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2013Gauss7Contest

发布时间:2014-02-10 10:48:48  

Grade7

Scoring:

Thereisnopenaltyforanincorrectanswer.

Eachunansweredquestionisworth2,toamaximumof10unansweredquestions.

PartA:Eachcorrectanswerisworth5.1.2.

Thevalueof(5×3)?2is(A)5(A)503.

(B)9(B)40

(C)6(C)35

(D)8(D)45

(E)13(E)55

Whichofthefollowingnumbersisamultipleof9?

Thirty-sixhundredthsisequalto(A)0.36

(B)360

(C)3.6

(D)0.036

(E)0.0036

4.Thevalueof1+1?2+3+5?8+13+21?34is(A)?32

(B)1

(C)88

(D)0

(E)?345.IfPQisastraightlinesegment,thenthevalueof

xis(A)160(D)20

(B)70(E)80

(C)110

Q

6.

Nickhassixnickels(5¢coins),twodimes(10¢coins)andonequarter(25¢coin).Incents(¢),howmuchmoneydoesNickhave?(A)65

(C)35(D)15??12157??

Thesmallestnumberintheset,,,,is

1

(B)75(E)55

7.

(A)8.

(B)

2(C)

1(D)

5(E)7Ahmedisgoingtothestore.Onequarterofthewaytothestore,hestopstotalkwithKee.Hethencontinuesfor12kmandreachesthestore.Howmanykilometresdoeshetravel

altogether?(A)15(D)48

(B)16(E)20

(C)24

9.

Anexpressionthatproducesthevaluesinthesecondrowofthetableshown,giventhevaluesofninthe?rstrow,is(A)3n?2(B)2(n?1)(C)n+4(D)2n

(E)2n?1

10.UVWandXYZareeach3-digitintegers.U,V,W,X,Y,andZaredi?erentdigits

chosenfromtheintegers1to9.WhatisthelargestpossiblevalueforUVW?XYZ?

(A)678

(B)864

(C)885

(D)888

(E)975

PartB:Eachcorrectanswerisworth6.

11.Thelengthofeachedgeofacubeis1cm.Thesurfaceareaofthecube,incm2,is

(A)24

(B)1

(C)4

(D)12

(E)6

Grade7

12.Whichofthefollowingpairsofnumbershasagreatestcommonfactorof20?

(A)200and2000(D)20and25

(B)40and50(E)40and80

(C)20and40

13.Jack,Kelly,Lan,Mihai,andNatearesittinginthe5chairsaroundacirculartable.

LanandMihaiaresittingbesideeachother.JackandKellyarenotsittingbesideeachother.The2peoplewhoareseatedoneithersideofNateare

(A)JackandLan(D)LanandMihai

(B)JackandKelly(E)MihaiandJack

(C)KellyandMihai

14.Ifx=4and3x+2y=30,whatisthevalueofy?

(A)18

(B)6

(C)3

(D)4

(E)9

15.Danielbeginswith64coinsinhiscoinjar.Eachtimehereachesintothejar,he

removeshalfofthecoinsthatareinthejar.Howmanytimesmusthereachinandremovecoinsfromhisjarsothatexactly1coinremainsinthejar?

(A)5

(B)32

(C)6

(D)7

(E)63

16.Themean(average)of?veconsecutiveevennumbersis12.Themeanofthesmallest

andlargestofthesenumbersis

(A)12

(B)10

(C)14

(D)8

(E)16

17.Forevery3chocolatesthatClairebuysattheregularprice,shebuysafourth

chocolatefor25cents.Clairebuys12chocolatesintotalfor$6.15.Whatistheregularpriceofonechocolate,incents?

(A)180

(B)45

(C)60

(D)54

(E)5718.JKLMisasquareandPQRSisarectangle.IfJKis

paralleltoPQ,JK=8andPS=2,thenthetotalareaoftheshadedregionsis

(A)32(B)16(C)56

(D)48

(E)

62

QR

19.Aspecialsix-sideddieisrolled.Theprobabilityofrollinganumberthatisamultiple

1

ofthreeis1.Theprobabilityofrollinganevennumberis.Apossibilityforthenumbersonthedieis

(A)1,2,3,5,5,6(D)1,2,3,3,4,6

(B)1,2,3,3,5,6(E)2,3,3,3,5,6

(C)1,2,3,4,6,6

20.Toothpicksareusedtomakerectangulargrids,asshown.

Notethatatotalof31identicaltoothpicksareusedinthe1×10grid.Howmanytoothpicksareusedina43×10grid?

(A)913(D)903

(B)860(E)

946

(C)871

Grade7

PartC:Eachcorrectanswerisworth8.

21.Intheadditionshown,PandQeachrepresentsingle

digits,andthesumis1PP7.WhatisP+Q?

(A)9(D)15

(B)12(E)13

(C)14

77P6QP+QQP1PP7

22.Anarithmeticsequenceisasequenceinwhicheachterm

afterthe?rstisobtainedbyaddingaconstanttothepreviousterm.Forexample,2,4,6,8and1,4,7,10arearithmeticsequences.

Inthegridshown,thenumbersineachrowmustformanarithmeticsequenceandthenumbersineachcolumnmustformanarithmeticsequence.Thevalueofxis(A)37(D)43.75

(B)28(E)46

(C)36

14710

36

25x

23.Intheright-angledtrianglePQR,PQ=QR.The

segmentsQS,TUandVWareperpendiculartoPR,andthesegmentsSTandUVareperpendiculartoQR,asshown.Whatfractionof??PQRisshaded?

(A)(D)

35P

(B)(E)

37

(C)

524.Onefaceofacubecontainsacircle,asshown.Thiscuberollswithoutslidingona

fourbyfourcheckerboard.Thecubealwaysbeginsapathonthebottomleftsquareinthepositionshownandcompletesthepathonthetoprightsquare.Duringeachmove,anedgeofthecuberemainsincontactwiththeboard.Eachmoveofthecubeiseithertotherightorup.Foreachpath,afaceofthecubecontactssevendi?erentsquaresonthecheckerboard,includingthebottomleftandtoprightsquares.Thenumberofdi?erentsquaresthatwillnotbecontactedbythefacewiththecircleonanypathis(A)9(B)11(C)8(D)12(E)

10

25.Aboxcontainsatotalof400ticketsthatcomein?vecolours:blue,green,red,yellowandorange.Theratioofbluetogreentoredticketsis1:2:4.Theratioofgreentoyellowtoorangeticketsis1:3:6.Whatisthesmallestnumberofticketsthatmustbedrawntoensurethatatleast50ticketsofonecolourhavebeenselected?(A)50(B)246(C)148(D)196(E)115

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