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HKIMO 2026 Grade 3 National Preliminary Set 05

Question 1

Find the missing number: $3,8,15,24,35,48,\underline{\phantom{00}}$.
  1. 35
  2. 68
  3. 63
  4. 38

Question 2

Tomorrow will be Sunday. What day of the week will it be 233 days later?
  1. Tuesday
  2. Monday
  3. Thursday
  4. Friday

Question 3

Lily's age 5 years ago equals Harley's age 9 years ago. How old is Harley when Lily is 23?
  1. 27
  2. 24
  3. 37
  4. 9

Question 4

A tree is planted every 7 m in a street from one end. There are 114 trees on one side. How long is the street in metres?

Editorial endpoint convention: trees include both ends of the measured street segment; its length is the span from the first tree to the last. The original wording does not explicitly specify the far endpoint.
  1. 791
  2. 798
  3. 960
  4. 132

Question 5

How many circled-cross symbols are there in the 8th group?

Question illustration
  1. 15
  2. 14
  3. 12
  4. 16

Question 6

Find $13+16+19+22+25+28+31+34+37$.
  1. 180
  2. 185
  3. 200
  4. 225

Question 7

Find $113\times39+39\times26-39\times39$.
  1. 2842
  2. 2871
  3. 3900
  4. 2929

Question 8

Find $3\times4\times5\times25$.
  1. 5200
  2. 1500
  3. 1000
  4. 2500

Question 9

Find $240\div6+240\div4+240\div2$.
  1. 220
  2. 225
  3. 250
  4. 300

Question 10

Find $100-98+96-94+92-90+\cdots+8-6$.
  1. 48
  2. 42
  3. 96
  4. 94

Question 11

Define $a\oplus b=a\times b-2\times a$. Find $(3\oplus6)\oplus4$.
  1. 9
  2. 24
  3. 27
  4. 21

Question 12

Amy and Jack have 57 apples in total. Jack has 13 more than Amy. How many does Amy have?
  1. 61
  2. 78
  3. 20
  4. 22

Question 13

The numbers form an arithmetic sequence. Find the 51st term: $15,21,27,33,39,\ldots$
  1. 313
  2. 595
  3. 601
  4. 315

Question 14

Five consecutive numbers sum to 510. Find the smallest.
  1. 97
  2. 100
  3. 98
  4. 104

Question 15

Helen and Masha have 174 pencils in total. Masha has twice as many as Helen. How many does Masha have?
  1. 150
  2. 175
  3. 116
  4. 125

Question 16

How many squares are there in the figure below?

Question illustration
  1. 18
  2. 12
  3. 21
  4. 14

Question 17

A square has side length 52. Find its perimeter.
  1. 208
  2. 250
  3. 195
  4. 300

Question 18

At least how many squares can be seen from the right of this figure?

Question illustration
  1. 6
  2. 11
  3. 7
  4. 9

Question 19

How many triangles are there in the figure below?

Question illustration
  1. 6
  2. 12
  3. 8
  4. 11

Question 20

At most how many lines can be formed using 9 points in a plane?
  1. 24
  2. 48
  3. 72
  4. 36