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IKMC 2009 - Grades 5-6

Question 1

Where is the kangaroo?

Question illustration
  1. In the circle and in the triangle but not in the square.
  2. In the circle and in the square but not in the triangle.
  3. In the triangle and in the square but not in the circle.
  4. In the circle but in neither the square nor the triangle.
  5. In the square but in neither the circle nor the triangle.

Question 2

Which of the following numbers is even?
  1. $2009$
  2. $2+0+0+9$
  3. $200-9$
  4. $200\times9$
  5. $200+9$

Question 3

How many natural numbers lie between 2.009 and 23.03?
  1. 20
  2. 21
  3. 22
  4. 23
  5. More than 23

Question 4

On the board there was a correct addition but one digit was erased, as shown. Which digit is the missing one?

Question illustration
  1. 2
  2. 4
  3. 5
  4. 7
  5. 8

Question 5

A bridge is being built over a 120m wide river. One quarter of the bridge continues on land on the left bank, another quarter continues on land on the right bank. How long is the bridge?
  1. 150m
  2. 180m
  3. 210m
  4. 240m
  5. 270m

Question 6

In front of me there are three boxes: one white, one red and one green. In one box there is a chocolate bar, in another an apple and the last one is empty. The chocolate bar is in either the white or red box. The apple is in neither the white nor the green box. In which box is the chocolate bar?
  1. White
  2. Red
  3. Green
  4. Red or green
  5. Not possible to answer.

Question 7

How many faces does the shown object (a prism with a hole) have?

Question illustration
  1. 3
  2. 5
  3. 6
  4. 8
  5. 12

Question 8

The diagram shows squares of different sizes. The side length of the smallest square is 20cm. What is the length of the bold line?

Question illustration
  1. 380cm
  2. 400cm
  3. 420cm
  4. 440cm
  5. 1680cm

Question 9

The different digits are built using sticks as shown. The “weight” of a number is the number of sticks used to build it. What is the weight of the heaviest two digit number?

Question illustration
  1. 10
  2. 11
  3. 12
  4. 13
  5. 14

Question 10

In a park, there are some cats and dogs. The number of cat feet is twice the number of dog noses. The number of cats is ... the number of dogs.
  1. twice
  2. half
  3. the same as
  4. a quarter of
  5. a sixth

Question 11

Which of the following is made using more than one piece of string?

Question illustration
  1. I, III, IV and V
  2. III, IV and V
  3. I, III and V
  4. All
  5. None of these answers.

Question 12

The quadrilateral shown in the figure has the following side lengths: $AB=11$, $BC=7$, $CD=9$ and $DA=3$. The angles at $A$ and $C$ are right angles. What is the area of the quadrilateral?

Question illustration
  1. 30
  2. 44
  3. 48
  4. 52
  5. 60

Question 13

In a dance group, there are 39 boys and 23 girls. Every week 6 more boys and 8 more girls join the group. After a few weeks there will be the same number of boys as girls in the dance group. How many boys and girls, in total, will there be in the dance group at that time?
  1. 144
  2. 154
  3. 164
  4. 174
  5. 184

Question 14

Two rectangles with sizes $8\times10$ and $9\times12$ overlap, as shown in the figure. The area of the dark grey part is 37. What is the area of the light grey part?

Question illustration
  1. 60
  2. 62
  3. 62.5
  4. 64
  5. 65

Question 15

What is the minimum number of digits that must be removed from the number 12323314, so that the resulting number is the same when read from either left to right or right to left?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 16

The “tower” in the diagram is made up of a square, a rectangle and an equilateral triangle. Those three shapes have the same perimeter. The side length of the square is 9cm. What is the width (indicated in the diagram) of the rectangle?

Question illustration
  1. 4cm
  2. 5cm
  3. 6cm
  4. 7cm
  5. 8cm

Question 17

We want to build a box with the measurements $40\times40\times60$ using all identical cubes. What is the minimum number of cubes needed?
  1. 6
  2. 12
  3. 96
  4. 1200
  5. 96000

Question 18

Today is Sunday, Francis starts reading a 290 page book. On Sundays he reads 25 pages and on all other days he reads 4 pages, with no exception. How many days does it take him to read the entire book?
  1. 5
  2. 46
  3. 40
  4. 35
  5. 41

Question 19

Andreas, Vasilis, Yiannis and Demetris have books in their bags. One of them has one book in his bag, another one has two, another has three and the last one has four. Andreas, Vasilis and Demetris together have 6 books in their bags. Vasilis and Yiannis together have 6 books in their bags. Vasilis has fewer books in his bag than Andreas. Who has only one book in his bag?
  1. Andreas
  2. Vasilis
  3. Yiannis
  4. Demetris
  5. We cannot find it.

Question 20

Helen has 18 equally sized squares. She places them side by side in order to form full rectangles. How many different rectangles can she make? (She has to use all the squares.)
  1. 1
  2. 2
  3. 3
  4. 5
  5. 10