2020年高斯数学竞赛7年级真题(Gauss7Contest)

sContestGrade7(TheGrade8Contestisonthereverseside)Wednesday,May13,2020(inNorthAmericaandSouthAmerica)Thursday,May14,2020(outsideofNorthAmericaandSouthAmerica)Time:1hour©2020UniversityofWaterlooCalculatingdevicesareallowed,providedthattheydonothaveanyofthefollowingfeatures:(i)internetaccess,(ii)theabilitytocommunicatewithotherdevices,(iii)informationpreviouslystoredbystudents(suchasformulas,programs,notes,etc.),(iv)acomputeralgebrasystem,(v)userulers,renotsure,estionisfollowedbyfivepossibleanswersmarkedA,B,C,D,uhavemadeyourchoice,g:Eachcorrectanswerisworth5inPartA,6inPartB,answeredquestionisworth2,ursupervisorinstructsyoutostart,e,schoolandlocationofsometop-scoringstudentswillbepublishedontheWebsite,website,youwillalsobeabletofindcopiesofpastContestsandexcellentresourcesforenrichment,7Scoring:answeredquestionisworth2,:costs$thecostof10pens?(A)$42.(B)$10(C)$12(D)$25432112345y(E)$20P

Inthediagramshown,whatarethecoordinatesofpointP?(A)(4,0)(D)(4,4)(B)(2,2)(E)(2,4)(B)100(C)100000(D)1000(C)(2,0)fthefollowingintegersisclosestto99×9?(A)10000(E)10Inthemorning,thetemperaturewas−3◦fternoon,thetemperaturewas5◦anydegreesCelsiusdidthetemperatureincrease?(A)8(B)3(C)5(D)2(E)shermean(average)numberofstepsperdayinApril?(A)7900(B)8100(C)8000(D)7100(E)iechartshown,ystudentschosemilk?(A)120(D)180(B)160(E)80(C)creasinglistofconsecutiveintegers,the6thnumberinthelist?(A)10(B)11(C)9(D)8P0(E)rksareequallyspacedalonganumberlinewiththenumbersP,Q,R,S,T,fthefollowingbestrepresentsthevalueofRdividedbythevalueofU?(A)0.25(D)1.25(B)0.50(E)1.50(C)0.7514 cm12 cm8 cmx iagram,thevalueofx?(A)8(D)14(B)10(E)15(C)itivedivisorsof12(otherthanitself)are1,2,3,4,um,1+2+3+4+6,dantnumberisanumberforwhichthesumofitspositivedivisors(otherthanitself)fthefollowingisalsoanabundantnumber?(A)8(B)10(C)14(D)18(E)22Grade7PartB:ookiesaresharedequallyamong5people,howmanycookiesdoeseachpersonreceive?(A)14(B)12(C)9(D)11(E)s9yearsolderthanSusie,yyearsolderisAbdulthanBinh?(A)11(B)9(C)14(D)2(E)7P (15, 55)Q (26, 55)P(15,55),Q(26,55)andR(26,35)aofthisrectangleis(A)360(D)580(B)800(E)330(C)220SR (26, 35)ntains15red,20blue,fioftheremainingjellybeansisequallylikelytobechosen,whatistheprobabilitythatJackchoosesaredjellybeannext?(A)1531(B)3449(C)1549(D)27(E)’stimewas4minuteslessthanOlivia’stime,howmanyminutesdidittakeOliviatoruntherace?(A)78(B)56(C)58(D)74(E)iagram,whichofthefollowingsquaresshouldbeshadedtomakeBDalineofsymmetryofsquareABCD?(A)PandS(B)QandS(C)PandT(D)QandT(E)$120inheraccounttodayandwillbeginsavingbymaking$akesmsuchdeposits,theexpressionthatbestrepresentsthenumberofdollarsinheraccountis(A)120+m(B)30m(C)30+120m(D)150m(E)120+scelestriangleseachhaveatleastoneanglethatmeasures70◦.Inthefirsttriangle,econdtriangle,firsttriangle,econdtriangle,ueofS+Tis(A)280◦(B)250◦(C)220◦(D)200◦(E)300◦iffbolonthefaceoppositeis(A)(D)(B)(E)(C)ridshown,ossesahead,ourtossesofthecoin,JanewillbeatoneofthedotsP,Q,R,S,theprobabilitythatJanewillbeatdotR?(A)(D)12716PQRSAT(B)(E)38516(C)916PartC:mple,1111ismadebyrepeating11,ysuchnumbersaretherebetween2000and10000?(A)80(B)81(C)79(D)72(E)bought300gramsofcandyAfor$5.00,andxgramsofcandyBfor$culatedthattheaveragepriceofallofthecandythatshepurchasedwas$thevalueofx?(A)525(B)600(C)500(D)450(E)t11,20,31,51,82isanexampleofanincreasinglistoffivepositiveintegersinwhichthefirstandsecondintegersaddtothethird,thesecondandthirdaddtothefourth,andthethirdandfourthaddtothefiysuchlistsoffivepositiveintegershave124asthefifthinteger?(A)10(B)7(C)9(D)6(E)10by10gridofsquaresshown,pointPcanbeatanyofthe41pointsofintersectionofpairsofgridlinesinside(andnoton)