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HKIMO 2026 Grade 7 National Preliminary Set 05

Question 1

Three prime numbers sum to 28. Let M be the largest. Find the maximum possible M.
  1. 23
  2. 19
  3. 17
  4. 11

Question 2

A box holds 180 candies:45 strawberry,72 lemon and the rest mint. What is the least number to draw at random to guarantee at least one of every type?
  1. 140
  2. 112
  3. 118
  4. 136

Question 3

According to the pattern, find the blank: $1,4,13,43,142,\_,\ldots$.
  1. 469
  2. 378
  3. 492
  4. 372

Question 4

A football team plays 20 matches with no draws. A win earns 3 points and a loss 1 point. The team earns 44 points. How many matches does it win?
  1. 10
  2. 11
  3. 12
  4. 13

Question 5

Mary takes 10 minutes to saw a board into two pieces. Working at the same pace, how many minutes does she need to saw another board into five pieces?
  1. 20
  2. 30
  3. 40
  4. 50

Question 6

Convert $0.38888\ldots$ to a fraction in lowest terms.
  1. $\frac7{18}$
  2. $\frac79$
  3. $\frac{35}{90}$
  4. $\frac{19}{50}$

Question 7

Find $230\div 1+230\div 2+230\div 3+230\div 6$.
  1. 460
  2. 200
  3. 380
  4. 120

Question 8

Given $A:B=5:9$, $B:C=4:7$ and $A+B+C=238$, find $B$.
  1. 72
  2. 64
  3. 48
  4. 36

Question 9

Five consecutive even numbers sum to 200. Find the smallest.
  1. 36
  2. 34
  3. 40
  4. 38

Question 10

How many integers $x$ satisfy $-2\le 2 x-16\le 24$?
  1. 17
  2. 16
  3. 15
  4. 14

Question 11

The eight-digit number $\overline{2022198 A}$ is divisible by 12. Find $A$.
  1. 0
  2. 2
  3. 4
  4. 6

Question 13

How many digits “5” are used to number all pages of a 250-page book?
  1. 45
  2. 46
  3. 47
  4. 48

Question 14

Find the number of positive factors of 900.
  1. 18
  2. 24
  3. 27
  4. 32

Question 15

How many three-digit numbers are divisible by 3 but not by 9?
  1. 150
  2. 200
  3. 250
  4. 100

Question 16

Seven cubes of side 1 cm form the solid below. Find its total surface area in $\mathrm{cm}^2$.

Question illustration
  1. 26
  2. 24
  3. 12
  4. 13

Question 17

The square below is formed with four identical quadrants. The total length of the curves is 44. Find the area bounded inside the curves. Take $\pi=22/7$.

Question illustration
  1. 35
  2. 42
  3. 56
  4. 63

Question 18

A right triangle has shorter sides 5 cm and 12 cm. Find its perimeter in cm.
  1. 30
  2. 29
  3. 26
  4. 13

Question 19

Combine 24 identical squares of side 3 cm into a rectangle. Find its minimum perimeter in cm.
  1. 60
  2. 64
  3. 75
  4. 56

Question 20

A wheel has radius 14 cm. At least how many revolutions are needed to cover 66 m? Take $\pi=22/7$.
  1. 75
  2. 56
  3. 50
  4. 35