Kangaroo2005—CadetMaxTime:75min
Cadet
3-Point-Problems
1.Thereareeightkangaroosinthecellsofthetable
(seethefigureontheright).Anykangaroocanjumpintoany
freecell.Findtheleastnumberofthekangarooswhichhaveto
jumpintoanothercellsothatexactlytwokangaroosremaininany
rowandinanycolumnofthetable.
(A)1(B)2(C)3(D)4
2.Howmanyhoursarethereinhalfofathirdofaquarterofaday?
11
(A)(B)(C)1(D)2
32
3.Wehaveacubewithedge12cm.Theantmovesonthe
cubesurfacefrompointAtopointBalongthetrajectoryshown
inthefigure.Findthelengthofant’spath.
(A)48cm(B)54cm
(C)60cm(D)itisimpossibletodetermine
4.AtNationalSchool,50%ofthestudentshavebicycles.Ofthestudentswhohave
bicycles,30%haveblackbicycles.WhatpercentofstudentsofNationalSchoolhaveblack
bicycles?
(A)15%(B)20%(C)25%(D)40%
5.IntriangleABC,theangleatAisthreetimesthesizeofthatatBandhalfthe
sizeoftheangleatC.WhatistheangleatA?
(A)30?(B)36?(C)54?(D)60?
6.Thediagramshowsthegroundplanofaroom.The
adjacentwallsareperpendiculartoeachother.Lettersa,brepresent
thedimensions(lengths)oftheroom.Whatistheareaofthe
room?
(A)2ab+a(b?a)(B)3a(a+b)?a2
(C)3a(b?a)+a2(D)3ab
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Kangaroo2005—CadetMaxTime:75min
7.Nidacutsasheetofpaperinto10pieces.Thenshetookonepieceandcutitagainto10pieces.
Shewentoncuttinginthesamewaythreemoretimes.Howmanypiecesofpaperdidshehave
afterthelastcutting?
(A)36(B