Đề thi Toán Kangaroo năm 2015 Cấp độ Benjamin, Khối 5-6

 Lietuvos Respublikos ˇsvietimoir mokslo ministerija VU Matematikos ir informatikos fakultetas
23. The sum of four natural numbers is 39. The product of two of them equals 80, the
 Keng¯uros organizavimo komitetas Leidykla TEV VU Matematikos ir informatikos institutas
 product of the rest two is also equal to 80. The largest of these four numbers is
 A) 8 B) 10 C) 16 D) 20 E) 25
24. The number 100 is multiplied either by 2 or by 3, then the result is increased either by KANGAROO 2015
 1 or by 2, and then the new result is divided either by 3 or by 4. The final result is a
 natural number. What is this final result?
 A) 50 B) 51 C) 67 D) 68 E) 76
25. In a 4-digit number ABCD, the digits A, B, C, and D are in increasing order from left Time allowed: 75 minutes Benjamin
 to right. What is the largest possible difference BD − AC of the 2-digit numbers BD Calculators are not permitted 5--6 grades
 and AC?
 A) 86 B) 61 C) 56 D) 50 E) 16 Questions for 3 points
 1. Which figure has one half shaded?
26. Mary writes a number on each face of a cube. Then, for each
 vertex, she adds the numbers on the three faces which share that
 vertex (for example, for vertex B she adds the numbers on faces
 BCDA, BAEF and BF GC). The numbers computed by Mary A) B) C) D) E)
 for vertices C, D and E are 14, 16 and 24, respectively. What
 number does she compute for vertex F ?
 2. My umbrella has KANGAROO written on top. It is shown in A
 A) 15 B) 19 C) 22 D) 24 E) 26 G R
 the picture. Which of the following pictures does not show my
 N O
 A
 umbrella? O
27. Jane is travelling by train. Each coach in the train has the same number of K
 compartments. Jane sat in the 7th coach in the 50th compartment from the engine.
 O
 A G
 How many compartments are there in each coach? R
 G
 K
 O A
 A) 7 B) 8 C) 9 D) 10 E) 12 N
 A) B) C) D) E)
28. In how many ways can you place the 3 kangaroos in 3 different cells so that no 2
 kangaroos are neighbours?
 3. Sam painted the 9 squares with the colours black, white and grey as shown.
 At least how many squares does he need to repaint so that no two squares
 with a common side have the same colour?
 A) 2 B) 3 C) 4 D) 5 E) 6
 A) 7 B) 8 C) 9 D) 10 E) 11
 4. There are 10 ducks. 5 of these ducks lay an egg every day. The other 5 lay an egg every
29. Four points lie on a line. The distances between them are, in increasing order: 2, 3, k, second day. How many eggs do the 10 ducks lay in a period of 10 days?
 11, 12, 14. What is k? A) 75 B) 60 C) 50 D) 25 E) 10
 A) 5 B) 6 C) 7 D) 8 E) 9
 5. The figure shows a board where each small square has an area of 4 cm2. What
30. Basil used small cubes with side 1 to construct a cube with side 4. After that, he painted is the length of the thick black line?
 3 faces of the big cube red and the other 3 faces blue. After he finished, there was no A) 16 cm B) 18 cm C) 20 cm D) 21 cm E) 23 cm
 small cube with 3 red faces. How many small cubes have both red and blue faces?
 A) 0 B) 8 C) 12 D) 24 E) 32
 6. Which of the following fractions is smaller than 2?
 19 20 21 22 23

c 2015 Keng¯uros konkurso organizavimo komitetas A) 8 B) 9 C) 10 D) 11 E) 12