IKMC 2021 - Grades 5-6 - Set 2 - Self-study

Question 1

Sofie wants to write KENGU using one letter from each of the five boxes shown. Which letter must she take from box 4?

1. K
2. E
3. N
4. G
5. U

Question 2

In how many places in the picture are two children holding each other with their left hands?

1. 1
2. 2
3. 3
4. 4
5. 5

Question 3

The digits 1 to 9 are placed in the square as shown. Starting at the star, follow a line and write the digits that it passes. The example gives 42685. Which option gives the greatest number?

Question 4

Which solid can be made using the six bricks shown: two white and four gray identical bricks?

Question 5

Fit the five pieces together to make a rectangle containing a calculation. What is the result?

1. 22
2. 32
3. 41
4. 122
5. 203

Question 6

A measuring tape is wound around a cylinder. What number is at the question mark?

1. 53
2. 60
3. 69
4. 77
5. 81

Question 7

The five figures may move only horizontally or vertically, in the arrow directions; they may not rotate. Which figure can leave through gate G?

1. A
2. B
3. C
4. D
5. E

Question 8

Mary folded a piece of paper exactly in half, then exactly in half again, obtaining the right triangle shown. Which of P, Q and R could be the original paper?

1. only P
2. only Q
3. only R
4. only P or Q
5. any of P, Q or R

Question 9

1. 1 part green + 3 parts white
2. 2 parts green + 6 parts white
3. 3 parts green + 9 parts white
4. 4 parts green + 12 parts white
5. They are all equally dark

Question 10

Question 11

1. 3244
2. 3444
3. 5172
4. 5217
5. 5444

Question 12

The map shows stations A, B and C. The tours A–Zoo–Port–A, B–Park–Zoo–B and C–Port–Park–C are 10 km, 12 km and 13 km. The tour Zoo–Park–Port–Zoo is 15 km. How long is the shortest tour A–B–C–A?

1. $18\text{ km}$
2. $20\text{ km}$
3. $25\text{ km}$
4. $35\text{ km}$
5. $50\text{ km}$

Question 13

Rosa wants to enter at one arrow, follow the line and leave at the other arrow. Which piece cannot be put in the middle to make this possible? Pieces may be rotated.

Question 14

Each hexagon has numbers at its six vertices whose sum is 30. Some numbers are hidden. What number is at the question mark?

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

Question 15

Three rectangles of equal height have areas 12, 18 and 22 square centimetres as shown. If AB is 6 cm, how long is CD?

1. $7\text{ cm}$
2. $7.5\text{ cm}$
3. $8\text{ cm}$
4. $8.2\text{ cm}$
5. $8.5\text{ cm}$

Question 16

A triangular pyramid is made of 10 identical balls. Two balls bear each of the letters A, B, C, D and E. The three side views are shown. What letter is on the ball with the question mark?

1. A
2. B
3. C
4. D
5. E

Question 17

Question 18

A four-digit bicycle lock uses digits 0–9 on each wheel. Starting from the correct combination, my brother turned every wheel the same amount in the same direction; it now shows 6348. Which option cannot have been the correct combination?

Question 19

1. Carl gets at least one pear
2. Carl gets as many apples as pears
3. Carl gets as many apples as Luca
4. Carl gets as many pears as Luca gets apples
5. Carl gets as many pears as Luca

Question 20

Two trains leave X and Y simultaneously on one track, at constant speeds. The X-to-Y train needs 180 minutes for the full trip; the Y-to-X train needs 60 minutes. Where should a short double-track section be built so they can pass safely?