Đề thi Toán Kangaroo năm 2005 Cấp độ Minor, Benjamin, Cadet, Junior, Student

 Minor (3and4grades) 105
 Questions of Kangaroo 2005
 MINOR (grades 3 and 4 )
3-POINT QUESTIONS
 M1. A butterfly sat down on a correctly solved
 exercise. What number is the butterfly co- 2005 – 205= 1300 +
 vering?
 A 250 B 400 C 500 D 910 E 1800
 M2. At noon the minute hand of a clock is in the position shown on the
 left and after the quarter of an hour – in the position shown on the
 right. Which position the minute hand will take after seventeen
 quarters from the noon?
 ABCDE
 M3. Erika bought cookies, each of them costs 3 euros. She gave 10 euros and obtained 1 euro
 of the change. How many cookies did Erika buy?
 A 2 B 3 C 4 D 5 E 6
 M4. In the diagram every of the eight kangaroos can jump to any empty
 square. What is the least number of kangaroos that must jump so
 that each row and each column have exactly two kangaroos?
 A 4 B 3 C 2 D 1 E 0
 M5. Helga lives in her home with father, mother, brother and also one dog, two cats, two parrots
 and four goldfishes. How many legs do they have altogether?
 A 22 B 40 C 28 D 32 E 24
 M6. John has a chocolate tablet consisting of square pieces of 11 cm
 1cm× 1 cm. He has eaten already some pieces in a corner
 (see the picture). How many pieces John still have?
 A 66 B 64 C 62 D 60 E 58 4cm
 6cm
 8cm
 M7. Daniel wants to fill a tank for his turtle with 4 buckets of water. At each trip he fills one
 bucket from a faucet but when walking to the tank he spills one half of the water. How
 many trips from the faucet to the tank does he have to do?
 A 4 B 5 C 6 D 7 E 8
 M8. What is the smallest possible number of children in a family if each child has at least one
 brother and one sister?
 A 2 B 3 C 4 D 5 E 6 Minor (3and4grades) 107
M18. You can make only one rectangle with the perimeter
 consisting of 6 matches (see the picture). How many
 different rectangles with the perimeter consisting of
 14 matches can you compose?
 A 2 B 3 C 4 D 6 E 12
M19. Each of seven boy paid exactly the same amount of money for the excursion. The total sum
 of the money they paid is a three-digital number 3∗0. What is the digit in the middle?
 A 3 B 4 C 5 D 6 E 7
M20. Two traffic signs mark the bridge in my vil-
 lage. These marks indicate the maximum width and
 the maximum possible weight. Which one of the 325 4300
 following trucks is allowed to cross that bridge? cm kg
 A The one 315 cm wide and weighing 4307 kg
 B The one 330 cm wide and weighing 4250 kg
 C The one 325 cm wide and weighing 4400 kg
 D The one 322 cm wide and weighing 4298 kg
 E No one of these
M21. The figure shows a rectangular garden with dimen-
 sions 16 m and 20 m. The gardener has planted six
 identical flowerbeds (they are gray in the diagram).
 What is the perimeter (in metres) of each of the flo-
 werbeds?
 A 20 B 22 C 24 D 26 E 28 16 m
 20 m
M22. Mike has chosen a three-digit number and a two-digit number. Find the sum of these
 numbers if their difference equals 989.
 A 1000 B 1001 C 1009 D 1010 E 2005
M23. Five cards are lying on the table in the order 5, 1, 4,
 3, 2. You must get the cards in the order 1, 2, 3, 4, 5 1 4 3 2
 5. Per move, any two cards may be interchanged.
 How many moves do you need at least?
 A 2 B 3 C 4 D 5 E 6
 1 2 3 4 5
M24. Which of the following cubes has been folded out
 of the plan on the right?
 ABCDE Benjamin (grades 5 and 6 ) 109
 B10. Which of the following cubes has been folded out
 of the plan on the right?
 ABCDE
4-POINT QUESTIONS
 B11. How many two-digit numbers have different odd digits?
 A 15 B 20 C 25 D 30 E 50
 B12. Mowgli needs 40 minutes to walk from home to the sea by foot and to return home on an
 elephant. When he rides both ways on an elephant, the journey takes 32 minutes. How long
 would the journey last, if he would walk both directions?
 A 24 minutes B 42 minutes C 46 minutes D 48 minutes E 50 minutes
 B13. In the diagram you see the rectangular garden of Green’s 2m
 2
 family. It has an area of 30 m and is divided into three Veg-
 rectangular parts. One side of the part where flowers are
 growing has a length of 2 m. Its area is 10 m2. The part etables
 with strawberries has one side of length 3 m. What is the Straw-
 Flowers
 area of the part where vegetables are growing? berries 3m
 A 4m2 B 6m2 C 8m2 D 10 m2 E 12 m2
 B14. How many hours are there in half the third of the quarter of a day?
 1 1
 A 1 B 2 C 3 D 3 E 2
 B15. In the diagram, the five circles have the same radii and
 touch as shown. The square joins the centres of the four
 outer circles. The ratio of the area of the shaded part of all
 five circles to the area of the unshaded parts of the circles
 is:
 A 1:3 B 2:3 C 2:5 D 1:4 E 5:4
 B16. If the sum of five consecutive positive integers is 2005, then the largest of these numbers is:
 A 401 B 403 C 404 D 405 E 2001
 B17. How many different factors (including 1 and 100) does 100 have?
 A 3 B 6 C 7 D 8 E 9
 B18. A frame of a rectangular picture is made from planks of
 equal width. What is the width of these planks (in centi-
 metres) if the outside perimeter of the frame is 8 cm more
 than the inside perimeter?
 A It depends on the dimensions of the picture
 B 8 C 4 D 2 E 1
 B19. There are seven squares in the picture. How many more
 triangles than squares are there in the picture?
 A 1 B 2 C 3 D 4 E 0 Cadet (grades 7 and 8) 111
 B28. To the series of letters AGKNORU (in alphabetical order) is associated a series of different
 digits, placed in increasing order. What is the biggest number one can associate to the word
 KANGOUROU?
 A 987654321 B 987654354 C 436479879 D 597354354 E 536479879
 B29. The lift can not carry more than 150 kg. Four friends weigh: 50 kg, 75 kg, 80 kg and 85 kg.
 At least how many runs of the lift are necessary to carry the four friends to the highest floor?
 A 1 B 2 C 7 D 4 E 3
 B30. Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the
 far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is
 not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of
 Dolly, but not necessarily next to her. Who is sitting at the far right end?
 A Cannot be determined B Dolly C Sally D Elly E Kelly
 CADET (grades 7 and 8)
3-POINT QUESTIONS
 C1. In the diagram every of the eight kangaroos can jump to
 any empty square. What is the least number of kangaroos
 that must jump so that each row and each column have
 exactly two kangaroos?
 A 0 B 1 C 2 D 3 E 4
 C2. How many hours are there in half the third of the quarter of a day?
 1 1
 A 3 B 2 C 1 D 2 E 3
 C3. The diagram shows a cube with sides of length 12 cm. An
 ant moves on the cube surface from point M to point N M
 following the route shown. Find the length of ant’s path.
 A It is impossible to determine
 B 40 cm C 48 cm D 50 cm E 60 cm
 N
 C4. Two girls and three boys ate 16 helpings of ice-cream together. Each boy ate twice as much
 as each girl. How many helpings will be eaten by three girls and two boys with the same
 passion for ice-cream?
 A 12 B 13 C 14 D 16 E 17
 C5. At Sobieski School, 50% of the students have bikes. Of the students who have bikes,
 30% have rollerblades. What percent of students of Sobieski School have both a bike and
 rollerblades?
 A 15% B 20% C 25% D 40% E 80%
 C6. In triangle ABC, the angle at A is three times the size of that at B and half the size of the
 angle at C. What is the angle at A?
 A 30◦ B 36◦ C 54◦ D 60◦ E 72◦ Cadet (grades 7 and 8) 113
 C15. Which of the following cubes has been folded out of
 the plan on the right?
 ABCDE
 C16. From noon till midnight Clever Cat is sleeping under the oak tree, and from midnight till
 noon he is telling stories. There is a poster on the oak tree saying: “Two hours ago Clever
 Cat was doing the same as he will be doing after an hour sharp.” How many hours a day
 the poster tells truth?
 A 6 B 12 C 18 D 3 E 21
 C17. The diagram shows an equilateral triangle and a regular
 pentagon. What is the size of the angle marked x?
 A 124◦ B 128◦ C 132◦ D 136◦ E 140◦
 x
 C18. Mike has chosen a three-digit number and a two-digit number. Find the sum of these
 numbers if their difference equals 989.
 A 1001 B 1010 C 2005 D 1000 E 1009
 C19. What is 1 + 2 − 3 − 4 + 5 + 6 − 7 − 8 +···+2001 + 2002 − 2003 − 2004 + 2005?
 A 0 B 2005 C 2004 D 1 E −4
 C20. For a positive integer n, by its length we mean the number of factors in the representation
 of n as a product of prime numbers. For example, the length of the number 90 = 2 · 3 · 3 · 5
 is equal to 4. How many odd numbers less than 100 have length 3?
 A 2 B 3 C 5 D 7 E Another answer
5-POINT QUESTIONS
 C21. Two rectangles ABCD and DBEF are shown in the figure. F
 What is the area (in cm2) of the rectangle DBEF?
 A 10 B 12 C 13 D 14 E 16 D C
 E
 3cm
 A 4cm B
 C22. Peter has a three-digit code lock. He has forgotten the code but he knows that all three digits
 are different, and that the first digit is equal to the square of the quotient of the second and
 third digit. How many combinations will Peter have to try in order to crack the code?
 A 1 B 2 C 3 D 4 E 8
 C23. How many two-digit numbers are more than trebled when their digits are reversed?
 A 6 B 10 C 15 D 22 E 33