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IKMC 2006 - Grades 7-8 - Self-study

Question 1

The contest Kangaroo in Europe has taken place every year since 1991. The 2006 contest is the:
  1. 15th
  2. 16th
  3. 17th
  4. 14th

Question 2

Calculate 20×(0+6)−(20×0)+6.
  1. 106
  2. 114
  3. 126
  4. 12

Question 3

O is the centre of a regular pentagon. What percentage of the pentagon is shaded?

Question illustration
  1. 20%
  2. 25%
  3. 30%
  4. 40%

Question 4

Fatima tells her grandchildren: “If I give each of you 2 toffees, I have 3 left. If I try to give each of you 3, I am 2 short.” How many grandchildren does she have?
  1. 3
  2. 4
  3. 5
  4. 6

Question 5

Which net folds into the cube with two holes shown?

Question illustration
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  2. Question illustration
  3. Question illustration
  4. Question illustration

Question 6

Of 2006 schoolchildren interviewed in Minsk, 1500 took part in Kangaroo and 1200 in Bear Cub. Six took part in neither. How many took part in both?
  1. 300
  2. 500
  3. 600
  4. 700

Question 7

A cube of edge 1 cm sits on a cube of edge 3 cm as shown. What is the surface area of the combined solid?

Question illustration
  1. $56\text{ cm}^2$
  2. $58\text{ cm}^2$
  3. $59\text{ cm}^2$
  4. $60\text{ cm}^2$

Question 8

A 12-litre container is $\frac34$ full. How many litres remain after 4 litres are poured out?
  1. 5
  2. 6
  3. 8
  4. 12

Question 9

Two sides of a triangle are each 7 cm long. The third side has integer length in centimetres. What is the greatest possible perimeter?
  1. 14
  2. 15
  3. 21
  4. 27

Question 10

An air temperature fell 10° in the night but has risen twice in the day and became the same. Find the night temperature of the air.

Original choices: A) 50; B) 40; C) 30; D) 20.
Editorial input note: enter the night temperature as a number, without the degree symbol. The printed choices may contain an error.

Question 11

If it is blue, it is round. If it is square, it is red. It is either blue or yellow. If it is yellow, it is square. It is either square or round. What follows?
  1. It is red and round
  2. It is a blue square
  3. It is blue and round
  4. It is yellow and round

Question 12

Three Tuesdays in a month fall on even dates. What day of the week was the 21st?
  1. Wednesday
  2. Thursday
  3. Friday
  4. Sunday

Question 13

Nizami saved 60% of the price of a tent. Ahmad saved 40% of the remaining price. Babar paid the rest, Rs.30. What was the tent price?
  1. 60 Rs
  2. 125 Rs
  3. 150 Rs
  4. 200 Rs

Question 14

On STAR 1, green spacemen have 2 arms, orange spacemen 3 and blue spacemen 5. There are equal numbers of green and orange spacemen and 10 more blue than green. They have 250 arms altogether. How many are blue?
  1. 15
  2. 20
  3. 30
  4. 40

Question 15

A kangaroo jumps 2 m using its left leg, 4 m using its right leg and 7 m using both legs. What is the least number of jumps needed for exactly 1000 m?
  1. 142
  2. 143
  3. 144
  4. 250

Question 16

Which number increases by 500% when squared?
  1. 5
  2. 6
  3. 7
  4. 10

Question 17

Raza and Ijaz drew a 4×4 square and marked the centres of the small squares. They added the obstacles shown. How many shortest paths from A to B go only horizontally or vertically from centre to centre and avoid all obstacles?

Question illustration
  1. 6
  2. 8
  3. 9
  4. 12

Question 18

Amna counts her fingers as shown. The first finger receives 1,9,17,… . What is the first number assigned to the finger that receives 2006?

Question illustration
  1. 1
  2. 2
  3. 3
  4. 4

Question 19

Complete the sentence correctly: “If your reflection looks at me, then …”

Question illustration
  1. you look at my reflection
  2. my reflection looks at you
  3. you look at me
  4. I look at your reflection

Question 20

One guava has as many seeds as 2 tangerines and 11 apples. Half a guava has as many seeds as 4 apples and 3 tangerines. How many apples have as many seeds as 100 tangerines?
  1. 25
  2. 50
  3. 75
  4. 100