IKMC 2027 - Grades 5-6 - Self-study SET 2 - Thematic Batch 3

Question 1

The picture shows five locks and keys labelled with the codes that open them. Each lock carries a clue to its code, with each letter replacing a digit. What code is on the last key?

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

Question 2

An isosceles triangle has base 17 cm. The median to one of its equal sides divides the triangle into two smaller triangles whose perimeters differ by 10 cm. What is the original triangle’s perimeter in centimetres?

1. 31
2. 41
3. 51
4. 61
5. 71

Question 3

Three ants nibble pieces from an intact leaf and carry away the three pieces shown. Which picture could show the remaining part of that leaf?

Question 4

The digits of the year 2012 have sum 5. How many years in the twenty-first century have this property?

1. 1
2. 2
3. 3
4. 4
5. 9

Question 5

Three women and two men attend a party. Before the party, every pair of people shakes hands. What is the ratio of handshakes between two women to all handshakes in the group?

1. 1/3
2. 3/5
3. 3/10
4. 2/3
5. 3/2

Question 6

In Kangcity there are two special flowering trees, named Childhood and Youth. Youth flowers every 17 years, while Childhood flowers every 3 years. Alice notices that both flowered in 2020. In which year will they next flower together?

1. 2024
2. 2032
3. 2035
4. 2052
5. 2071

Question 7

Each ball in Kangcity’s ball pit is labelled with a positive integer. Alia likes even numbers, Bin likes multiples of 3, and David likes multiples of 5. Only eight balls remain. The three enter one at a time and each takes every remaining ball with a favourite number. Afterwards Alia has 32 and 52; Bin has 114,153,165; David has 35,95,130. In what order did they enter?

1. Alia, Bin, David
2. David, Bin, Alia
3. Bin, Alia, David
4. Bin, David, Alia
5. David, Alia, Bin

Question 8

John visits a park with his mother, who buys him a ticket for a ball-throwing game. He initially receives 12 balls. After each successful throw into the basket, he receives two more balls. John makes 20 throws altogether. How many throws went into the basket?



Editorial clarification: The worked solution assumes the game ends after John has used all the balls he receives.

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

Question 9

Tony has the piece shown. Which of the pieces below can be combined with it to form a rectangle?

Question 10

The picture is a neighbourhood map. There are several routes from Hannah’s house to Mick’s house. A route may visit each road intersection at most once. How many routes are there?

1. 9
2. 8
3. 7
4. 6
5. 5

Question 11

In the diagram, what is the difference between the numbers of white and black square cells?

1. 0
2. 1
3. 5
4. 9
5. 10

Question 12

Rectangle ABCD is made from 24 small squares, each of side 2 cm. What is the area of triangle DEF?

1. 20cm²
2. 22cm²
3. 24cm²
4. 26cm²
5. 28cm²

Question 13

Tony has two identical pieces as shown. By rotating and moving them, without flipping them over, which shape can he NOT make?

Question 14

What is the last digit in the decimal representation of $2^{2020}$?

1. 0
2. 2
3. 4
4. 6
5. 8

Question 15

Mango village and Orange village are separated by a river. At the same time, Ann starts rowing from landing A in Mango village and Bob from landing B in Orange village, each crossing to obtain fruit to sell. They meet at 8 a.m. Ann reaches B at noon, and Bob reaches A at 9 a.m. When did they start? Both row at constant speeds.



Figure labels: Bản Xoài = Mango village; Bản Cam = Orange village.

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

Question 16

Tèo makes a playful survey of his male classmates using seven traits: often gets high marks; sleeps 8 hours a day; completes all homework; silly; stubborn; often drinks tea in the principal’s office; handsome. He draws the shown Venn diagram. A person inside a coloured closed curve has the trait attached to that curve. What is Tí like, if Tí is the smiling face? Colour legend: yellow = high marks; red = 8 hours of sleep; pink = all homework; purple = silly; blue = stubborn; light green = tea in the principal’s office; dark green = handsome.

1. Stubborn; often drinks tea in the principal’s office; sleeps 8 hours; completes all homework; handsome.
2. Silly; stubborn; often drinks tea in the principal’s office; sleeps 8 hours; completes all homework.
3. Silly; stubborn; often drinks tea in the principal’s office; sleeps 8 hours; gets high marks; handsome.
4. Silly; stubborn; often drinks tea in the principal’s office; sleeps 8 hours; completes all homework; handsome.
5. Silly; stubborn; sleeps 8 hours; completes all homework.

Question 17

Emily draws a square of area 81 cm². Outside the square she draws four equilateral triangles, each sharing a side with it, as shown. What is the perimeter of the resulting shape in centimetres?

1. 144
2. 120
3. 108
4. 90
5. 72

Question 18

Robot Tikti starts at A2, facing the arrow in the diagram. It always continues straight ahead if possible. On encountering an obstacle, it turns right. It stops if it encounters another obstacle immediately after turning right. Where will it stop on this floor plan?

1. B2
2. A1
3. E1
4. D1
5. Tikti never stops.

Question 19

An wants to divide a large rectangle into small rectangles using 10 straight lines. A small rectangle means one that contains no other rectangle inside it. What is the greatest number of small rectangles that the 10 lines can create?



Editorial clarification: Count the elementary regions of a rectangular grid made by ten full cuts parallel to the sides.

1. 22
2. 25
3. 30
4. 36
5. 40

Question 20

A garage contains 29 vehicles, including motorcycles and cars. Ben says that every motorcycle has two wheels and every car four, with 84 wheels altogether. How many cars are in the garage?

1. 13
2. 26
3. 16
4. 8
5. Cannot be determined