International Kangroo Maths Contest

[champ-student]

hi everyone, em gonna participate n a maths compitition n if anyone can help meh wid following questionzz,,...

 

[champ-student]

5. A dragon has fi ve heads. Every time a head is chopped of, new heads grow. If six
heads are chopped of one by one, how many heads will the dragon finally have?
(A) 25 (B) 28 (C) 29 (D) 30 (E) 35

 

[champ-student]

8. The diagram shows two triangles. In how many ways can
you choose two vertices, one in each triangle, so that the straight line through the vertices does
not cross either triangle?
(A) 1 (B) 2 (C) 3 (D) 4 (E) more than 4

 

[champ-student]

http://www.kangaroo.edu.pk/download/12/Papers/Cadet2012.pdf
Q.8
Q.10

 

[Steel Arm]

5. A dragon has fi ve heads. Every time a head is chopped of, new heads grow. If six
heads are chopped of one by one, how many heads will the dragon finally have?
(A) 25 (B) 28 (C) 29 (D) 30 (E) 35

ok so at first there are 5 heads
if u cut one, 5 new crop up which leaves you with 9
basically, each time you add 4 heads (removing 1 and adding 5 new)
if 6 heads are cut you are kinda adding 6 x 4 heads, which makes 24
you add those to your starting 5 heads which gives 29 in the end
ans (C) 29

 

[Steel Arm]

8. The diagram shows two triangles. In how many ways can
you choose two vertices, one in each triangle, so that the straight line through the vertices does
not cross either triangle?
(A) 1 (B) 2 (C) 3 (D) 4 (E) more than 4

here vertices are the 'corners' of the triangles lyk here the red points

now you join one corner from each triangle to the other one in such a way that it doesnt cross any triangle

you repeat this procedure like this

thats the maximum number of lines you can put through vertices
ans is D) 4

 

[Steel Arm]

for question 10
i proceeded by elimination
it cant be A, B and C when you look at it
its either D or E
it cannot be E since it says 'each piece consists of 4 cubes'
the 4th black cube gotta be below the top right white cube
which leaves us with D
Ans is D)

 

[champ-student]

here vertices are the 'corners' of the triangles lyk here the red points

now you join one corner from each triangle to the other one in such a way that it doesnt cross any triangle

you repeat this procedure like this

thats the maximum number of lines you can put through vertices
ans is D) 4

thx a lot.......! u dnt knwhw mch u hlpd....thx again bro...

 

[Steel Arm]

thx a lot.......! u dnt knwhw mch u hlpd....thx again bro...

its alrity!!