MAT GRAND PRIX

Rev your brainsfeel the heat... Circuit#1

Time:30minsDate:10.08.10

1)Youareonanislandandtherearethreecratesoffruitthathavewashedupinfrontofyou.Onecratecontainsonlyapples.Onecratecontainsonlyoranges.Theothercratecontainsbothapplesandoranges.Eachcrateislabelled.Onereads"apples",onereads"oranges",andonereads"applesandoranges".YouknowthatNONEofthecrateshavebeenlabelledcorrectlytheyareallwrong.Ifyoucanonlytakeoutandlookatjustoneofthepiecesoffruitfromjustoneofthecrates,howcanyoulabelALLofthecratescorrectly?2)Barbarahasboxesinthreesizes:large,standard,andsmall.Sheputs11largeboxesonatable.Sheleavessomeoftheseboxesempty,andinalltheotherboxessheputs8standardboxes.Sheleavessomeofthesestandardboxesempty,andinalltheotherstandardboxessheputs8(empty)smallboxes.Now,102ofalltheboxesonthetableareempty.HowmanyboxeshasBarbarausedintotal?3)Twofriends,AlexandBob,gotoabookshop,togetherwiththeirsonsPeterandTim.Allfourofthembuysomebooks;eachbookcostsawholeamountinshillings.Whentheyleavethebookshop,theynoticethatbothfathershavespent21shillingsmorethantheirrespectivesons.Moreover,eachofthempaidperbookthesameamountofshillingsasbooksthathebought.ThedifferencebetweenthenumberofbooksofAlexandPeterisfive.Howmanybooksdideachpersonbuy?4)Jackandhiswifewenttoapartywherefourothermarriedcoupleswerepresent.Everypersonshookhandswitheveryoneheorshewasnotacquaintedwith.Whenthehandshakingwasover,Jackaskedeveryone,includinghisownwife,howmanyhandstheyshook.Tohissurprise,Jackgotninedifferentanswers.HowmanyhandsdidJack'swifeshake?5)ThelegendarykingMidaspossessedahugeamountofgold.Hehidthistreasurecarefully:inabuildingconsistingofanumberofrooms.Ineachroomtherewereanumberofboxes;thisnumberwasequaltothenumberofroomsinthebuilding.Eachboxcontainedanumberofgoldencoinsthatequalledthenumberofboxesperroom.Whenthekingdied,oneboxwasgiventotheroyalbarber.Theremainderofthecoinshadtobedividedfairlybetweenhissixsons.Isafairdivisionpossibleinallsituations?6)EightexecutivesJ,K,L,M,N,O,P,andQaresittingaroundacirculartableforameeting.JissecondtotherightofPwhoisthirdtotherightofK.MissecondtotheleftofOwhositsbetweenPandJ,LisnotaneighbourofKorN.Whichofthefollowinggroupsofpersonshavethefirstpersonsittingbetweentheothertwo?(1)PJO (2)OPJ (3)OPM(4)MPO(5)Noneofthese7)Givenarectangular(cuboidalforthepuritans)cakewitharectangularpieceremoved(anysizeororientation),howwouldyoucuttheremainderofthecakeintotwoequalhalveswithonestraightcutofaknife?

8)FourfriendsArjan,Bhuvan,GuranandLakhawerecomparingthenumberofsheepthattheyowned.ItwasfoundthatGuranhadtenmoresheepthanLakha.IfArjangaveonethirdtoBhuvan,andBhuvangaveaquarterofwhathethenheldtoGuran,whothenpassedonafifthofhisholdingtoLakha,theywouldallhaveanequalnumberofsheep.Howmanysheepdideachofthempossess?Givetheminimalpossibleanswer9)WhenIwasmarried10yearsbackmywifewasthesixthmemberofmyfamily.TodaymyfatherdiedandIhadanewbaby.NowtheaverageageofmyfamilyisthesameasthatwhenIwasmarried.Findtheageofmyfatherwhenhedied.10)Therearetwolengthsofrope.Eachonecanburninexactlyonehour.Theyarenotnecessarilyofthesamelengthorwidthaseachother.Theyalsoarenotofuniformwidth(maybewiderinmiddlethanontheend),thusburninghalfoftheropeisnotnecessarily1/2hour.Byburningtheropes,howdoyoumeasureexactly45minutesworthoftime?11)Grassinlawngrowsequallythickandinauniformrate.Ittakes24daysfor70cowsand60daysfor30cowstoeatthewholeofthegrass.Howmanycowsareneededtoeatthegrassin96days?12)Completetheseries:0,6,24,60,120,210,___,___13)Thereisafivedigitnumber.The4thdigitisfourgreaterthan2nddigit,while3rddigitis3lessthan2nddigit.Thefirstoneisthricethelastdigit.Therearethreepairswhosesumis11.Findthenumber.

15)Thereisaescalatorand2personsmovedownit.Atakes50stepsandBtakes75stepswhiletheescalatorismovingdown.GiventhatthetimetakenbyAtotake1stepisequaltotimetakenbyBtotake3steps.Findtheno.ofstepsintheescalatorwhileitisstationary.?

16)Somepeoplewentforavacation.Unfortunatelyitrainedfor13dayswhentheywerethere.Butwheneveritrainedinthemorning,theyhadcleanafternoonandviceversa.Inalltheyenjoyed11morningand12afternoons.Howmanydaysdidtheystaytheretotally?

17)Twopipescan filla tank in10and12hours respectivelywhile thirdpipewillmake the tankempty in20hours.Ifallthreepipesoperatesimultaneously,inhowmanyhoursthetankwillbefilled?18)Atadinnerpartyeverytwoguestsusedadishofricebetweenthem.Everythreeguestsusedadishofdhalbetweenthemandeveryfourusedadishofmeatbetweenthem.Therewerealtogether65dishes.Howmanyguestswerepresent?19)Threebanditsdivided somebullets equally among themselves.After allof them shot4bullets the totalnumberofbulletsremainingwasequaltothebulletseachhadafterdivision.Findtheoriginalnumberdivided20)Twoseriesare16,21,26,..and17,21,25,Whatisthesumoffirst100commonnumbers?

a.101100 b.110100 c.101110 d.110101

14)BigJim,engineeroftheOvalExpresssays:"Weblewoffacylinderheadanhourafterhavingthestationandhadtocontinuethetripatthreefifthsoftheformerspeed,whichbroughtusintwohourslate.Iftheaccidenthadoccurredfiftymilesfartheron,thetrainwouldhavearrivedfortyminutessooner".Howlongwastherunbetweenstations?