+119f,wheretisrhetemperatureindegreesFahrenheit.Ifatnoonyesterdaythe

windspeedwas9milesperhour,wasthewind-chillfactorgreaterthan0?(1)The

temperatureatnoonyesterdaywasgreaterthan10degreesFahrenheit.(2)The

temperatureatnoonyesterdaywaslessthan20degreesFahrenheit.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and(2)TOGETHERarcNOTsufficient.

標(biāo)準(zhǔn)答案：E

知識點解析:Determinewhether-17.366+1.19tisgreaterthan0.(1)Giventhatt>10,

itfollowsthat-17.366+7.366+1.19(10),or-17.366+1.19t>-5.466.However,

itisnotpossibletodeterminewhether-17.366+1.19tisgreaterthan0.Forexample,ift

=19,then-17.366+I.19t=5.244isgreaterthan0.However,ift=11,then-17.366+

l.l9t=-4.276,whichisnotgreaterthan0;NOTsufficient.(2)Giventhatt<20,the

sameexamplesusedin(1)showthatitisnotpossibletodeterminewhether-17.366+

I.19tisgreaterthan0;NOTsufficient.Taking(1)and(2)togetherisofnomorehelp

thaneither(1)or(2)takenseparatelybecausethesameexampleswereusedinboth(1)

and(2).ThecorrectanswerisE;bothstatementstogetherarestillnotsufficient.

____B

Ar

9、'Whatisthevolumeofthecubeabove?(I)10^3surfaceareaofthe

cubeis600squareinches.(2)ThelengthofdiagonalABis10inches.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(I)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(I)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：D

知識點解析：Thisproblemcanbesolvedbydeterminingthesidelength,s,ofthecube.

(1)Thisindicatesthat6s-=600,fromwhichitfollowsthats2=100ands=10;

SUFFICIENT.(2)TodeterminediagonalAB,firstdeterminediagonalANbyapplying

thePythagoreantheoremtoAAMN:AN==曰.NowdetermineABbyapplying

thePythagoreantheoremtoAANB:AB=曲而不而F=+，=用=訴Itisgiventhat

AB=iM.,andsos=10;SUFFICIENT,ThecorrectanswerisD;

eachstatementaloneissufficient.

10、Inthefigureshown,quadrilateralABCDisinscribedinacircleof

radius5.WhatistheperimeterofquadrilateralABCD?(1)ThelengthofABis6andthe

lengthofCDis8.(2)ACisadiameterofthecircle.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(I)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：C

知識點解析：DeterminetheperimeterofquadrilateralABCD,whichisgivenbyAB+

BC+CD+DA.(I)ThisindicatesthatAB=6andCD=8,butgivesnoinformationabout

BCorDA.Forexample,theperimeterofABC1D1isclearly

differentthantheperimeterofABC2D2andCDcouldbepositionedwhereG。isonthe

diagramoritcouldbepositionedwhereG0isonthediagram;NOTsufficient.(2)This

indicatesthatAC=2(5)=10sinceACisadiameterofthecircleandtheradiusofthe

circleis5.ItalsoindicatesthatZ.ABCandZ.ADCarerightanglessinceeachisinscribed

inasemicircle.However,thereisnoinformationaboutAB,BC,CD,orDA.For

example,ifAB=CD=6,thenBC=DA=jio*-?>,=8andtheperimeterofABCDis

2(6+8)=28.However,ifAB=DA=2,thenBC=CD=而口7"/andtheperimeter

ofABCD=2(2+屈)；NOTsufficient.Taking(1)and(2)together,AABCisaright

trianglewithAC=10andAB=6.ItfollowsfromthePythagoreantheoremthatBC=

J10'二6：=4M=8.Likewise,AADCisarighttrianglewithAC=10andCD=8.It

followsfromthePythagoreantheoremthatDA=河*=欣=6.Thus,theperimeierof

quadrilateralABCDcanbedetermined.ThecorrectanswerisC;bothstatementstogether

aresufficient.

11、Howmanymembersofacertainlegislaturevotedagainstthemeasuretoraisetheir

salaries?(I)1/4ofthemembersofthelegislaturedidnotvoteonthemeasure.(2)If5

additionalmembersofthelegislaturehadvotedagainstthemeasure,thenthefractionof

membersofthelegislaturevotingagainstthemeasurewouldhavebeen1/3.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(I)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(I)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：E

知識點解析：Thetaskinthisquestionistodeterminewhether,onthebasisof

statements1and2,itispossibletocalculatethenumberofmembersofthelegislature

whovotedagainstacertainmeasure.(1)Thisstatement,that1/4ofthemembersofthe

legislaturedidnotvoteon(hemeasure,iscompatiblewithanynumberofmembersofthe

legislaturevotingagainstthemeasure.Afterall,anynumberamongthe3/4ofthe

remainingmemberscouldhavevotedagainstthemeasure.Furthermore,basedon

statement1,wedonotknowthenumberofmembersofthelegislature(althoughwedo

know,basedonthisstatement,thatthenumberofmembersofthelegislatureisdivisible

by4);NOTsufficient.(2)Thisstatementdescribesascenario,of5additionalmembers

ofthelegislaturevotingagainstthemeasure,andstipulatesthat1/3ofthemembersofthe

legislaturewouldhavevotedagainstthemeasureinthescenario.Giventhiscondition,

weknowthatthenumberofmembersofthelegislaturewasdivisibleby3,andthatthe

legislaturehadatleast15members(toallowforthe"5additionalmembersofthe

legislature"thatcouldhavevotedagainstthemeasure,foratotalof1/3ofthemembers

votingagainstit).However,beyondthisweknowessentiallynothingfromstatement2.

Inparticular,dependingcnthenumberofmembersofthelegislature(whichwehavenot

beengiven),anynumberofmemberscouldhavevotedagainstthemeasure.Forexample,

exactlyonemembercouldhavevotedagainstthemeasure,inwhichcasethelegislature

wouldhavehad(I+5)x3=18members.Exactlytwomemberscouldhavevotedagainst

themeasure,inwhichcasethelegislaturewouldhavehad(2+5)x3=21members,and

soonfor3membersvotingagainst,4membersvotingagainst,etc.;NOTsufficient.

Consideringthestatements1and2together,thereasoningissimilartothereasoningfor

statement2,butwiththefurtherconditionthatthetotalnumberofmembersofthe

legislatureisdivisibleby12(soastoallowthatbothexactly1/4ofthemembersdidnot

voteonthemeasurewhileexactly1/3couldhavevotedagainstthemeasure).For

example,itcouldhavebeenthecasethatthelegislaturehad24members.Inthiscase,1/3

ofthememberswouldhavebeen8members,and,consistentwithstatements1and2,3

ofthemembers(8-5)couldhavevotedagainstthemeasure.Orthelegislaturecould

havehad36members,inwhichcase,consistentwithstatements1and2,(l/3)(36)-5=

12-5=7memberscouldhavevotedagainstthemeasure.ThecorrectanswerisE;both

statementstogetherarestillnotsufficient.

12、Ify,0,is|x|=1?(1)x=y/|y|(2)|x|=-x

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：A

知識點解析：Canwedeterminewhether|x|=1?(1)Giventhatx=y/|y|,weconsider

twocases:y>0andy<0.Ify>0,then|y|=yandy/|y|=y/|y|=I.Soify>0,thenx=1

and,ofcourse,|x|=1.Ify<0,then|y|=(-1)yandx=y/|y|=y/(-l)y=(-l)(y/y)=(-1)(1)=-

1.So|x|=1.Ify<0,then|x|=1.Inbothofthetwocases,|x|=1;SUFFICIENT.(2)

Giventhat|x|=-x,allweknowisthatxisnotpositive.Forexample,both-4and-5

satisfythisconditiononx|-4|=4=-(-4)and|-5|=5=-(-5);NOTsufficient.Thecorrect

answerisA;statement1aloneissufficient.

13、Ifxisapositiveinteger,whatisthevalueofx?(1)x2=?(2)n/x=nandn找.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：D

知識點解析：(1)Itisgiventhatxisapositiveinteger.Then,x2=?givenx4=x

squarebothsidesx4-x=0subtractxfrombothsidesx(x-l)(x2+x+1)=0factorleft

sideThus,thepositiveintegervalueofxbeingsoughtwillbeasolutionofthisequation.

Onesolutionofthisequationisx=0,whichisnotapositiveinteger.Anothersolutionis

x=1,whichisapositiveinteger.Also,x-+x+1isapositiveintegerforallpositive

integervaluesofx,andsox~+x+1=0hasnopositiveintegersolutions.Thus,theonly

possiblepositiveintegervalueofxis1:SUFFICIENT.(2)Itisgiventhatn#).Then,n/x

=ngivenn=nxmultiplybothsidesbyx1=xdividebothsidesbyn,wheren#0Thus,

x=1;SUFFICIENT.ThecorrectanswerisD;eachstatementaloneissufficient.

14、Isthemedianofthefivenumbersa,b,c,d,andeequaltod?(1)a<c<e(2)b<d

<c

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(I)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(I)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：E

知識點解析：Determineifthemedianofthefivenumbers,a,b,c,d,ande,isequaltod.

(I)Thisindicatesthata<c<e,butdoesnotindicatearelationshipofbanddwitha,c,

ande.Forexample,ifa=5,b=l,c=10,d=7,ande=15.thena<c<e,anddisthe

median.However,ifa=5,b=1,c=10,d=2,ande=15,thena<c<e,anda,notcl,is

themedian;NOTsufficient.(2)Thisindicatesthatb<d<c,butdoesnotindicatea

relationshipofaandewithb,d,andc.Forexample,ifa=5,b=1,c=10,d=7,ande=

15,thenb<d<c,anddisthemedian.However,ifa=5,b=l,c=10,d=2,ande=15,then

b<d<c,anda,notd,isthemedian;NOTsufficieni.Taking(1)and(2)togetherisofno

morehelpthaneither(1)or(2)takenseparatelysincethesameexamplesusedtoshow

that(1)isnotsufficientalsoshowthat(2)isnotsufficient.ThecorrectanswerisE;both

statementstogetherarestillnotsufficient.

15、Duringacertainbicycleride,wasSherry'saveragespeedfasterthan24kilometers

perhour?(1kilometer=1,000meters)(1)Sherry'saveragespeedduringthebicycleride

wasfasterthan7meterspersecond.(2)Sherry'saveragespeedduringthebicycleride

wasslowerthan8meterspersecond.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B>Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E^Statements(1)and(2)TOGETHERarcNOTsufficient.

標(biāo)準(zhǔn)答案：A

知識點解析:Thisproblemcanbesolvedbyconverting24kilometersperhourinto

meterspersecond.First,24kilometersisequivalentto24,000metersand1houris

equivalentto3,600seconds.Then,traveling24kilometersin1hourisequivalentto

6-

traveling24,000metersin3,600seconds,or24000/3600=3meterspersecond.(l)This

indicatesthatSherry'saveragespeedwasfosterthan7meterspersecond,whichisfaster

2

than63meterspersecondand,therefore,fasterthan24kilometersperhour;

SUFFICIENT.(2)ThisindicatesthatSherry'saveragespeedwasslowerthan8meters

persecond.Heraveragespeedcouldhavebeen7meterspersecond(since7<8),in

2

whichcaseheraveragespeedwasfasterthan63meterspersecondand,therefore,faster

than24kilometersperhour.Orheraveragespeedcouldhavebeen5meterspersecond

2

(since5<8),inwhichcaseheraveragespeedwasnotfasterthan63meterspersecond

and,therefore,notfasterthan24kilometersperhour;NOTsufficient.Thecorrectanswer

isA;statement1aloneissufficient.

16、Workingtogether,RafaelandSalvadorcantabulateincertainsetofdatain2hours.

InhowmanyhourscanRafaeltabulatethedataworkingalone?(1)Workingalone,

Rafaelcantabulatethedatain3hourslesstimethanSalvador,workingalone,can

tabulatethedata.(2)Workingalone,Rafaelcantabulatethedatain1/2thetimethat

Salvador,workingalone,cantabulatethedata.

A、Statement(1)ALONEissufficient,butstatement(2)aloneisnotsufficient.

B、Statement(2)ALONEissufficient,butstatement(1)aloneisnotsufficient.

C、BOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEis

sufficient.

D、EACHstatementALONEissufficient.

E、Statements(1)and(2)TOGETHERareNOTsufficient.

標(biāo)準(zhǔn)答案：D

知識點解析：WearegiventhatRafaelandSalvador,workinglogeiher,cantabulatethe

setofdataintwohours.Thatis,ifRafaeltabulatesdataaltherateofRunitsofdataper

hourandSalvadortabulatesthedataattherateofSunitsperhour,then,iftheseiofdata

ismadeupofDunits,then2R+2S=D.Canwedeterminehowmuchtime,inhours,it

takesRafaeltotabulatethedataifworkingalone?(1)Firstofall,notethatthechoiceof

unitsusedtomeasuretheamountsofdatadoesn'tmatter.Inparticular,wecandefineone

uritofdatatobeD.Thus,2R+2S=1.Withthisinmird,considertheconditionthat

Rafael,whenworkingalone,cantabulatethedatain3hourslesstimethanSalvadorean

whenworkingalone.GiventhatRafaeltabulatesRunitsofdataperunittime,hetakes

1/Runitsoftimetotabulateoneunitofdata.Similarly.Salvadortakes1/Sunitsoftime

totabulateoneunitofdata.Thisunit,asdefined,issimplytheentiresetofdata.Our

givenconditionthusbecomes1/R=1/S,andwehavethesetofsimultaneousequations

madeupofthisequationandtheequation2R+2S=1.Onewaytodeterminethenumber

ofhoursitwouldtakeRafaeltotabulatethedataistosolveoneoftheseequationsforS

andthensubstitutethissolutionintotheotherequation.Consideringthefirstofthese

equations,wemultiplybothsidesbyRSandthenmanipulatetheresultasfollows.S=R

-3RSS+3RS=RS(1+3R)=RS=R/(1+3R)Substitutingintotheequation2R+2S=1,

2R+2R/(1+3R)=1Multiplyingbothsidesby1+3Rtoeliminatethefraction,2R(1+

3R)+2R=1+3R2R+6R2=1+R6R2+R-1=0(3R-l)(2R+1)=0Thisequationhas

twosolutions,-l/2and1/3.However,becausetherateRcannotbenegative,wefindthat

Rafaeltabulates1/3ofaunitofdataeveryhour.Sinceoneunitistheentireset,ittakes

Rafael3hourstotabulatetheentireset;SUFFICIENT.(2)WearegiventhatRafael,

workingalone,cantabulatethedatain1/2theamountoftimeittakesSalvador,working

alone,totabulatethedata.Asinthediscussionofstatement1,wehavethatRafael

tabulatesRunitsofdataeveryhour,andtakes1/Rhourstotabulateoneunitofdata.

Similarly,ittakesSalvador1/Shourstotabulateoneunitofdata.Oneunitofdatahas

beendefinedtobethesizeoftheentiresettobetabulated,sostatement2becomesthe

expressionR/l=1/2x|/S=1/2SWcthushave2S=R.Substitutingthisvaluefor2Sin

theequation2R+2S=I,wehaveR+2R=1,and3R=I.SolvingforRweget1/3;

SUFFICIENT.Notethat,forbothstatements1and2,itwouldhavebeenpossibletoslop

calculatingoncewehaddeterminedwhetheritwaspossibl