IKMC 2027 - Grades 5-6 - Self-study SET 15 - Thematic Batch 3

Question 1

A cube has six differently coloured faces. Paul sees blue, white, yellow; Sally sees black, blue, red; Betty sees green, black, white. What colour is opposite white?

1. Red
2. Blue
3. Black
4. Green
5. Yellow

Question 2

Tùng rides from home to work at 30 km/h. Returning, he travels half the distance at the same speed, then spends 10 minutes repairing his motorbike. To make the total return time equal to his morning journey time, he travels the remaining half at 50 km/h. How far is work from home?

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

Question 3

Alice cuts and folds the illustrated 6 dm square sheet into a tray. The corner cuts are 1 dm squares. What is the tray’s volume in cubic decimetres?



The source text reverses “right” and “left” when referring to the sheet and tray; the labelled diagram identifies them unambiguously.

1. 25
2. 36
3. 30
4. 16
5. 24

Question 4

Tom may place a counter in any cell of a 3 × 3 grid, then move horizontally or vertically, never diagonally. From how many starting cells can he visit every cell exactly once?

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

Question 5

Among Tom’s classmates, there are twice as many boys as girls. Which listed number could be the total number of pupils in Tom’s class?



Tom’s classmates are the other pupils, excluding Tom.

1. 30
2. 32
3. 35
4. 40
5. 45

Question 6

Jenny places six dice in a straight row. Opposite faces of each die have a total of 7 dots. What is the greatest possible sum of dots over all exterior faces of the resulting block?



As in the source, count every exterior face, including the underside and the two ends.

1. 106
2. 91
3. 102
4. 84
5. 96

Question 7

Tom cuts a square sheet into three pieces. Two pieces are shown. Which option can be the third piece?

Question 8

Emma has T-shaped tetrominoes. What is the greatest number she can place on a 4 × 7 board without overlap?

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

Question 9

Three cars enter a roundabout from different roads simultaneously, as shown. None completes a full circuit, and no two leave by the same road. How many different assignments of exit roads are possible?

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

Question 10

Kelly cuts a 27 cm ribbon into four rectangles of arbitrary lengths. She joins the centres of the first pair and of the last pair of adjacent rectangles as shown. What is the sum of the two segment lengths?

1. 12 cm
2. 13.5 cm
3. 14 cm
4. 14.5 cm
5. Cannot be determined

Question 11

Six identical tables stand in a straight row spanning 820 cm. The largest gap between two tables is 580 cm. How long is each table?



The distance between two tables means the gap between their nearest edges.

1. 30
2. 60
3. 85
4. 150
5. 120

Question 12

A three-digit number is called “certain” if its hundreds digit equals the sum of its other two digits. For example, 431 is certain because 4=3+1. How many three-digit certain numbers exist?

1. 55
2. 54
3. 45
4. 36
5. 35

Question 13

What is the fewest number of die rolls that guarantees some face has appeared at least twice?

1. 5
2. 6
3. 7
4. 12
5. 36

Question 14

Seven equal-length rulers are arranged in two staggered rows as shown. Each ruler is 14 cm long and the whole span is 80 cm. What is the marked overlap length?

1. 1
2. 2
3. 3
4. 5
5. 8

Question 15

Snow White gives whole candies to seven dwarfs, at least one each. The youngest gets twice as many as the oldest, and the other five get equal numbers. Which statement about the total is certainly correct?

1. Cannot be 19
2. Cannot be 20
3. Cannot be 21
4. Cannot be 22
5. Each of 19, 20, 21, 22 is possible

Question 16

Julia fills the illustrated number tower using a rule. Which two numbers go in the cells marked with question marks?



Source-intended rule: differences upwards from the middle row, sums downwards.

1. 2 & 14
2. 2 & 30
3. 3 & 221
4. 4 & 14
5. 4 & 30

Question 17

Alice cuts off one corner of a cardboard cube. Which illustrated net can result when she unfolds the cardboard?

Question 18

Xuka needs to bake 24 cakes. Her recipe uses 2 eggs for 6 cakes, and eggs are sold in boxes of 6. What is the fewest number of boxes she must buy?

1. 1
2. 2
3. 3
4. 4
5. 8

Question 19

Friends encode natural numbers using horizontal bars and dots. One symbol is worth 1 and the other 5. Which diagram can represent 17?

Question 20

The first day of 2018 was Monday. How many Fridays were there in that year?

1. 50
2. 52
3. 60
4. 65
5. 68