IKMC 2018 - Grades 5-6 - Self-study

Question 1

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

Question 2

Three objects are on the table as shown. What does Peter see when looking at the table from above?

Question 3

Diana first scored 14 points with two arrows on the target. The second time she scored 16. How many points did she score the third time?

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

Question 4

A garden is divided into identical squares. A slow snail and a fast snail start at corner S and move along its perimeter in opposite directions, at 1 m/h and 2 m/h respectively. At which marked point will they meet?

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

Question 5

Alice subtracted two two-digit numbers, then painted over two cells as shown. What is the sum of the two hidden digits?

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

Question 6

A star is made from four equilateral triangles and a square. The perimeter of the square is 36 cm. What is the perimeter of the star?

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

Question 7

The picture shows a calendar for a certain month. An ink spot covers most dates. What day of the week 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

There are three squares in the figure. The smallest has side length 6 cm. What is the side length of the largest square?

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

Question 10

The circles are light bulbs connected as shown. Initially all are off. Touching a bulb lights it and all its neighbours. What is the least number of bulbs you must touch to light them all?

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

Question 11

In which of the four squares is the fraction of the area coloured black largest?

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

Question 12

Nine cars arrive at a crossroads and drive off as indicated by the arrows. Which figure shows the cars after they leave the crossroads?

Question 13

Each spot hides one of the numbers 1,2,3,4,5 so that both calculations following the arrows are correct. What number is under the spot with the star?

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

Question 14

A lion is behind one of three doors. Each door bears a sentence, but only one sentence is true. Door 1: “The lion is not behind this door.” Door 2: “The lion is behind this door.” Door 3: “The sum of two and three is five.” Behind which door is the lion?

1. Door 1
2. Door 2
3. Door 3
4. All three doors are possible
5. Both doors 1 and 2 are possible

Question 15

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

Question 16

Emily enters a number in each cell of the triangular table. The sum in any two cells sharing an edge must be the same. Two numbers are already entered. What is the sum of all the numbers in the table?

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

John adds the three-digit numbers ABC and CBA and obtains DDDD, as shown. A, B, C and D are digits. Which digit is B?

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

Question 20

Four ladybugs occupy different cells of a $4\times4$ grid. One sleeps and never moves. At each whistle, the other three move to free neighbouring cells, up, down, left or right, without returning to the cell they just left. The initial position and first three results are shown. Which image might be the result after the fourth whistle?