2023AMC10美国数学竞赛A卷1.Acellphoneplancosts$20eachmonth,plus5¢pertextmessagesent,plus10¢foreachminuteusedover30hours.InJanuaryMichellesent100textmessagesandtalkedfor30.5hours.Howmuchdidshehavetopay?(A)$24.00(B)$24.50(C)$25.50(D)$28.00(E)$30.002.Asmallbottleofshampoocanhold35millilitersofshampoo,Whereasalargebottlecanhold500millilitersofshampoo.Jasminewantstobuytheminimumnumberofsmallbottlesnecessarytocompletelyfillalargebottle.Howmanybottlesmustshebuy?(A)11(B)12(C)13(D)14(E)153.Suppose[ab]denotestheaverageofaandb,and{abc}denotestheaverageofa,b,andc.Whatis{{110}[01]0}?(A)(B)(C)(D)(E)4.LetXandYbethefollowingsumsofarithmeticsequences:X=10+12+14+…+100.Y=12+14+16+…+102.Whatisthevalueof?(A)92(B)98(C)100(D)102(E)1125.Atanelementaryschool,thestudentsinthirdgrade,fourthgrade,andfifthgraderunanaverageof12,15,and10minutesperday,respectively.Therearetwiceasmanythirdgradersasfourthgraders,andtwiceasmanyfourthgradersasfifthgraders.Whatistheaveragenumberofminutesrunperdaybythesestudents?(A)12(B)(C)(D)13(E)146.SetAhas20elements,andsetBhas15elements.WhatisthesmallestpossiblenumberofelementsinA∪B,theunionofAandB?(A)5(B)15(C)20(D)35(E)3007.WhichofthefollowingequationsdoesNOThaveasolution?(A)(B)(C)(D)(E)8.Lastsummer30%ofthebirdslivingonTownLakeweregeese,25%wereswans,10%wereherons,and35%wereducks.Whatpercentofthebirdsthatwerenotswansweregeese?(A)20(B)30(C)40(D)50(E)609.Arectangularregionisboundedbythegraphsoftheequationsy=a,y=-b,x=-c,andx=d,wherea,b,c,anddareallpositivenumbers.Whichofthefollowingrepresentstheareaofthisregion?(A)ac+ad+bc+bd(B)ac–ad+bc–bd(C)ac+ad–bc–bd(D)–ac–ad+bc+bd(E)ac–ad–bc+bd10.Amajorityofthe20studentsinMs.Deameanor’sclassboughtpencilsattheschoolbookstore.Eachofthesestudentsboughtthesamenumberofpencils,andthisnumberwasgreaterthan1.Thecostofapencilincentswasgreaterthanthenumberofpencilseachstudentbought,andthetotalcostofallthepencilswas$17.71.Whatwasthecostofapencilincents?(