2010代数部分1-1

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1、2010AMC8竞赛培训-代数部分（第一讲）数的运算1.(1996AJHSME-4)(A)(B)(C)(D)(E)Key:B2.（2007GAUSS8-18）Thenumbernisdoubledandthenhasyaddedtoit.Theresultisthendividedby2andhastheoriginalnumbernsubtractedfromit.Thefinalresultis(A)n(B)y(C)n+y(D)(E)Key:E3.（2007AMC8-10）Foranypositiveintegern,define□ntobeth

2、esumofthepositivefactorsofn.Forexample,□6=1+2+3+6=12.Find□(□11).(A)13(B)20(C)24(D)28(E)30Key:D4.（2007AMC8-15）Leta,bandcbenumberswith0

3、d78onthefourtests.Jennyscored10pointshigherthanBlakeonthefirsttest,10pointslowerthanhimonthesecondtest,and20pointshigheronboththethirdandfourthtests.WhatisthedifferencebetweenJenny'saverageandBlake'saverageonthesefourtests?(A)10(B)15(C)20(D)25(E)40Key:A整数的性质6.(2003AMC8-19)Howma

4、nyintegersbetween1000and2000haveallthreeofthenumbers15,20and25asfactors?(A)4(B)5(C)6(D)8(E)15Key:C51.(2007GAUSS8-15)Sallypicksfourconsecutivepositiveintegers.Shedivideseachintegerbyfour,andthenaddstheremainderstogether.Thesumoftheremaindersis?(A)6(B)1(C)2(D)3(E)4Key:A2.（2004AMC

5、8-19）Awholenumberlargerthan2leavesaremainderof2whendividedbyeachofthenumbers3,4,5and6.Thesmallestsuchnumberliesbetweenwhichtwonumbers?(A)40and49(B)60and79(C)100and129(D)210and249(E)320and369Key:B3.(2007AMC8-18)Theproductofthetwo99-digitnumbers303,030,303,…,030,303and505,050,505

6、,...,050,505hasthousandsdigitAandunitsdigitB.WhatisthesumofAandB?(A)3(B)5(C)6(D)8(E)10Key:D4.（2002GAUSS8-20）Theunitsdigit(thatis,thelastdigit)ofis?(A)7(B)1(C)3(D)9(E)5Key:D5.（2008GAUSS8-24）Thesumofallofthedigitsoftheintegersfrom98to101is9+8+9+9+1+0+0+1+0+1=38.Thesumofallofthedi

7、gitsoftheintegersfrom1to2008is(A)30054(B)27018(C)28036(D)30036(E)28054Key:E6.（2003GAUSS8-23）Inherbackyardgarden,Gabriellahas12tomatoplantsinarow.Asshewalksalongtherow,shenoticesthateachplantintherowhasonemoretomatothantheplantbefore.Ifshecounts186tomatoesintotal,howmanytomatoes

8、arethereonthelastplantintherow?(A)15(B)16(C)20(D)21(E)