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HKIMO 2026 Grade 3 National Preliminary Set 04

Question 1

How many squares are there in the first 42 figures, counting from the left?

Question illustration
  1. 27
  2. 24
  3. 8
  4. 25

Question 2

Fill in the missing English letter: B, E, H, K, __.
  1. L
  2. M
  3. N
  4. O

Question 3

Find the number represented by the question mark: $251,249,245,239,231,\underline{\phantom{000}},?,\ldots$
  1. 221
  2. 209
  3. 231
  4. 195

Question 4

How many club symbols are there in the next figure?

Question illustration
  1. 25
  2. 31
  3. 33
  4. 29

Question 5

Today is Sunday, 16 January. What day of the week is 30 January of the same year?
  1. Sunday
  2. Saturday
  3. Monday
  4. Friday

Question 7

Find $11+17+23+29+35+41+47+53+59$.
  1. 351
  2. 315
  3. 280
  4. 208

Question 8

Find $16\times8+8\times30+8\times104$.
  1. 1200
  2. 800
  3. 1020
  4. 1500

Question 11

Define $a\Delta b=(a-b)\times(a+b)-5$. Find $5\Delta3$.
  1. 15
  2. 11
  3. 8
  4. 2

Question 12

The numbers form an arithmetic sequence. Find the sum of the 7th and 9th terms: $10,13,16,19,22,\ldots$
  1. 28
  2. 35
  3. 34
  4. 62

Question 13

Ben has 15 apples and Bob has 36. How many apples must Bob give Ben so that Bob has twice as many as Ben?
  1. 2
  2. 17
  3. 5
  4. 8

Question 14

Find the largest 3-digit number divisible by 7.
  1. 998
  2. 990
  3. 984
  4. 994

Question 15

Three consecutive odd numbers sum to 21. Find their product.
  1. 336
  2. 693
  3. 315
  4. 105

Question 16

How many rectangles are there in the figure below?

Question illustration
  1. 210
  2. 105
  3. 150
  4. 126

Question 17

How many rectangles contain both asterisks in the figure below?

Question illustration
  1. 6
  2. 18
  3. 12
  4. 15

Question 18

A rectangle has perimeter 224 cm. Its length is 10 cm more than its width. Find its width.
  1. 61 cm
  2. 51 cm
  3. 107 cm
  4. 117 cm

Question 19

How many triangles are there in the picture of the boat below?

Question illustration
  1. 9
  2. 10
  3. 11
  4. 12

Question 20

At least how many squares can be seen when observing the figure below from the right?

Question illustration
  1. 10
  2. 11
  3. 12
  4. 9