Đề thi Toán Kangaroo năm 2014 Cấp độ Benjamin, Khối 5-6

 Lietuvos Respublikos ˇsvietimoir mokslo ministerija VU Matematikos ir informatikos fakultetas
23. Dan entered the numbers 1 to 9 in the cells of a 3 3 table. He began by
 Keng¯uros organizavimo komitetas Leidykla TEV VU Matematikos ir informatikos institutas
 placing the numbers 1, 2, 3 and 4 as shown in the× picture. It happened
 that for the number 5, the sum of the numbers in the adjacent cells
 (having a common side) is equal to 9. What is the sum of the numbers
 adjacent to the number 6? KANGAROO 2014
 A) 14 B) 15 C) 17 D) 28 E) 29
24. Trees grow on only side of Park Avenue. There are 60 trees in total. Every second tree
 is a maple, and every third tree is either a linden or a maple. The remaining trees are
 birches. How many birches are there?
 A) 10 B) 15 C) 20 D) 24 E) 30 Time allowed: 75 minutes Benjamin
 Calculators are not permitted 5--6 grades
25. Three equal rectangles are placed inside a square with side 24 cm, Questions for 3 points
 as shown in the diagram. What is the area of one rectangle?
 A) 24 cm2 B) 32 cm2 C) 36 cm2 D) 48 cm2 E) 72 cm2 1. 2014 is the current year. The sum of the digits of 2014 is equal to 7. After at least how
 many years the number of the year will have the sum of its digits equal to 7 again?
 A) 18 B) 36 C) 90 D) 9 E) 990
26. The king and his messengers are travelling from the castle to the summer palace at
 a speed of 5 km/h. Every hour, the king sends a messenger back to the castle, who
 2. A cake weights 900 g. Paul cuts it in 4 pieces. The biggest piece is as heavy as the 3
 travels at a speed of 10 km/h. What is the time interval between any two consecutive
 others weight altogether. What’s the weight of the biggest piece?
 messengers arriving at the castle?
 A) 250 g B) 300 g C) 400 g D) 450 g E) 600 g
 A) 30 min B) 60 min C) 75 min D) 90 min E) 120 min
 3. Two great rings, one grey, one white, are linked in each other. Peter, in
27. There were 3 one-digit numbers on the blackboard. Ali added them up, and got 15.
 front of the rings, sees the rings as in the picture. Paul is behind the
 Then he erased one of the numbers and wrote the number 3 in its place. Then Reza
 rings. What does he see?
 multiplied the three numbers on the blackboard and got 36. What are the possibilities
 for the number that Ali erased?
 A) Either 6 or 7 B) Either 7 or 8 C) Only 6 D) Only 7 E) Only 8
28. Rabbit Vasya loves cabbages and carrots. In a day, he eats either 9 carrots, or 2 cabbages, A) B) C) D) E)
 or 1 cabbage and 4 carrots. But some days he only eats grass. Over the last 10 days, 1 2
 Vasya ate a total of 30 carrots and 9 cabbages. On how many of these 10 days did he 4. In the addition on the right, some of the digits have been replaced by stars. ∗
 What is the sum of the missing digits? + 1 3
 eat only grass? 1 ∗ 4
 A) 0 B) 1 C) 2 D) 3 E) 10 ∗
 A) 0 B) 1 C) 2 D) 3 E) 4 3 0 9
 5. What is the difference of the smallest 5-digit number and the largest 4-digit number?
29. In Fabuland, every sunny day is immediately preceded by two consecutive rainy days.
 A) 1 B) 10 C) 1111 D) 9000 E) 9900
 Also, the fifth day after any rainy day is again rainy. It is sunny today. For at most how
 many consequtive days can we predict the weather with certainty?
 6. A square of perimeter 48 is cut into 2 pieces to make
 A) 1 day B) 2 days C) 4 days D) We cannot predict even one day ahead
 a rectangle (see picture). What is the perimeter of the
 E) We can predict the weather every day from here on
 rectangle?
 A) 24 B) 30 C) 48 D) 60 E) 72
30. Granny has 10 grandchildren. Alice is the eldest. One day, Granny notices that her
 grandchildren all have different ages. If the sum of her grandchildrens’ ages is 180, what 7. Katrin has 38 matches. She builds a triangle and a square, using all the matches. Each
 is the youngest Alice could be? side of the triangle consists of 6 matches. How many matches are in each side of the
 A) 19 B) 20 C) 21 D) 22 E) 23 square?

c 2014 Keng¯uros konkurso organizavimo komitetas A) 4 B) 5 C) 6 D) 7 E) 8