Đề thi Toán Kangaroo năm 2020 Cấp độ Benjamin, Khối 5-6

 Lietuvos Respublikos §svietimo, mokslo ir sporto ministerija Vilniaus universitetas
22. We call a -digit number nice if its middle digit is greater than the sum of its rst and
 3 Keng©uros konkurso organizavimo komitetas Lietuvos matematikudraugija
 last digits. What is the largest possible number of consecutive nice 3-digit numbers?
 A) 5 B) 6 C) 7 D) 8 E) 9
23. Nine tokens are laid on a table. Tokens are black on one side and white on the other.
 Initially, four tokens have the black side upwards. In each turn you have to ip three
 tokens. What is the least number of turns you need to have all tokens showing the same KANGAROO 2020
 colour?
 A) 1 B) 2 C) 3 D) 4 E) 5
24. Which of the following options will denitely balance the third scale? Time allowed: 75 minutes Benjamin
 Calculators are not permitted 5--6 grades
 ?
 Questions for 3 points
 1. A large square is made up of smaller white and grey squares. What does
 A) B) C) D) E) the large square look like if the colours of the white and grey squares are
 interchanged?
25. A test consists of 12 problems, which are distributed among the members of a grading
 team in such a way that each problem is graded by two members and each member
 grades exactly three dierent problems. How many members are there in the grading
 A) B) C) D) E)
 team? 2. As Amira is walking from Atown to Betown she passes the ve signposts shown. One of
 A) 6 B) 8 C) 12 D) 18 E) 24 them is incorrect. Which one?
26. Three small squares are drawn inside a larger square as shown on the
 right. What is the length of the line marked with a question mark? 22 Atown 2 km Atown 3 km Atown 5 km Atown 6 km Atown 9 km
 ? 15
 A) 17 B) 17.5 C) 18 D) 18.5 E) 19
 Betown 9 km Betown 8 km Betown 6 km Betown 7 km Betown 2 km
 28
27. Squire Hlawa agreed to serve knight Zbyszko one year for 180 ducats and a sword.
 A) B) C) D) E)
 However, after ve months Hlawa dissmised his service. For the time served Zbyszko
 3. Pictures below show ve pieces of transparent lm. Flora folded one of them along
 gave him 40 ducats and a sword. How much is the sword worth?
 the dotted lines and got the result shown on the right. Which piece did Flora fold?
 A) 140 ducats B) 35 ducats C) 105 ducats D) 75 ducats E) 60 ducats
28. Gabija bought a bouquet consisting of 10 owers: 4 roses, 3 tulips, 2 carnations and
 1 lily. Four owers were red, three were white, two pink and one yellow. None of the
 owers were the same (by species and colour). Which ower was not in the bouquet? A) B) C) D) E)
 A) White tulip B) Red lily C) Red rose D) Pink carnation E) Yellow rose 4. Mikas wants to bake 24 muns for his birthday party. To bake six muns two eggs are
29. Magnus has to play 15 games in a chess tournament. At some point during the needed. Eggs are sold in boxes of six. How many boxes does Mikas need to buy?
 tournament he has won half of the games he has played, he has lost one third of the A) 1 B) 2 C) 3 D) 4 E) 8
 1 1 1 1 1
 games he has played and two have ended in a draw. How many games has Magnus still 5. A dog and a cat run in the park along the path marked by the 1
 to play? thick black line. The dog starts from P at the same time as the
 A) 2 B) 3 C) 4 D) 5 E) 6 cat starts from K. The dogs runs three times as fast as the cat.
 At which point do they meet?
30. Don builds a pyramid with balls. The square base consists of A) At A B) At B C) At C D) At D E) At E
 3×3 balls (see pic. 1). The middle layer has 2×2 balls, and there
 is one ball at the top (see pic. 2). There is glue at each contact 6. Kim has several chains of length 5 and of length 7. By joining some of these chains one
 point between two balls. How many glue points are there? after the other, Kim has created a longer chain. Which number cannot be the length of
 A) 20 B) 24 C) 28 D) 32 E) 36 Pic. 1 Pic. 2 this chain?
 A) 10 B) 12 C) 13 D) 14 E) 15

c 2020 Keng©uros konkurso organizavimo komitetas