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IKMC 2012 - Grades 7-8 - Self-study

Question 1

Four chocolate bars cost 6 EUR more than one chocolate bar. What is the cost of one chocolate bar?
  1. 1 EUR
  2. 2 EUR
  3. 3 EUR
  4. 4 EUR
  5. 5 EUR

Question 3

A watch is placed face up so its minute hand points north-east. How many minutes pass before it first points north-west?
  1. 45
  2. 40
  3. 30
  4. 20
  5. 15

Question 4

Mary has scissors and five cardboard letters. She cuts each letter exactly once along a straight line to make as many pieces as possible. Which letter falls apart into the most pieces?
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Question 5

A dragon has five heads. Every time one head is chopped off, five new heads grow. Six heads are chopped off one by one. How many heads remain?
  1. 25
  2. 28
  3. 29
  4. 30
  5. 35

Question 6

In which expression can every occurrence of 8 be replaced by the same positive number other than 8 without changing the result?
  1. $(8+8)\div8+8$
  2. $8(8+8)\div8$
  3. $8+8-8+8$
  4. $(8+8-8)8$
  5. $(8+8-8)\div8$

Question 7

Each of the nine paths is 100 m long. Ann goes from A to B without using any path more than once. What is the longest possible route?

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  1. 900 m
  2. 800 m
  3. 700 m
  4. 600 m
  5. 400 m

Question 8

Choose one vertex of each triangle. In how many ways does the full straight line through the two vertices avoid crossing either triangle?

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  1. 1
  2. 2
  3. 3
  4. 4
  5. more than 4

Question 9

Werner folds paper as shown and makes two straight cuts, then opens it. Which shape cannot result?

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Question 10

The cuboid consists of four single-colour pieces, each made of four cubes. What is the shape of the white piece?

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Question 11

Using digits 1,2,3,4,5,6,7,8 exactly once, Kanga makes two four-digit numbers with the smallest possible sum. What is that sum?
  1. 2468
  2. 3333
  3. 3825
  4. 4734
  5. 6912

Question 12

Mrs Gardner makes the rectangular pea bed square by lengthening one side by 3 m. The strawberry area decreases by 15 m². What was the original pea-bed area?

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  1. 5 m²
  2. 9 m²
  3. 10 m²
  4. 15 m²
  5. 18 m²

Question 13

Barbara fills the three empty cells. The first three numbers must sum to 100, the middle three to 200, and the last three to 300. What goes in the middle cell?

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  1. 50
  2. 60
  3. 70
  4. 75
  5. 100

Question 15

Four cards bear respectively the phrases “divisible by 7”, “prime”, “odd”, “greater than 100”, and the numbers 2,5,7,12 in some order on the reverse. Every phrase is false for its card’s number. Which number is with “greater than 100”?
  1. 2
  2. 5
  3. 7
  4. 12
  5. impossible to determine

Question 16

Three equal small equilateral triangles are removed from the corners of an equilateral triangle of side 6 cm. Their total perimeter equals the remaining hexagon’s perimeter. What is their side length?

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  1. 1 cm
  2. 1.2 cm
  3. 1.25 cm
  4. 1.5 cm
  5. 2 cm

Question 17

Mice steal pieces of cheese. Each steals a different positive number less than 10, and no mouse steals exactly twice as many as another. What is the largest number of mice?
  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 18

A moving walkway is 500 m long and moves at 4 km/h. Ann and Bill step on together. Ann walks at 6 km/h on the walkway; Bill stands still. When Ann reaches the end, how far ahead of Bill is she?
  1. 100 m
  2. 160 m
  3. 200 m
  4. 250 m
  5. 300 m

Question 19

A magical square starts with side 8 cm. Each true statement shortens every side by 2 cm; each lie doubles its perimeter. It makes two true and two false statements in some order. What is its largest final perimeter?
  1. 28
  2. 80
  3. 88
  4. 112
  5. 120

Question 20

A cube rolls along the numbered squares 1,2,3,4,5,6,7 in order. Which two positions have the same bottom face?

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  1. 1 and 7
  2. 1 and 6
  3. 1 and 5
  4. 2 and 7
  5. 2 and 6