Đề thi Toán Kangaroo năm 2013 Cấp độ Benjamin, Khối 5-6

 Lietuvos Respublikos §svietimoir mokslo ministerija VU Matematikos ir informatikos fakultetas
24. There are four buttons in a row as shown in the picture. Two
 Keng©uros organizavimo komitetas Leidykla TEV VU Matematikos ir informatikos institutas
 of them show happy faces, and two of them show sad faces. If
 we press on a face, its expression turns to the opposite (e.g. a funny face turns into a
 sad face after the touch). In addition to this, the adjacent buttons also change their
 expressions. What is the least number of times you need to press the buttons in order KANGAROO 2013
 to get all happy faces?
 A) 2 B) 3 C) 4 D) 5 E) 6
25. 40 boys and 28 girls stand in a circle, hand in hand, all facing inwards. Exactly 18 boys
 give their right hand to a girl. How many boys give their left hand to a girl?
 A) 18 B) 9 C) 28 D) 14 E) 20 Time allowed: 75 min Benjamin
 Calculators are not permitted 5--6 grades
26. How many 3-digits numbers possess the following property: after subtracting 297 from
 Questions for 3 points
 such a number, we get a 3-digit number consisting of the same digits in the reverse
 order? 1. We put 2, 0, 1, 3 into an adding machine, as shown. What is the
 A) 6 B) 7 C) 10 D) 60 E) 70 result in the box with the question mark?
 A) 2 B) 3 C) 4 D) 5 E) 6
27. When Matthew and Marten found their old model railway,
 Matthew quickly made a perfect circle from 8 identical 2. Nathalie wanted to build a cube as shown in the picture
 track parts, Marten starts to make another track with two on the left. However, she ran out of small cubes and built
 of these pieces as shown in the picture. He wants to use as only the part of the cube, as shown on the right. How
 few pieces as possible to make a closed track. How many many small cubes Nathalie need to nish the cube?
 pieces does his track consist of? A) 5 B) 6 C) 7 D) 8 E) 9
 A) 11 B) 12 C) 14 D) 15 E) 16 3. Children went out for a walk. Everytime Martin makes 9 steps, David makes 8 steps
28. There were 2013 inhabitants on an island. Some of them were knights and the others and Peter makes 7. Martin makes 90 steps a minute. How many steps they will make
 were liars. The knights always tell the truth and the liars always lie. Every day, one of all together during a 10 minute walk?
 the inhabitants said: After my departure the number of knights on the island will equal A) 240 B) 2013 C) 2400 D) 2700 E) 900
 the number of liars and then left the island. After 2013 days there was nobody on the
 island. How many liars were there initially? 4. Nick is learning to drive. He knows how to turn right but
 A) 0 B) 1006 C) 1007 D) 2013 E) It is impossible to determine. cannot turn left. What is the smallest number of turns he
 must make in order to get from A to B (see the picture),
29. Starting with a list of three numbers, the changesum procedure creates a new list starting in the direction of the arrow?
 A) 3 B) 4 C) 6 D) 8 E) 10
 by replacing each number by the sum of the other two. For example, from f3; 4; 6g
 changesum gives f10; 9; 7g and a new changesum leads to f16; 17; 19g. If we begin
 5. The sum of the ages of Ann, Bob and Chris is 31 years.
 with the list f20; 1; 3g, what is the maximum dierence between two numbers of the list
 after 2013 consecutive changesums? What will the sum of their ages be in three years time?
 A) 1 B) 2 C) 17 D) 19 E) 2013 A) 32 B) 34 C) 35 D) 37 E) 40
30. Alice forms 4 identical numbered cubes using the net shown. She then
 6. What digit must be placed in all three boxes  ·  = 176, in order to make the
 glues them together to form a 2 × 2 × 1 block, as shown. Only faces with multiplication work?
 identical numbers are glued together. Alice then nds the total of all the A) 6 B) 4 C) 7 D) 9 E) 8
 numbers on the surface of the block. What is the largest total that Alice
 can get?
 7. Michaels father eats an apple every 15 minutes. He ate his rst apple at 11:05. What
 A) 66 B) 68 C) 72 D) 74 E) 76
 time did he eat his fourth apple?

c 2013 Keng©uros konkurso organizavimo komitetas A) 11:40 B) 11:50 C) 11:55 D) 12:00 E) 12:05