2001年美国数学竞赛-AMC_12

美国数学AMC竞赛历届试卷

20011ThesumoftwonumbersisS.Suppose3isaddedtoeachnumberandtheneachoftheresultingnumbersisdoubled.Whatisthesumofthe naltwonumbers?

(A)2S+3(B)3S+2(C)3S+6(D)2S+6(E)2S+122LetP(n)andS(n)denotetheproductandthesum,respectively,ofthedigitsoftheintegern.Forexample,P(23)=6andS(23)=5.SupposeNisatwo-digitnumbersuchthatN=P(N)+S(N).WhatistheunitsdigitofN?

(A)2(B)3(C)6(D)8(E)93ThestateincometaxwhereKristinlivesisleviedattherateofp%ofthe rst$28000ofannualincomeplus(p+2)%ofanyamountabove$28000.Kristinnoticedthatthestateincometaxshepaidamountedto(p+0.25)%ofherannualincome.Whatwasherannualincome?

(A)$28000(B)$32000(C)$35000(D)$42000(E)$560004Themeanofthreenumbersis10morethantheleastofthenumbersand15lessthanthegreatest.Themedianofthethreenumbersis5.Whatistheirsum?

(A)5(B)20(C)25(D)30(E)365Whatistheproductofalloddpositiveintegerslessthan10000?

(A)10000!

(5000!)(B)10000!

2(C)9999!

2(D)10000!

2·5000!(E)5000!

26AtelephonenumberhastheformABC DEF GHIJ,whereeachletterrepresentsadi erentdigit.Thedigitsineachpartofthenumbersareindecreasingorder;thatis,A>B>C,D>E>F,andG>H>I>J.Furthermore,D,E,andFareconsecutiveevendigits;G,H,I,andJareconsecutiveodddigits;andA+B+C=9.FindA.

(A)4(B)5(C)6(D)7(E)87Acharitysells140bene tticketsforatotalof$2001.Someticketssellforfullprice(awholedollaramount),andtherestsellsforhalfprice.Howmuchmoneyisraisedbythefull-pricetickets?

(A)$782(B)$986(C)$1158(D)$1219(E)$14498Whichoftheconescanbeformedfroma252 sectorofacircleofradius10byaligningthetwostraightsides?

(A)Aconewithslantheightof10andradius6(B)Aconewithheightof10andradius6

(C)Aconewithslantheightof10andradius7(D)Aconewithheightof10andradius7(E)Aconewithslantheightof10andradius8This lewasdownloadedfromtheAoPS MathLinksMathOlympiadResourcesPagedoc.guandang.net