2021加拿大滑铁卢大学高斯数学竞赛(CEMC).docx

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1、2021加拿大滑铁卢大学高斯数学竞赛(CEMC)2.Thevalueof10(5?2)is(A)13(B)70(C)7(D)30(E)503.Thegraphshowsthetotaldistancethateachof?verunnersranduringaone-hourtrainingsession.Whichrunnerrantheleastdistance?(A)Phil(B)Tom(C)Pete(D)Amal(E)SanjayPhilTom4.Theequal-armscaleshownisbalanced.Onehasthesamemassas(A)(B)(C)(D)(E)5.W

2、hichofthefollowingisclosestto5cm?(A)Thelengthofafullsizeschoolbus(B)Theheightofapicnictable(C)Theheightofanelephant(D)Thelengthofyourfoot(E)Thelengthofyourthumb6.Thenumberofcentimetresin3.5metresis(A)350(B)30.5(C)3.05(D)3.50(E)3057.Theperimeterofthe?gureshownis(A)18(B)17(C)23(D)20(E)258.Hannahscored

3、312pointsduringthebasketballseason.Ifheraverage(mean)was13pointspergame,howmanygamesdidsheplay?(A)24(B)41(C)17(D)13(E)309.Thenumber6hasexactlyfourpositivedivisors:1,2,3,and6.Howmanypositivedivisorsdoes20have?(A)2(B)6(C)3(D)5(E)812.Apieceofpaperisfoldedinhalf,creatingtwolayersofpaper.Thepaperisthenfo

4、ldedinhalfagain.Thisiscontinueduntilthepaperhasbeenfoldedinhalfatotalof?vetimes.Thetotalnumberoflayersofpaperinthefoldedsheetis(A)16(B)32(C)25(D)8(E)6413.Howmanyevenwholenumbersbetween1and99aremultiplesof5?(A)5(B)7(C)9(D)11(E)1314.Inthe33tableshown,thenumbers1,2and3areplacedsothateachnumberoccursonl

5、yonceineachrowandonlyonceineachcolumn.ThevalueofX+Yis(A)3(B)2(C)5(D)6(E)415.Intherectangleshown,theareaoftheshadedregionis(A)60cm2(B)20cm2(C)30cm2 (D)40cm2(E)50cm25cm16.Youhaveexactly$4.40(440)inquarters(25coins),dimes(10coins),andnickels(5coins).Youhavethesamenumberofeachtypeofcoin.Howmanydimesdoyo

6、uhave?(A)20(B)11(C)10(D)12(E)417.Onecornerofacubeiscuto?,creatinganewtriangularface,asshown.Howmanyedgesdoesthisnewsolidhave?(A)18(B)14(C)24(D)15(E)1318.Inthegraphshown,whichofthefollowingrepresentstheimageofthelinesegmentPQafterare?ectionacrossthex-axis?(A)PS(B)TU(C)MN(D)WV(E)FGdecimalpointwillther

7、ealsobea2?(A)119th(B)121st(C)123rd(D)125th(E)126th20.Inatriangle,themeasureofoneoftheanglesis45?.Themeasuresoftheothertwoanglesinthetriangleareintheratio4:5.Whatisthemeasureofthelargestangleinthetriangle?(A)80?(B)90?(C)75?(D)85?(E)100?PartC:Eachcorrectanswerisworth8.21.Thenumbers1through25arearrange

8、dinto5rowsand5columnsinthetablebelow.12345109876111213141520191817162122232425Whatisthelargestpossiblesumthatcanbemadeusing?veofthesenumberssuchthatnotwonumberscomefromthesamerowandnotwonumberscomefromthesamecolumn?(A)75(B)73(C)71(D)70(E)6822.Thewidthofarectangleisdoubledandthelengthishalved.Thispro

9、ducesasquarewithaperimeterofP.Whatistheperimeteroftheoriginalrectangle?(A)P(B)2P(C)12P(D)54P(E)52P23.Apalindromeisapositiveintegerthatisthesamewhenreadforwardsorbackwards.Thenumbers101and4554areexamplesofpalindromes.Theratioofthenumberof4-digitpalindromestothenumberof5-digitpalindromesis(A)4:5(B)5:2

10、(C)2:7(D)4:3(E)1:1024.Inthediagram,rectanglePQRSismadeupofsixidenticalsquares.PointsU,V,W,X,Y,andZaremidpointsofsidesofthesquares,asshown.Whichofthefollowingtriangleshasthegreatestarea?(A)PVU(B)PXZ(C)PVX(D)PYS(E)PQWPQ25.Twodi?erent2-digitpositiveintegersarecalledareversalpairifthepositionofthedigitsinthe?rstintegerisswitchedinthesecondinteger.Forexample,52and25areareversalpair.Theinteger2021hasthepropertythatitisequaltotheproductofthreedi?erentprimenumbers,twoofwhichareareversalpair.Including2021,howmanypositiveintegerslessthan10000havethissameproperty?(A)18(B)14(C)20(D)17(E)19