Đề thi Toán Kangaroo năm 2015 Cấp độ Minor, Khối 3-4

 Lietuvos Respublikos ˇsvietimoir mokslo ministerija VU Matematikos ir informatikos fakultetas
18. We have three transparent sheets with the
 Keng¯uros organizavimo komitetas Leidykla TEV VU Matematikos ir informatikos institutas
 following patterns. We can only rotate the three
 sheets without turning over. Then we put them
 exactly on top of each other. What is the
 maximum possible number of black squares seen KANGAROO 2015
 in the obtained square if looked at from above?
 A) 5 B) 6 C) 7 D) 8 E) 9
19. The numbers 2, 3, 5, 6 and 7 are written in the squares of the cross
 (see fig.) so that the sum of the numbers in the row is equal to the sum
 of the numbers in the column. Which of the numbers can be written
 Time allowed: 75 minutes Minor
 in the center square of the cross? Calculators are not permitted 3--4 grades
 A) Only 3 B) Only 5 C) Only 7 D) 5 or 7 E) 3, 5 or 7
 Questions for 3 points
20. Peter has ten balls, numbered from 0 to 9. He distributed
 these balls among three friends: John got three balls, George 01234 1.
 four and Ann three. Then he asked each of his friends to
 multiply the numbers on the balls they got and the results 56789
 were: 0 for John, 72 for George and 90 for Ann. What is the
 sum of the numbers on the balls that John received? A) 6 B) 7 C) 8 D) 10 E) 15
 A) 11 B) 12 C) 13 D) 14 E) 15
21. Three ropes are laid down on the floor as shown. You can make one big, 2. Eric had 10 equal metal strips. He has screwed pairs of them together into five long
 complete loop with three other pieces of rope. Which of the ropes shown strips. Which strip is the longest?
 will give you one big loop?
 A) B) C) D) E)
22. During 3 days Joy the cat was catching mice. Each next day Joy caught 2 mice more
 than in the previous day. On the third day Joy has caught twice as many mice as on
 the first day. In total, how many mice did Joy catch during the three days?
 A) 12 B) 15 C) 18 D) 20 E) 24
 A) A B) B C) C D) D E) E
23. The Kangaroo jumps from circle S along the line to the next 3. Which number is hidden behind the square?
 circle in one jump. It is not allowed to jump into any circle A) 2 B) 3 C) 4 D) 5 E) 6
 more than once. In how many different ways, by taking only S F
 4 jumps, can the Kangaroo reach circle F?
 9
 A) 3 B) 4 C) 5 D) 6 E) 7 8 1
 4. We start drawing a line at every second dot on the circle until we are 7 2
24. Anna, Berta, Charlie, David and Elisa were baking cookies during the weekend, on back at the number 1. The first two lines are drawn already. What figure
 Saturday and Sunday. Over the whole weekend Anna made 24 cookies, Berta 25, Charlie do we get? 6 3
 5 4
 26, David 27 and Elisa 28. After the whole weekend one of them had twice as many 9 9 9 9 9
 cookies as after Saturday, one 3 times, one 4 times, one 5 times and one 6 times as many. 8 1 8 1 8 1 8 1 8 1
 Who baked the most cookies on Saturday? 7 2 7 2 7 2 7 2 7 2
 A) Anna B) Berta C) Charlie D) David E) Elisa
 6 3 6 3 6 3 6 3 6 3

c 2015 Keng¯uros konkurso organizavimo komitetas A) 5 4 B) 5 4 C) 5 4 D) 5 4 E) 5 4