IKMC 2018 - Grades 5-6 - Set 2 - Self-study

Question 1

1. 41531766
2. 41521766
3. 51431766
4. 41531677
5. 41532766

Question 2

There are three objects on a table as shown. What does Peter see when looking straight down from above?

Question 3

Diana scores 14 points with her first two arrows and 16 with her next two, as shown. How many points do her third two arrows score?

1. 17
2. 18
3. 19
4. 20
5. 22

Question 4

A garden is divided into equal squares. Two snails start at S and follow its perimeter in opposite directions, at 1 m/h and 2 m/h as indicated. Where do they first meet?

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

Question 5

Alice subtracts two two-digit numbers. Two digits in the displayed calculation are covered. What is their sum?

1. 8
2. 9
3. 12
4. 13
5. 15

Question 6

A star consists of a square and four equilateral triangles. The square’s perimeter is 36 cm. What is the star’s perimeter?

1. 144 cm
2. 120 cm
3. 104 cm
4. 90 cm
5. 72 cm

Question 7

The calendar shows part of a month; an ink spot hides most dates. What weekday is the 25th?

1. Monday
2. Wednesday
3. Thursday
4. Saturday
5. Sunday

Question 8

1. 5
2. 6
3. 7
4. 12
5. 18

Question 9

The figure contains three squares. The smallest has side 6 cm, and the two indicated gaps are 2 cm. What is the side of the largest square?

1. 8
2. 10
3. 12
4. 14
5. 16

Question 10

All the bulbs in the network are initially off. Touching a bulb lights it and every bulb directly connected to it. What is the smallest number of bulbs that must be touched to light them all?

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

Question 11

Which of the four pictured squares has the largest fraction of black area?

1. A
2. B
3. C
4. D
5. They are all the same

Question 12

Nine cars approach a crossroads and leave in the directions indicated by their arrows and signals. Which diagram shows the cars after they have left?

Question 13

Each coloured spot hides one of 1,2,3,4,5. Both calculations following the arrows equal 8. What number is hidden by the starred spot?

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

Question 14

A lion is behind one of three doors. Door 1 says “The lion is not behind this door”; door 2 says “The lion is behind this door”; door 3 says “Two plus three is five.” Exactly one statement is true. Where is the lion?

1. Door 1
2. Door 2
3. Door 3
4. Any of the three doors
5. Either door 1 or door 2

Question 15

1. Adam
2. Eva
3. Isaac
4. Olga
5. Urban

Question 16

Emily fills the triangular table. Every pair of cells sharing an edge has the same sum. Two values are already shown. What is the sum of all entries?

1. 18
2. 20
3. 21
4. 22
5. Impossible to determine

Question 17

1. Wednesday
2. Thursday
3. Friday
4. Saturday
5. Sunday

Question 18

Question 19

The digit calculation is $\overline{ABC}+\overline{CBA}=\overline{DDDD}$. What digit is B?

1. 0
2. 2
3. 4
4. 5
5. 6

Question 20

Four ladybugs occupy a 4×4 grid. One sleeps and stays fixed. At each whistle the other three move to free edge-neighbouring cells, without immediately returning to their previous cells. The first four positions are shown. Which option can follow the fourth whistle?