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HKIMO 2026 Grade 5 National Preliminary Set 04

Question 1

Refer to the pattern below. How many triangles are there among the first 2021 figures, counted from left to right?

Question illustration
  1. 674
  2. 673
  3. 809
  4. 336

Question 2

Andy has some cans for gasoline. Pouring 3 liters into each can leaves 10 liters over. Pouring 4 liters into each can leaves 2 liters over. How many liters of gasoline does he have?
  1. 24
  2. 34
  3. 38
  4. 8

Question 3

What is the 8th number in this patterned sequence?

$1,2,5,14,41,\ldots$
  1. 1049
  2. 1000
  3. 122
  4. 1094

Question 4

Observe the pattern below and find $A+B+C$.

Question illustration
  1. 75
  2. 62
  3. 72
  4. 57

Question 5

A math test has 10 questions. Each correct answer earns 1 point; a wrong or blank answer earns 0. What is the smallest number of students taking the test that guarantees two have the same score?
  1. 12
  2. 11
  3. 10
  4. 20

Question 6

Find $\frac1{2\times4}+\frac1{4\times6}+\frac1{6\times8}+\cdots+\frac1{2020\times2022}$.
  1. $\frac12$
  2. $\frac{505}{1011}$
  3. $\frac{505}{2022}$
  4. $\frac14$

Question 7

Find the value of $\frac1{2+\frac34}$.
  1. $\frac{11}{4}$
  2. $\frac4{11}$
  3. $\frac45$
  4. $\frac54$

Question 8

Find $2+7+12+17+\cdots+197+202$.
  1. 4281
  2. 8364
  3. 10302
  4. 4182

Question 9

Find $P$ so that $2\times P=2+6+18+54+\cdots+4374$.
  1. 3820
  2. 3280
  3. 2380
  4. 2830

Question 10

Each letter $M,A,T,H,K,I,O$ represents a different digit. Find $I$ in the addition below.

Question illustration
  1. 3
  2. 2
  3. 4
  4. 5

Question 11

Ashley and Ben together weigh 75 kg; Ben and Chelsea weigh 81 kg; Chelsea and Ashley weigh 84 kg. Dan weighs 3 kg more than the average weight of all four friends. Find Dan’s weight in kg.
  1. 44
  2. 43
  3. 42
  4. 41

Question 12

Find the largest 3-digit number that leaves remainder 6 when divided by 7.
  1. 1000
  2. 993
  3. 994
  4. 995

Question 13

The 10-digit number $\overline{20212022AB}$ is divisible by 18. Find the maximum possible value of $A$.
  1. 8
  2. 9
  3. 5
  4. 3

Question 14

Given $2*3=3+5$, $3*4=4+7+10$, and $4*5=5+9+13+17$, find $4*6$.
  1. 50
  2. 72
  3. 10
  4. 48

Question 15

How many zeros are needed to write all page numbers of a 100-page book?
  1. 9
  2. 10
  3. 11
  4. 12

Question 16

Each square grid cell below has side length 4. Find the red area.

Question illustration
  1. 150
  2. 300
  3. 600
  4. 664

Question 17

Ten small cubes with side length 2 cm form the solid below. Find its total surface area in cm².

Question illustration
  1. 160
  2. 80
  3. 40
  4. 200

Question 18

How many rectangles are there in the figure below?

Question illustration
  1. 24
  2. 54
  3. 34
  4. 44

Question 19

Nine identical squares form the figure below, whose perimeter is 48. Find the shaded area.

Question illustration
  1. 24
  2. 18
  3. 16
  4. 27

Question 20

Andy has a square sheet with perimeter 72, shown in Figure 1. He cuts it into two identical pieces and combines them into the rectangle in Figure 2. Find the perimeter of Figure 2.

Question illustration
  1. 80
  2. 78
  3. 76
  4. 74