Đề thi Toán Kangaroo năm 2017 Cấp độ Benjamin, Khối 5-6
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Lietuvos Respublikos §svietimoir mokslo ministerija VU Matematikos ir informatikos fakultetas 23. 8 kangaroos stood in a line as shown in Picture 1. At some point, two kangaroos standing Keng©uros konkurso organizavimo komitetas VU Matematikos ir informatikos institutas side by side and facing each other exchanged places by jumping past each other (see Lietuvos matematikudraugija Picture 2). This was repeated until no further jumps were possible. Picture 1 KANGAROO 2017 2 0 1 7 Picture 2 How many exchanges were made? Time allowed: 75 minutes 2 0 1 7 Benjamin A) 2 B) 10 C) 12 D) 13 E) 16 2 7 1 0 Calculators are not permitted 2 0 1 7 5--6 grades 24. After having driven 5 of the distance, there is 54 km left. What is the total distance? Questions for 3 points 2 7 1 0 0 1 2 7 8 2 0 1 7 A) 120 km B) 140 km C) 144 km D) 160 km E) 192 km 2 7 1 0 0 1 2 7 1 0 2 7 1. Four cards lie in a row. Which row of cards can you not obtain if you 25. How many three-digit numbers have the product of their digits less than 2? 2 0 1 7 2 0 1 7 can only swap two cards?2 7 1 0 0 1 2 7 1 0 2 7 0 2 1 7 A) 1 B) 181 C) 180 D) 171 E) 172 2 7 1 0 0 1 2 7 1 0 2 7 0 2 1 7 2 0 7 1 26. A bag contains only red marbles and green marbles. For any 5 marbles we pick, at least A) B) C) D) E) 2 7 1 0 one is red; for any 6 marbles we pick, at least one is green. What is the largest number 2. A y0 has1 2 67 legs, a spider1 0 has2 8.7 Together,0 32 ies1 7 and 2 spiders2 0 have7 1 as many0 legs1 2 as7 9 of marbles that the bag can contain? chickens1 0 and2 7 ... 0 2 1 7 2 0 7 1 1 0 2 7 A) 11 B) 10 C) 9 D) 8 E) 7 A) 2 cats B) 3 cats C) 4 cats D) 5 cats E) 6 cats 0 2 1 7 2 0 7 1 27. Ala likes even numbers, Beata likes numbers divisible by 3, Celina likes numbers divisible 0 2 1 7 3. Alice has 4 pieces of this shape: . Which picture can she not make from these 4 by 5. Each of these three girls went separately to a basket containing 8 balls with numbers 2 0 7 1 2 0 7 1 1 written on them, and took all the balls with numbers she likes. It turned out that Ala pieces? 1 collected balls with numbers 32 and 52, Beata 24, 33 and 45, Celina 20, 25 and 35. In what order did the girls approach the basket? A) B) C) 1D) E) A) Ala, Celina, Beata B) Celina, Beata, Ala C) Beata, Ala, Celina 1 D) Beata, Celina, Ala E) Celina, Ala, Beata 4. Kalle knows that 1111 1111 = 1234321. How much is 1111 2222? A) 3456543 B)1 2345432× C) 2234322 D) 2468642 E)×4321234 28. John wants to write a natural number in each box in the diagram 1 such that each number above the bottom row is the sum of the 5. On a planet there are 10 islands and 12 bridges. All bridges two numbers in the boxes immediately underneath. What is the are open for trac right now. What is the smallest number A largest number of odd numbers that John can write? of bridges that must be closed in order to stop the trac B A) 4 B) 5 C) 6 D) 7 E) 8 between A and B? 29. Julia has four dierent coloured pencils and wants to use some A) 1 B) 2 C) 3 D) 4 E) 5 or all of them to paint the map of an island divided into four 6. Jane, Kate and Lynn go for a walk. Jane walks up front, Kate walks in the middle and nations, as in the picture. If two nations with a common border Lynn walks behind. Jane weighs 500 kg more than Kate. Kate weighs 1000 kg less than cannot have the same colour, in how many ways can she colour Lynn. Which of the following pictures shows Jane, Kate and Lynn in the right order? the map of the island? A) 12 B) 18 C) 24 D) 36 E) 48 A) B) C) 30. In each cell of a 6 6 board there is a lamp. We say that two lamps in this board are neighbors if they× lie in cells with a common side. Initially some lamps are lit and, each minute, every lamp having at least two lit neighboring lamps is lit. What is the D) E) minimum number of lamps that need to be lit initially, in order to ensure that, at some 7. A special dice has a number on each face. The sums of the numbers on opposite faces time, all lamps will be lit? are all equal. Five of the numbers are 5, 6, 9, 11 and 14. What number is on the sixth A) 4 B) 5 C) 6 D) 7 E) 8 face? c 2017 Keng©uros konkurso organizavimo komitetas A) 4 B) 7 C) 8 D) 13 E) 15
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