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IKMC 2009 - Grades 5-6 - Self-study

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?

Source notation: these middle dots are decimal points (2.009 and 23.03), not multiplication signs. The printed German “und” means “and”.
  1. 20
  2. 21
  3. 22
  4. 23
  5. More than 23 (source: mehr als 23)

Question 4

What is the minimum number of digits that must be removed from 12323314 so that the resulting number reads the same from left to right and right to left?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 5

There are three boxes, one white, one red and one green. One contains a chocolate bar, another an apple and one is empty. The chocolate 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?
  1. White
  2. Red
  3. Green
  4. Red or green
  5. Not possible to answer

Question 6

How many faces has the object shown? (Prism with a hole.)

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

Question 7

The diagram shows squares of different sizes. The side length of the smallest square is 20 cm. How long is the black line?

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

Question 8

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

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

Question 9

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

Question 10

In a park there are cats and dogs. The number of cats’ feet is twice the number of dogs’ noses. The number of cats is … of the number of dogs.
  1. Double
  2. Half
  3. The same
  4. A quarter
  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 has side lengths AB=11, BC=7, CD=9 and DA=3. The angles at A and C are right angles. What is its area?

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

Question 13

A dance group has 39 boys and 23 girls. Every week 6 more boys and 8 more girls join. After a few weeks there are equal numbers of boys and girls. How many boys and girls are in the group then?
  1. 144
  2. 154
  3. 164
  4. 174
  5. 184

Question 14

The tower is made of a square, a rectangle and an equilateral triangle. All three shapes have the same perimeter. The square’s side is 9 cm. How long is the indicated side of the rectangle?

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

Question 15

We want to build a box measuring 40×40×60 using identical cubes. What is the minimum number of cubes needed?
  1. 6
  2. 12
  3. 96
  4. 1200
  5. 96000

Question 16

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

Question 17

Two rectangles measuring 8×10 and 9×12 overlap. The dark grey area 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 18

Eight cards numbered 1 to 8 are placed in boxes A and B with equal sums. Exactly 3 cards are in A. Which statement is definitely true?
  1. Three cards in B are odd.
  2. Four cards in B are even.
  3. Card 1 is not in B.
  4. Card 2 is in B.
  5. Card 5 is in B.

Question 19

Andrea, Branimir, Celestin and Doris rank 1 to 4 in a fencing tournament. Andrea’s, Branimir’s and Doris’ ranks sum to 6. Branimir’s and Celestin’s ranks also sum to 6. Who won, if Branimir did better than Andrea?
  1. Andrea
  2. Branimir
  3. Celestin
  4. Doris
  5. It cannot be determined

Question 20

The object shown has 6 triangular faces. Each vertex has a number (two are shown). The sums at the three vertices of every triangular face are equal. What is the sum of all 5 numbers?

Question illustration
  1. 9
  2. 12
  3. 17
  4. 18
  5. 24