USAAMC820061 Mindymadethreepurchasesfor$1.98, $5.04and$9.89.
Whatwashertotal, tothenearestdollar?(A)$10 (B)$15 (C)$16 (D)$17
(E)$182 OntheAMC8contestBillyanswers13questionscorrectly,
answers7questionsincorrectlyanddoesntanswerthelast5.
Whatishisscore?(A)1 (B)6 (C)13 (D)19 (E)263
Elisaswimslapsinthepool. Whensherststarted,
shecompleted10lapsin25minutes.Nowshecannish12lapsin24minutes.
Byhowmanyminuteshassheimprovedherlaptime?(A)12(B)34(C)1 (D)2 (E)34
Initially,a spinner points west. Chenille moves it clockwise
214revolutions and then counter-clockwise334revolutions.
Inwhatdirectiondoesthespinnerpointafterthetwomoves?NW ES(A)north
(B)east (C)south (D)west (E)northwest5 Points A, B, Cand Dare
midpoints of the sides of the larger square. If the larger square
hasarea60,whatistheareaofthesmallersquare?ABCDhttp://www.artofproblemsolving.com/ThislewasdownloadedfromtheAoPSMathOlympiadResourcesPage
Page1USAAMC82006(A)15 (B)20 (C)24 (D)30 (E)406
TheletterTisformedbyplacingtwo2 4inchrectanglesnexttoeachother,
asshown.WhatistheperimeteroftheT,ininches?(A)12 (B)16 (C)20 (D)22
(E)247 CircleXhasaradiusof. CircleY hasacircumferenceof8.
CircleZhasanareaof9.Listthecirclesinorderfromsmallesttolargestradius.(A)X,
Y, Z (B)Z, X, Y (C)Y, X, Z (D)Z, Y, X (E)X, Z, Y8
ThetableshowssomeoftheresultsofasurveybyradiostationKAMC.Whatpercentageofthemalessurveyedlistentothestation?Listen
DontListen TotalMales ? 26 ?Females 58 ? 96Total 136 64 200(A)39
(B)48 (C)52 (D)55 (E)759 Whatistheproductof32 43 54 20062005?(A)1
(B)1002 (C)1003 (D)2005 (E)200610
Jorgesteacheraskshimtoplotalltheorderedpairs(w,
l)ofpositiveintegersforwhichwisthewidthandlisthelengthofarectanglewitharea12.
Whatshouldhisgraphlooklike?(A)http://www.artofproblemsolving.com/ThislewasdownloadedfromtheAoPSMathOlympiadResourcesPage
Page2USAAMC82006lw(B)lw(C)lw(D)lwhttp://www.artofproblemsolving.com/ThislewasdownloadedfromtheAoPSMathOlympiadResourcesPage
Page3USAAMC82006(E)lw11
Howmanytwo-digitnumbershavedigitswhosesumisaperfectsquare?(A)13
(B)16 (C)17 (D)18 (E)1912 Antonette gets 70% on a 10-problem test,
80% on a 20-problem test and 90% on a 30-problemtest.
Ifthethreetestsarecombinedintoone60-problemtest,whichpercentisclosesttoheroverallscore?(A)40
(B)77 (C)80 (D)83 (E)8713 Cassie leaves Escanaba at 8:30 AM heading
for Marquette on her bike. She bikes at a
uniformrateof12milesperhour.
BrianleavesMarquetteat9:00AMheadingforEscanabaonhisbike.
Hebikesatauniformrateof16milesperhour.
Theybothbikeonthesame62-mileroutebetweenEscanabaandMarquette.
Atwhattimeinthemorningdotheymeet?(A)10 : 00 (B)10 : 15 (C)10 : 30
(D)11 : 00 (E)11 : 3014 Problems14,15and16involveMrs.
ReedsEnglishassignment.ANovelAssignmentThe students in Mrs. Reeds
English class are reading the same 760-page novel. Three
friends,Alice,Bob and Chandra,are in the class. Alice reads a page
in 20 seconds,Bob reads a
pagein45secondsandChandrareadsapagein30seconds.If
BobandChandrabothreadthewholebook, Bobwill
spendhowmanymoresecondsreadingthanChandra?(A)7, 600 (B)11, 400
(C)12, 500 (D)15, 200 (E)22, 80015 Problems14,15and16involveMrs.
ReedsEnglishassignment.ANovelAssignmentThe students in Mrs. Reeds
English class are reading the same 760-page novel. Three
friends,Alice,Bob and Chandra,are in the class. Alice reads a page
in 20 seconds,Bob reads a
pagein45secondsandChandrareadsapagein30seconds.http://www.artofproblemsolving.com/ThislewasdownloadedfromtheAoPSMathOlympiadResourcesPage
Page4USAAMC82006Chandra and Bob, who each have a copy of the book,
decide that they can save time by teamreading the novel. In this
scheme, Chandra will read from page 1 to a certain page and Bobwill
readfromthenextpagethroughpage760, nishingthebook.
Whentheyarethroughthey will tell each other about the part they
read. What is the last page that Chandra
shouldreadsothatsheandBobspendthesameamountoftimereadingthenovel?(A)425
(B)444 (C)456 (D)484 (E)50616 Problems14,15and16involveMrs.
ReedsEnglishassignment.ANovelAssignmentThe students in Mrs. Reeds
English class are reading the same 760-page novel. Three
friends,Alice,Bob and Chandra,are in the class. Alice reads a page
in 20 seconds,Bob reads a
pagein45secondsandChandrareadsapagein30seconds.BeforeChandraandBobstartreading,Alicesaysshewouldliketoteamreadwiththem.
Iftheydividethebookintothreesectionssothateachreadsforthesamelengthoftime,howmanysecondswilleachhavetoread?(A)6400
(B)6600 (C)6800 (D)7000 (E)720017 JerotatesspinnersP,
QandRandaddstheresultingnumbers.
Whatistheprobabilitythathissumisanoddnumber?PQR1 232 46 81 357
911(A)14(B)13(C)12(D)23(E)3418
Acubewith3-inchedgesismadeusing27cubeswith1-inchedges.
Nineteenofthesmallercubesarewhiteandeightareblack.
Iftheeightblackcubesareplacedatthecornersofthelargercube,whatfractionofthesurfaceareaofthelargercubeiswhite?(A)19(B)14(C)49(D)59(E)192719
TriangleABCisanisoscelestrianglewithAB= BC.
PointDisthemidpointofbothBCand AE, and CEis 11 units long. Triangle
ABDis congruent to triangle ECD. What is
thelengthofBD?http://www.artofproblemsolving.com/ThislewasdownloadedfromtheAoPSMathOlympiadResourcesPage
Page5USAAMC82006ABCDE(A)4 (B)4.5 (C)5 (D)5.5 (E)620
Asinglestournamenthadsixplayers.
Eachplayerplayedeveryotherplayeronlyonce,withnoties.
IfHelenwon4games,Ineswon3games,Janetwon2games,Kendrawon2gamesandLarawon2games,howmanygamesdidMonicawin?(A)0
(B)1 (C)2 (D)3 (E)421
Anaquariumhasarectangularbasethatmeasures100cmby40cmandhasaheightof50cm.
Theaquariumistilledwithwatertoadepthof37cm.
Arockwithvolume1000cm3isthenplacedintheaquariumandcompletelysubmerged.
Byhowmanycentimetersdoesthewaterlevelrise?(A)0.25 (B)0.5 (C)1
(D)1.25 (E)2.522
Threedierentone-digitpositiveintegersareplacedinthebottomrowofcells.
Numbersinadjacentcellsareaddedandthesumisplacedinthecell abovethem.
Inthesecondrow,continue the same process to obtain a number in the
top cell. What is the dierence
betweenthelargestandsmallestnumberspossibleinthetopcell?+ ++(A)16
(B)24 (C)25 (D)26
(E)35http://www.artofproblemsolving.com/ThislewasdownloadedfromtheAoPSMathOlympiadResourcesPage
Page6USAAMC8200623 Aboxcontainsgoldcoins.
Ifthecoinsareequallydividedamongsixpeople, fourcoinsareleftover.
Ifthecoinsareequallydividedamongvepeople,threecoinsareleftover.
Iftheboxholdsthesmallestnumberofcoinsthatmeetsthesetwoconditions,howmanycoinsareleftwhenequallydividedamongsevenpeople?(A)0
(B)1 (C)2 (D)3 (E)524
Inthemultiplicationproblembelow,A,B,CandDaredierentdigits.
WhatisA+B?A B A C DC D C D(A)1 (B)2 (C)3 (D)4 (E)925
Barrywrote6dierentnumbers, oneoneachsideof3cards,
andlaidthecardsonatable,asshown. Thesumsof thetwonumbersoneachof
thethreecardsareequal.
Thethreenumbersonthehiddensidesareprimenumbers. Whatistheaverageof
thehiddenprimenumbers?44 59 38(A)13 (B)14 (C)15 (D)16 (E)17The
problems onthis page are copyrightedbythe Mathematical
AssociationofAmericasAmericanMathematicsCompetitions.http://www.artofproblemsolving.com/ThislewasdownloadedfromtheAoPSMathOlympiadResourcesPage
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