IKMC 2016 — Grades 5–6

Question 1

Question 2

1. A third
2. A quarter
3. A seventh
4. An eighth
5. A twelfth

Question 3

A thread of length 10 cm is folded into equal parts as shown in the figure. The thread is cut at the two marked places. What are the lengths of the three parts?

1. 2 cm, 3 cm, 5 cm
2. 2 cm, 2 cm, 6 cm
3. 1 cm, 4 cm, 5 cm
4. 1 cm, 3 cm, 6 cm
5. 3 cm, 3 cm, 4 cm

Question 4

On Lisa's refrigerator, 8 strong magnets (the black circles in the picture) are holding some postcards.



What is the largest number of magnets that she could remove so that no postcard falls to the ground?

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

Question 5

Cathy draws a square with side length 10 cm. She joins the midpoints of the sides to make a smaller square. What is the area of the smaller square?

1. $10\text{ cm}^2$
2. $20\text{ cm}^2$
3. $25\text{ cm}^2$
4. $40\text{ cm}^2$
5. $50\text{ cm}^2$

Question 6

Alice's mother wants to see a knife on the right-hand side of each plate and a fork on the left-hand side. At least, how many interchanges of a knife and a fork does Alice need to make in order to please her mother?

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

Question 7

1. 15
2. 20
3. 35
4. 50
5. 75

Question 8

Tom and John build rectangular boxes using the same number of identical cubes. Tom's box looks like this:



The first level of John's box looks like this:



How many levels will John's box have?

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

Question 9

On the left side of the room, Bea and Pia are sleeping with their heads on their pillows facing each other. On the right side of the room, Mary and Karen are sleeping with their heads on their pillows with their backs to each other. How many girls are sleeping with their right ear on their pillow?

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

Question 10

The piece of paper shown is folded along the dotted lines to make an open box. The box is put on a table with the top open. Which face is at the bottom of the box?

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

Question 11

Which of the following figures cannot be formed by gluing these two identical squares of paper together?

Question 12

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

Question 13

Five squirrels A, B, C, D, and E are sitting on the line. They will pick up 6 nuts marked by crosses. At one moment the squirrels start running to the nearest nut at the same speed. As soon as a squirrel picks up a nut it starts running to the next closest nut. Which squirrel will get two nuts?

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

Question 14

There are 30 students in class 5A. They sit in pairs so that each boy is sitting with a girl, and exactly half of the girls are sitting with a boy. How many boys are there in class 5A?

1. 25
2. 20
3. 15
4. 10
5. 5

Question 15

1. 2675
2. 2975
3. 2978
4. 4217
5. 4298

Question 16

Bart is having his hair cut. When he looks in the mirror, the clock looks like this.



What would he have seen if he had looked in the mirror ten minutes earlier?

Question 17

Grandmother bought enough cat food for her four cats for 12 days. On her way home, she brought back two stray cats. If she gives each cat the same amount of food every day, how many days will the cat food last?

1. 8
2. 7
3. 6
4. 5
5. 4

Question 18

Each letter in BENJAMIN represents one of the digits 1, 2, 3, 4, 5, 6 and 7. Different letters represent different digits. The number BENJAMIN is odd and divisible by 3. Which digit corresponds to N?

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

Question 19

1. 53
2. 54
3. 56
4. 59
5. 60

Question 20

The perimeter of the rectangle $ABCD$ is 30 cm. Three other rectangles are placed so that their centers are at the points $A$, $B$ and $D$ (see the figure). The sum of their perimeters is 20 cm. What is the total length of the thick line?

1. 50 cm
2. 45 cm
3. 40 cm
4. 35 cm
5. Impossible to determine