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QUANTQUIZONL.C.MandH.C.F1.Aboutthenumberofpairswhichhave16astheirHCFand136astheirLCM,theconclusioncanbea.onlyonesuchpairexistsb.onlytwosuchpairsexistc.manythreepairsexistd.manysuchpairsexiste.nosuchpairexists

2.TheHCFoftwonumbersis12andtheirdifferenceisalso12.Thenumbersarea.66,78b.94,106c.70,82d.84,96e.50.62

3.TheHCFoftwonumbersis16andtheirLCMis160.Ifoneofthenumbersis32,thentheothernumberisa.48b.80c.96d.112e.108

4.HCFofthreenumbersis12.Iftheyareintheratio1:2:3,thenthenumbersarea.12,24,36b.10,20,30c.5,10,15d.4,8,12e.15,30,45

5.Sixbellscommencetollingtogetherandtollatintervalsof2,4,6,8,10and12secondsrespectively.In30minutes,howmanytimesdotheytolltogether?a.4b.10c.15d.16e.18

6.Thelargestnaturalnumberwhichexactlydividestheproductofanyfourconsecutivenaturalnumbersis:a.6b.12c.24d.120e.150

7.Thetrafficlightsatthreedifferentroadcrossingchangeafterevery48sec72secand108sec.,respectively.Iftheyallchangesimultaneouslyat8:20:00hrs,thentheywillagainchangesimultaneouslyata.8:27:12Hrsb.8:27:24Hrsc.8:27:36Hrsd.8:27:48Hrse.8:27:53Hrs

8.Thegreatestnumberbywhichif1657and2037aredividedtheremainderswillbe6and5respectivelyisa.127b.235c.260d.305e.310

9.Thetotalnumberofprimefactorsoftheproduct(8)20(15)24(7)15isa.59b.98c.123d.4e.14

10.TheHCFandLCMoftwonumbersare44and264respectively.Ifthefirstnumberisdivisibleby3,thenthefirstnumberis

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firstnumberisdivisibleby3,thenthefirstnumberisa.264b.132c.Bothaandbd.33e.36

11.Whatleastnumbermustbesubtractedfrom1294sothattheremainderwhendivided9,11,13willleaveineachcasethesameremainder6?a.0b.1c.2d.3e.4

12.Theleastnumberwhichisdivisibleby12,15,20andisaperfectsquare,isa.400b.900c.1600d.3600e.4200

13.Theleastperfectsquarenumberwhichisdivisibleby3,4,5,6and8isa.900b.1200c.2500d.3600e.1500

14.Threepieceoftimber42m,49mand63mlonghavetobedividedintoplanksofthesamelength.Whatisthegreatestpossiblelengthofeachplank?a.7mb.14mc.42md.63me.78

15.Thegreatestnumberwhichcandivide1354,1866,2762leavingthesameremainder10ineachcaseis:a.64b.124c.156d.260e.280

Answers1.eHCFisalwaysafactorofLCM.ie.,HCFalwaysdividesLCMperfectly.

2.dThedifferenceofrequirednumbersmustbe12andeverynumbermustbedivisibleby12.Therefore,theyare84,96.

3.bThenumber=HCFLCMGivennumber=1616032=80

4.ALetthenumbersbea,2aand3a.Then,theirHCF=asoa=12Thenumbersare12,24,36

5.dLCMof2,4,6,8,10and12is120.So,thebellswilltollsimultaneouslyafter120seconds.i.e.2minutes.In30minutes,they(302+1)tolltimesie.16times.

6.CTherequirednumbercanbefindoutbyfollowingway.1234=24

7.(A)Thechangeofinterval=(LCMof48,72,108)sec.=432.So,forevery432secondsi.e.7min.12sec.thelightswillchange.Soadd7min.12sec.to8:20:00Hrs.i.e.8:27:12Hrs.

8.ATheneedednumberisHCFof(16576)and(20375)=HCFof1651&2032=127.

9.DTheprimenumbersare2,3,5,17intheexpression.Theexpressioncanbewrittenas(23)20(35)24(17)152603245241715Sonumberofprimefactorsare4.i.e.,2,3,5,17

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10.CLetthenumbersareah,bhrespectively.HerehisHCFoftwonumbers.(obviouslya,barecoprimesi.e.,HCF(a,b)=1)GiventhatHCF=h=44andLCM=abh=264DividingLCMbyHCFwegetab=6.abcanbewrittenas1x6,2x3,3x2,6x1.Butgiventhatthefirstnumberisdivisibleby3.SoonlytwooptionspossibleforA.3x44,6x44.SooptionCiscorrect

11.BLCMof9,11,13is1287.Dividing1294with1287,theremainderwillbe7,togetremainder6,1istobedeductedfrom1294sothat1293whendividedby9,11,13leaves6asremainder.

12.bLCM=5322=60Tomakethisnumberasaperfectsquare,wehavetomultiplythisnumberby53Thenumberis6015=90013.DLCM=22235=2335Buttheleastperfectsquareis=2335(235)=243252=3600astheperfectsquareshavetheirpowerseven.

14.AThemaximumpossiblelength=(HCFof42,49,63)=7

15.A

Theneedednumber=HCFof1344,1856and2752=64

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