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HKIMO 2026 Grade 8 National Preliminary Set 04

Question 1

There are some 1-dollar, 2-dollar and 5-dollar coins. The number of 1-dollar coins is twelve times the number of 2-dollar coins. Their total value is 100 dollars. Find the number of 5-dollar coins.

Editorial reading of “some”: at least one coin of each named denomination is present.
  1. 6
  2. 20
  3. 14
  4. 8

Question 2

Five consecutive odd numbers have sum 125. Find the smallest.
  1. 25
  2. 23
  3. 21
  4. 19

Question 3

The calendar shows four dates $a,b,c,d$ with $a+b+c+d=52$. Find $ad$.

Question illustration
  1. 144
  2. 153
  3. 180
  4. 128

Question 4

A car takes 20 minutes from A to B and 40 minutes from B to C. Given AB=10 km and BC=30 km, find its average speed from A to C.
  1. 37.5 km/h
  2. 75 km/h
  3. 40 km/h
  4. 23 km/h

Question 5

Five coloured disks are stacked as shown. Move the top two disks to the bottom, keeping their order (red remains above blue on the first move). Repeat this operation for a total of 2022 moves. Which disk is on the bottom?

Question illustration
  1. yellow
  2. blue
  3. red
  4. green

Question 6

Compute $\left(1+\frac12\right)\left(1+\frac13\right)\left(1+\frac14\right)\cdots\left(1+\frac1{2021}\right)$.
  1. 2022
  2. 1010
  3. 1011
  4. 2021

Question 7

Solve $2000x+2002x+2004x+\cdots+2020x+2022x=4022$ for x.
  1. $\frac1{12}$
  2. $\frac16$
  3. $\frac13$
  4. $\frac14$

Question 8

Given $\begin{cases}3x+9y=7,\\9x-3y=-4,\end{cases}$ find $x-y$.
  1. 2
  2. -2
  3. 1
  4. -1

Question 9

Compute $501^2+499^2$.
  1. 500000
  2. 500002
  3. 500001
  4. 499999

Question 10

How many negative integers x satisfy $-2021<40x+19<2021$?
  1. 100
  2. 51
  3. 50
  4. 101

Question 11

How many three-digit numbers leave remainder 4 when divided by 5 and remainder 5 when divided by 6?
  1. 30
  2. 37
  3. 74
  4. 38

Question 12

The ten-digit number $\overline{A20213101B}$ is divisible by 72. Find $A+B$.
  1. 17
  2. 8
  3. 9
  4. 18

Question 13

Find the remainder when $2^{2021}$ is divided by 7.
  1. 4
  2. 2
  3. 1
  4. 3

Question 14

How many trailing zeros does $321!$ have?
  1. 64
  2. 78
  3. 76
  4. 80

Question 15

Find the number of proper simplified fractions with denominator 30.
  1. 10
  2. 9
  3. 7
  4. 8

Question 16

The two longest sides of a right-angled triangle have lengths 42 and 58. Find its perimeter.
  1. 140
  2. 150
  3. 160
  4. 170

Question 17

Find the sum of the two marked angles in the figure.

Question illustration
  1. $240^\circ$
  2. $320^\circ$
  3. $180^\circ$
  4. $270^\circ$

Question 18

A rectangle has area 180 and integer length and width. Find the smallest possible perimeter.
  1. 58
  2. 56
  3. 54
  4. 52

Question 19

Eighteen unit cubes are stacked to form the solid shown. Find its total surface area.

Editorial convention: the drawing depicts the complete solid; include all exposed faces, including the underside.

Question illustration
  1. 48
  2. 34
  3. 36
  4. 54

Question 20

The rectangle has perimeter 38. D is the circle centre and CD is a radius. Find the perimeter of the shaded region. Take $\pi=22/7$.

Question illustration
  1. 45.5
  2. 38
  3. 46
  4. 35