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AMC82016Problem1Thelongestprofessionaltennismatcheverplayedlastedatotalofhoursandminutes.Howmanyminuteswasthis?SolutionProblem2Inrectangle,and.Pointisthemidpointof.Whatistheareaof?SolutionProblem3Fourstudentstakeanexam.Threeoftheirscoresareand.Iftheaverageoftheirfourscoresis,thenwhatistheremainingscore?SolutionProblem4WhenCheenuwasaboyhecouldrunmilesinhoursandminutes.Asanoldmanhecannowwalkmilesinhours.Howmanyminuteslongerdoesittakeforhimtotravelamilenowcomparedtowhenhewasaboy?SolutionProblem5Thenumberisatwo-digitnumber.•Whenisdividedby,theremainderis.•Whenisdividedby,theremainderis.Whatistheremainderwhenisdividedby?SolutionProblem6Thefollowingbargraphrepresentsthelength(inletters)ofthenamesof19people.Whatisthemedianlengthofthesenames?SolutionProblem7Whichofthefollowingnumbersisnotaperfectsquare?SolutionProblem8FindthevalueoftheexpressionSolutionProblem9Whatisthesumofthedistinctprimeintegerdivisorsof?SolutionProblem10SupposethatmeansWhatisthevalueofifSolutionProblem11Determinehowmanytwo-digitnumberssatisfythefollowingproperty:whenthenumberisaddedtothenumberobtainedbyreversingitsdigits,thesumisSolutionProblem12JeffersonMiddleSchoolhasthesamenumberofboysandgirls.Three-fourthsofthegirlsandtwo-thirdsoftheboyswentonafieldtrip.Whatfractionofthestudentsweregirls?SolutionProblem13Twodifferentnumbersarerandomlyselectedfromthesetandmultipliedtogether.Whatistheprobabilitythattheproductis?SolutionProblem14Karl'scarusesagallonofgaseverymiles,andhisgastankholdsgallonswhenitisfull.Oneday,Karlstartedwithafulltankofgas,drovemiles,boughtgallonsofgas,andcontinueddrivingtohisdestination.Whenhearrived,hisgastankwashalffull.HowmanymilesdidKarldrivethatday?SolutionProblem15Whatisthelargestpowerofthatisadivisorof?SolutionProblem16AnnieandBonniearerunninglapsarounda-meterovaltrack.Theystartedtogether,butAnniehaspulledahead,becausesherunsfasterthanBonnie.HowmanylapswillAnniehaverunwhenshefirstpassesBonnie?SolutionProblem17AnATMpasswordatFred'sBankiscomposedoffourdigitsfromto,withrepeateddigitsallowable.Ifnopasswordmaybeginwiththesequencethenhowmanypasswordsarepossible?SolutionProblem18InanAll-Areatrackmeet,sprintersenterameterdashcompetition.Thetrackhaslanes,soonlysprinterscancompeteatatime.Attheendofeachrace,thefivenon-winnersareeliminated,andthewinnerwillcompeteagaininalaterrace.Howmanyracesareneededtodeterminethechampionsprinter?SolutionProblem19Thesumofconsecutiveevenintegersis.Whatisthelargestoftheseconsecutiveintegers?SolutionProblem20Theleastcommonmultipleofandis,andtheleastcommonmultipleofandis.Whatistheleastpossiblevalueoftheleastcommonmultipleofand?SolutionProblem21Aboxcontains3redchipsand2greenchips.Chipsaredrawnrandomly,oneatatimewithoutreplacement,untilall3oftheredsaredrawnoruntilbothgreenchipsaredrawn.Whatistheprobabilitythatthe3redsaredrawn?SolutionProblem22Rectanglebelowisarectanglewith.Whatistheareaofthebatwings(shadedarea)?SolutionProblem23Twocongruentcirclescenteredatpointsandeachpassthroughtheothercircle'scenter.Thelinecontainingbothandisextendedtointersectthecirclesatpointsand.Thecirclesintersectattwopoints,oneofwhichis.Whatisthedegreemeasureof?SolutionProblem24Thedigits,,,,andareeachusedoncetowriteafive-digitnumber.Thethree-digitnumberisdivisibleby,thethree-digitnumberisdivisibleby,andthethree-digitnumberisdivisibleby.Whatis?SolutionProblem25Asemicircleisinscribedinanisoscelestrianglewithbaseandheightsothatthediameterofthesemicircleiscontainedinthebaseofthetriangleasshown.Whatistheradiusofthesemicircle?