math24.docx

math24.docx

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math24MATH.1If25（5x）=1thenx=A.2B.1C.0D.1E.2Answer:

-2ifp,s,andtarepositiveprimenumbers,whatisthevalueofp3s3t3?

（1）p3st=728

（2）t=13Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-3inacertaingameplayedwithredchipsandbluechips,eachredchiphasapointvalueofXandeachbluechiphasapointvalueofY,whereXYandXandYarepositiveintegers.Ifaplayerhas5redchipsand3bluechips,whatistheaverage（arithmeticmean）pointvalueofthe8chipsthattheplayerhas?

（1）Theaveragepointvalueofoneredchipandonebluechipis5.

（2）Theaveragepointvalueofthe8chipsthattheplayerhasisaninteger.-Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-4Ashipmentof8televisionsetscontains2black-and-whitesetsand6colorsets.If2televisionsetsaretobechosenatrandomfromthisshipment,whatistheprobabilitythatatleast1ofthe2setschosenwillbeablack-and-whiteset?

A.1/7B.C.5/14D.11/28E.13/26Answer:

-5ThetensdigitofpositiveintegerXis3.IstheunitsdigitofXgreaterthan4?

（1）Theunitsdigitof2XislessthantheunitsdigitofX.

（2）Thetensdigitof2Xis7.-Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-6|-4|（|-20|-|5|）=A.100B.60C.60D.75E.100Answer-7WhatisthemaximumintegervalueofMforwhich12!

/2Misaninteger?

A.2B.4C.6D.10E.12Answer-8Canacertainrectangularsheetofglassbepositionedonarectangulartabletopsothatitcoverstheentiretabletopanditsedgesareparalleltotheedgesofthetabletop?

（1）Thetabletopis36incheswideby60incheslong.

（2）Theareaofonesideofthesheetofglassis2400squareinches.Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-9Theoperation*representseitheraddition,subtraction,ormultiplicationofintegers,whatisthevalueof1*0?

（1）0*2=2

（2）2*0=2Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-10Ifeachofthe12teamsparticipatinginacertaintournamentplaysexactlyonegamewitheachoftheotherteams,howmanygameswillbeplayed?

A.144B.132C.66D.33E.23Answer-11Anequilateraltrianglethathasanareaof931/2isinscribedinacircle.Whatistheareaofthecircle?

A.6piB.9piC.12piD.9pi31/2E.18pi31/2Answer-12Duringa10-weeksummervacation,wastheaverage（arithmeticmean）numberofbooksthatCarolynreadperweekgreaterthantheaveragenumberofbooksthatJacobreadperweek?

（1）TwicetheaveragenumberofbooksthatCarolynreadperweekwasgreaterthan5lessthantwicetheaveragenumberofbooksthatJacobreadperweek.

（2）Duringthelast5weeksofthevacation,Carolynreadatotalof3booksmorethanJacob.Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-13IfX,Y,andZarepositiveintegers,isYX?

（1）Y2=XZ

（2）Z-X0Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-14OfthefamiliesinCityXin1994,40percentownedapersonalcomputer.ThenumberoffamiliesinCityXowningacomputerin1998was30percentgreaterthanitwasin1994,andthetotalnumberoffamiliesinCityXwas4percentgreaterin1998thanitwasin1994.whatpercentofthefamiliesinCityXownedapersonalcomputerin1998?

A.50%B.52%C.56%D.70%E.74%answer-15Whichofthefollowingexpressionscanbewrittenasaninteger?

（1）（821/2+821/2）2

（2）（82）（821/2）（3）（821/2）（821/2）82A.NoneB.

（1）onlyC.（3）onlyD.

（1）and

（2）E.

（1）and（3）answer-16FromMay1toMay30inthesameyear,thebalanceinacheckingaccountincreased.WhatwasthebalanceinthecheckingaccountonMay30?

（1）If,duringthisperiodoftime,theincreaseinthebalanceinthecheckingaccounthadbeen12percent,thenthebalanceintheaccountonMay30wouldhavebeen$504

（2）Duringthisperiodoftime,theincreaseinthebalanceinthecheckingaccountwas8percent.Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-17IfNispositive,whichofthefollowingisequalto1（n+1）1/2-n1/2A.1B.（2n+1）1/2C.（n+1）1/2n1/2D.（n+1）1/2-n1/2E.（n+1）1/2+n1/2Answer-18Theannualinterestrateearnedbyaninvestmentincreasedby10percentfromlastyeartothisyear.Iftheannualinterestrateearnedbytheinvestmentthisyearwas1percent,whatwastheannualinterestratelastyear?

A.1%B.1.1%C.9.1%D.10%E.10.8%Answer-19ColorXinkiscreatedbyblendingred,blue,green,andyellowinksintheratio6:

5:

2:

2.whatisthenumberoflitersofgreeninkthatwasusedtocreateacertainbatchofcolorXink?

（1）Theamountofredinkusedtocreatethebatchis2litersmorethantheamountofblueinkusedtocreatethebatch.

（2）Thebatchconsistsof30litersofcolorXink.Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-20Ofthe32studentsinacertainclass,15areinamusiccluband20areinadanceclub.If10ofthestudentsarenotineitherclub,howmanyofthestudentsareinonlyoneofthetwoclubs?

A.5B.9C.10D.17E.25Answer-21IfPandRarepositive,is25percentofPequalto10percentofR?

（1）Ris150percentgreaterthanP

（2）Pis60percentlessthanR.Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-22IfX2+Y2=1,isX+Y=1?

（1）XY=0

（2）Y=0Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-23IfAB=A2+B2forallrealnumbersAandB.then（AB）C=A.A2+B2+C2B.2A2+2B2+C2C.A4+B4+C2D.A4+B4+2A2B2+C2Answer-24EachweekJohnearnsXdollarsperhourforthefirst40hoursthatheworksthatweekandYdollarsforeachadditionalhour.HowmuchdoesJohnearnperhourforthefirst40hours?

（1）Y=15X

（2）IfJohnworks45hoursinaweek,heearnsatotalof$570thatweek.Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-25MachineA,operatingaloneatitsconstantrate,produces500feetofaparticularfiberin2hours.MachineB,operatingaloneatitsconstantrate,produces500feetofthesamefiberin3hours.MachineC,operatingaloneatitsconstantrate.Produces500feetofthesamefiberin5hours.HowmanyhourswillittakemachinesA.B,andC,operatingtogetherattheirrespectiveconstantrates,toproduce1000feetofthefiber?

A.60/31B.15/7C.25/11D.10/2E.20/3Answer-26DoesthedecimalequivalentofP/Q,wherePandQarepositiveintegers,containonlyafinitenumberofnonzerodigits?

（1）PQ

（2）Q=8Statement

（1）ALONEissufficient,butstatement

（2）aloneisnotsufficientStatement

（2）ALONEissufficient,butstatement

（1）aloneisnotsufficientBOTHstatementsTOGETHERaresufficient,butNEITHERstatementALONEissufficient.EACHstatementALONEissufficientStatements

（1）and

（2）TOGETHERareNOTsufficientAnswer-27（1/2）（-2）

（2）（-2）A.16B.8C.4D.1/8E.1/16Answer-28Ifk=-1,whichofthefollowingis（are）true?

1.kk=k2.|k|=-k.3.k0=-kA.1onlyB.1and2onlyC.1and3onlyD.2and3onlyE.1.2.and3.Answer-29Atotalof22menand26womenwereataparty,andtheaverage（arithmeticmean）ageofalloftheadultsatthepartywasexactly35years.Iftheaverageageofthemenwas