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HKIMO 2026 Grade 5 National Preliminary Set 03

Question 1

Today is 17th October, Sunday. Which day of the week will it be on 16th July of the same year?
  1. Friday
  2. Saturday
  3. Thursday
  4. Sunday

Question 2

What number should replace “?” in the following sequence?

$6,9,14,21,30,41,54,?,\ldots$
  1. 82
  2. 67
  3. 69
  4. 86

Question 3

Ricky’s father’s age this year adds 8, subtracts 9, is divided by 3 and multiplied by 9. The result is 153 years old. How old is Ricky’s father this year?
  1. 47
  2. 43
  3. 53
  4. 52

Question 4

A book store had a box of books. One half and 7 more books were sold on the first day. One half of the remaining books and 2 more books were sold on the second day. Finally, 11 books were left. How many books did the store have originally?
  1. 66
  2. 54
  3. 38
  4. 22

Question 5

According to the pattern below, how many ◇ are there in the next figure?

Question illustration
  1. 29
  2. 33
  3. 35
  4. 25

Question 6

Find $x$ given that $7\times x-16=145$.
  1. 18
  2. 25
  3. 21
  4. 23

Question 7

Find the value of $7+11+15+19+\cdots+43$.
  1. 450
  2. 225
  3. 250
  4. 500

Question 8

Calculate $24\times143+68\times24-11\times24$.
  1. 2500
  2. 2400
  3. 1200
  4. 4800

Question 9

Find $S$ given that $S=3+6+12+24+\cdots+3072$.
  1. 5025
  2. 6141
  3. 6015
  4. 5283

Question 10

Find $\frac1{1\times2}+\frac1{2\times3}+\cdots+\frac1{48\times49}+\frac1{49\times50}$.
  1. $\frac{49}{100}$
  2. $\frac1{50}$
  3. $\frac{49}{50}$
  4. $\frac12$

Question 11

Define $a\oplus b=a\times5-b-7$. Find $8\oplus(6\oplus11)$.
  1. 21
  2. 25
  3. 15
  4. 117

Question 12

The sum of $A$ and $B$ is 120. $B$ is five times $A$. Find the difference of $A$ and $B$.
  1. 20
  2. 100
  3. 96
  4. 80

Question 13

If the 5-digit number $\overline{2022A}$ is divisible by 9, find digit $A$.
  1. 0
  2. 6
  3. 9
  4. 3

Question 14

How many 3-digit numbers are divisible by 2?
  1. 300
  2. 450
  3. 150
  4. 250

Question 15

A teacher gives candies to all students in class 5B. If each student gets 7 candies, 1 candy is left. If each student gets 6 candies, 33 candies are left. How many students are there in class 5B?
  1. 31
  2. 32
  3. 33
  4. 34

Question 16

How many rectangles are there in the figure below?

Question illustration
  1. 36
  2. 48
  3. 60
  4. 65

Question 17

A rectangle has area 60 cm². Its length and width are natural numbers in cm. Find the minimum possible perimeter.
  1. 16 cm
  2. 32 cm
  3. 46 cm
  4. 38 cm

Question 18

A rectangle has perimeter 28 cm. When its length increases by 3 cm, the area increases by 18 cm². Find the area of the new rectangle in cm².
  1. 48
  2. 34
  3. 64
  4. 66

Question 19

Seven small cubes with side length 1 cm form the solid below. What is its total surface area in cm²?

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

Question 20

Linda puts two differently colored square sheets next to each other to form a rectangle. After putting the yellow sheet on the red sheet, the rectangle’s area decreases by 12 cm² and its perimeter decreases by 4 cm. Find the original rectangle’s area in cm².

Question illustration
  1. 72
  2. 18
  3. 48
  4. 36