Đề thi Toán Kangaroo năm 2003 Cấp độ Minor, Benjamin, Cadet, Junior, Student

 Questions of Kangaroo 2003
 MINOR (grades 3 and 4 )
3-POINT QUESTIONS
 M1. How much is 0 + 1 + 2 + 3 + 4 − 3 − 2 − 1 − 0?
 A 0 B 2 C 4 D 10 E 16
 M2. There are 10 boxes in the first van. Every further van contains twice as many boxes as the
 previous one. How many boxes are there in the fifth van?
 A 100 B 120 C 140 D 160 E 180
 M3. Sophie draws kangaroos: a blue one, then a green, then a red, then a black, then a yellow,
 a blue, a green, a red, a black, and so on. What colour is the 17th kangaroo?
 A Blue B Green C Red D Black E Yellow
 M4. In the teachers’ room there are 6 tables with 4 chairs each, 4 tables with 2 chairs each, and
 3 tables with 6 chairs each. How many chairs are there altogether?
 A 40 B 25 C 50 D 36 E 44
 M5. A coin is lying on the table. What is the maximum number of such coins which can be put
 on the table in such a way that each of them touches this coin?
 A 4 B 5 C 6 D 7 E 8
 M6. In the picture the distance KM = 10, LN = 15, KN = 22. Find the distance LM.
 KLM N
 A 1 B 2 C 3 D 4 E 5
 M7. Hedgehog Mark complained to his friends: “If I had picked twice as many apples as I really
 did, I would have 24 apples more than I have now.” How many apples did Mark pick?
 A 48 B 24 C 42 D 12 E 36
 M8. Chris constructed the brick on the picture using red and blue cubes
 of the same size. The outside of the brick is completely red, but
 all cubes used inside are blue. How many blue cubes did Chris
 use?
 A 12 B 24 C 36 D 40 E 48 Benjamin (grades 5 and 6 ) 103
M18. I surrounded the wooden circle (see picture) using a cm of thread. After that I surrounded by
 thread the wooden square –– b cm of thread was enough for that. How much thread (in cm)
 would be enough to surround the three wooden circles without moving them?
 ?
 A 3a B 2a + b C a + 2b D 3b E a + b
M19. The picture on the right has been drawn on paper and cut out
 to make a house. Which of the houses does it make?
 A B C D E
M20. Kangaroo bought 3 types of sweets: big, medium and small ones. Big sweets cost 4 coins
 per 1, medium –– 2 coins per 1, small –– 1 coin per 1. Kangaroo bought 10 sweets and he
 paid 16 coins. How many big sweets did kangaroo buy?
 A 5 B 4 C 3 D 2 E 1
M21. A bar-code is formed by 17 alternating black and white
 bars (the first and the last bars are black). The black bars
 are of two types: wide and narrow. The number of white
 bars is greater by 3 than the number of wide black bars.
 Then the number of narrow black bars is
 A 1 B 2 C 3 D 4 E 5
M22. A rectangular parallelepiped was composed of 3 pieces, each
 consisting of 4 little cubes. Then one piece was removed (see
 picture). Which one?
 A B C D E
M23. In the toy shop the price for one dog and three bears is the same as for four kangaroos.
 Three dogs and two bears together also have the same price as four kangaroos. What is
 more expensive and how many times –– the dog or the bear?
 A The dog is two times more expensive
 B The bear is two times more expensive
 C The same price
 D The bear is three times more expensive
 E The dog is three times more expensive
M24. The composite board shown in the picture consists of 20
 fields 1 × 1. How many possibilities are there to cover all
 18 white fields with 9 rectangular stones 1×2? (The board
 cannot be turned. Two possibilities are different if at least
 one stone lies in another way.)
 A 2 B 4 C 6 D 8 E 16 Benjamin (grades 5 and 6 ) 105
4-POINT QUESTIONS
 B11. The picture shows the clown Dave dancing on top of two balls and one
 cubic box. The radius of the lower ball is 6 dm, the radius of the upper
 ball is three times less. The side of the cubic box is 4 dm longer than the
 radius of the upper ball. At what height (in dm) above the ground is the
 clown Dave standing?
 A 14 B 20 C 22 D 24 E 28
 ?
 B12. We take two different numbers from 1, 2, 3, 4, 5 and find their sum. How many different
 sums can we obtain?
 A 5 B 6 C 7 D 8 E 9
 B13. The rectangle in the picture consists of 7 squares. The
 lengths of the sides of some of the squares are shown.
 Square K is the biggest one, square L –– the smallest one. K
 How many times is the area of K bigger than the area of
 L?
 A 16 B 25 C 36 D 49 E Impossible to find L
 2
 3
 B14. I surrounded the wooden circle (see picture) using a cm of thread. After that I surrounded
 by thread the wooden square –– b cm of thread was enough for that. How much thread (in
 cm) would be enough to surround the three wooden circles without moving them?
 ?
 A 3a B 2a + b C a + 2b D 3b E a + b
 B15. Benito has 20 small balls of different colours: yellow, green, blue and black. 17 of the balls
 are not green, 5 are black, 12 are not yellow. How many blue balls does Benito have?
 A 3 B 4 C 5 D 8 E 15
 B16. There are 17 trees along the road from Basil’s home to a pool. Basil marked some trees with
 a red strip as follows. On his way to bathe he marked the first tree and then each second
 tree, and on his way back he marked the first tree and then each third tree. How many trees
 have no mark after that?
 A 4 B 5 C 6 D 7 E 8
 B17. Square ABCD is comprised of one inner square (white) and four D C
 shaded congruent rectangles. Each shaded rectangle has a perimeter
 of 40 cm. What is the area (in cm2) of square ABCD?
 A 400 B 200 C 160 D 100 E 80
 A B
 B18. Today’s date is 20.03.2003. What date will it be 2003 minutes after the hour 20:03?
 A 21.03.2003 B 22.03.2003 C 23.03.2003 D 21.04.2003 E 22.04.2003 Cadet (grades 7 and 8) 107
 B25. You have six line segments of lengths 1 cm, 2 cm, 3 cm, 2001 cm, 2002 cm and 2003 cm.
 You have to choose three of these segments to form a triangle. How many different choices
 of three segments are there which work?
 A 1 B 3 C 5 D 6 E More than 10
 B26. There were completely red and completely green dragons in the dungeon. Each red dragon
 had 6 heads, 8 legs and 2 tails. Each green dragon had 8 heads, 6 legs and 4 tails. In all
 the dragons had 44 tails. The number of green legs was 6 fewer than of red heads. How
 many red dragons were there in the dungeon?
 A 6 B 7 C 8 D 9 E 10
 B27. What is the length (in cm) of the line (see picture) M
 connecting vertices M and N of the square?
 A 10 200 B 2 500 C 909 D 10 100 E 9 900 1cm
 1cm
 100 cm
 100 cm
 N
 B28. Every figure in the picture replaces some digit. What is the sum  +?
 A 6 B 7 C 8 D 9 E 13 +
 2003
 B29. The figure in the drawing consists of five isosceles right triang-
 les of the same size. Find the area (in cm2) of the shaded figure.
 A 20 B 25 C 35 D 45 E Cannot be found 30 cm
 B30. Ann has the box containing 9 pencils. At least one of them is blue. Among every 4 of the
 pencils at least two have the same colour, and among every 5 of the pencils at most three
 have the same colour. What is the number of blue pencils?
 A 2 B 3 C 4 D 1 E Impossible to determine
 CADET (grades 7 and 8)
3-POINT QUESTIONS
 C1. There were 5 parrots in a pet shop. Their average price was 6 000 dollars. One day the
 most expensive parrot was sold. The average price of the remaining four parrots was 5 000
 dollars. What was the price (in dollars) of the parrot sold?
 A 1 000 B 2 000 C 5 500 D 6 000 E 10 000
 C2. A folded napkin was cut through (see picture). What does it look
 like when unfolded?
 A B C D E
 C3. A straight line is drawn across a 4 × 4 chessboard. What is the greatest number of 1 × 1
 squares which can be cut into two pieces by the line?
 A 3 B 4 C 6 D 7 E 8 Cadet (grades 7 and 8) 109
 C13. Jeffrey shoots three arrows at each of four identical targets. He scores 29 points on the first
 target, 43 on the second and 47 on the third. How many points does Jeffrey score on the
 last target?
 A 31 B 33 C 36 D 38 E 39
 C14. The weight of a truck without a load is 2000 kg. Today the load initially comprised 80%
 of the total weight. At the first stop, a quarter of the load was left. What percentage of the
 total weight does the load then comprise?
 A 20% B 25% C 55% D 60% E 75%
 C15. Two quadrates with the same size cover a circle, the radius of which
 is 3 cm. Find the total area (in cm2) of the shaded figure.
 6π
 A 8(π − 1) B 6(2π − 1) C 9π − 25 D 9(π − 2) E
 5
 C16. You have six line segments of lengths 1 cm, 2 cm, 3 cm, 2001 cm, 2002 cm and 2003 cm.
 You have to choose three of these segments to form a triangle. How many different choices
 of three segments are there which work?
 A 1 B 3 C 5 D 6 E More than 10
 C17. How many positive integers n possess the following property: among the positive divisors
 of n different from 1 and n itself, the largest is 15 times the smallest.
 A 0 B 1 C 2 D 3 E Infinitely many
 C18. Six points K, L, M, N, P , R are marked on a line from left to right, in the same order as
 listed. It is known that KN = MR and LN = NR. Then, necessarily
 A KL = LM B LM = NP C LN = PR D KL = MN E MN = PR
 C19. Mary has 6 cards with natural numbers written on them (one number on each card). She
 chooses 3 cards and calculates the sum of the corresponding numbers. Having done this for
 all 20 possible combinations of 3 cards, she discovers that 10 sums are equal to 16, and the
 other 10 sums are equal to 18. Then the smallest number on the cards is
 A 2 B 3 C 4 D 5 E 6
 C20. Paul, Bill, John, Nick and Tim stood in a circle, the distances between any two neighbours
 being different. Each of them said the name of the boy standing closest to him. The names
 Paul and Bill were said two times each, and the name John was said once. Then
 A Paul and Bill were not neighbours
 B Nick and Tim were not neighbours
 C Nick and Tim were neighbours
 D The situation described is impossible
 E None of the above