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IKMC 2017 - Grades 5-6 - Self-study

Question 1

Four cards lie in a row. Which row of cards can you not obtain if you can only swap two cards?

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Question 2

A fly has 6 legs, a spider has 8. Together, 3 flies and 2 spiders have as many legs as 9 chickens and … .
  1. 2 cats
  2. 3 cats
  3. 4 cats
  4. 5 cats
  5. 6 cats

Question 3

Alice has 4 pieces of the shape shown. Which picture can she not make from these 4 pieces?

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Question 4

Kalle knows that $1111\times1111=1234321$. How much is $1111\times2222$?
  1. 3456543
  2. 2345432
  3. 2234322
  4. 2468642
  5. 4321234

Question 5

On a planet there are 10 islands and 12 bridges. All bridges are open for traffic right now. What is the smallest number of bridges that must be closed in order to stop the traffic between A and B?

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Question 6

Jane, Kate and Lynn go for a walk. Jane walks up front, Kate walks in the middle and Lynn walks behind. Jane weighs 500 kg more than Kate. Kate weighs 1000 kg less than Lynn. Which picture shows Jane, Kate and Lynn in the right order?
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Question 7

A special dice has a number on each face. The sums of the numbers on opposite faces are all equal. Five of the numbers are 5, 6, 9, 11 and 14. What number is on the sixth face?
  1. 4
  2. 7
  3. 8
  4. 13
  5. 15

Question 8

Martin wants to colour the squares of the rectangle so that $1/3$ of all squares are blue and half of all squares are yellow. The rest are red. How many squares will he colour red?

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Question 9

While Peter is solving 2 problems in the Kangaroo contest, Nick manages to solve 3. In total the boys solve 30 problems. How many more problems did Nick solve than Peter?
  1. 5
  2. 6
  3. 7
  4. 8
  5. 9

Question 10

Bob folded a piece of paper and punched exactly one hole in the folded paper. The unfolded paper is shown. Which picture shows the lines along which Bob folded it?

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Question 11

The Modern Furniture store sells sofas, loveseats and chairs made from identical modular pieces as shown. Including the armrests, the sofa is 220 cm wide and the loveseat is 160 cm wide. What is the width of the chair?

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  1. 60 cm
  2. 80 cm
  3. 90 cm
  4. 100 cm
  5. 120 cm

Question 12

The 5 keys fit the 5 padlocks. The numbers on the keys refer to the letters on the padlocks. What is written on the last key?

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  1. 382
  2. 282
  3. 284
  4. 823
  5. 824

Question 13

Tom writes the numbers from 1 to 20 in a row, obtaining the 31-digit number 1234567891011121314151617181920. He deletes 24 digits so that the remaining number is as large as possible. Which number does he get?
  1. 9671819
  2. 9567892
  3. 9781920
  4. 9912345
  5. 9818192

Question 14

Morten wants to put the construction into a regular box. Which of the following boxes is the smallest he can use?

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  1. $3\times3\times4$
  2. $3\times5\times5$
  3. $3\times4\times5$
  4. $4\times4\times4$
  5. $4\times4\times5$

Question 15

Adding the numbers in each row and column gives the results shown. Which statement is true?

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  1. $a=d$
  2. $b=c$
  3. $a>d$
  4. $a<d$
  5. $c>b$

Question 16

Peter hiked for 5 days, from Monday to Friday. Each day he walked 2 km more than the day before. His total distance was 70 km. How far did he walk on Thursday?
  1. 12 km
  2. 13 km
  3. 14 km
  4. 15 km
  5. 16 km

Question 17

A kangaroo is drawn in the first triangle. Dotted lines act as mirrors. The first 2 reflections are shown. What does the reflection look like in the shaded triangle?

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Question 18

Boris has some money and three magic wands, each usable once. One adds 1 EUR, one subtracts 1 EUR, and one doubles the amount. In which order must he use them to obtain the largest amount?

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Question 19

Rafael has three squares. The first has side 2 cm. The second has side 4 cm and one vertex at the centre of the first. The last has side 6 cm and one vertex at the centre of the second, as shown. What is the area of the figure?

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  1. 32 cm²
  2. 51 cm²
  3. 27 cm²
  4. 16 cm²
  5. 6 cm²

Question 20

Four players scored different numbers of goals in a handball match. Mike scored the least. The other three scored 20 goals in total. What is the largest number Mike could have scored?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6