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HKIMO 2026 Grade 5 National Preliminary Set 05

Question 1

According to the pattern below, what number replaces the question mark?

$20,15,18,18,16,21,?,\ldots$
  1. 14
  2. 18
  3. 10
  4. 24

Question 2

There are chickens and rabbits. The number of chickens is 28 more than the number of rabbits. If there are 320 legs altogether, how many rabbits are there?
  1. 34
  2. 62
  3. 44
  4. 72

Question 3

A bookstore had a box of books. One half and 2 more books were sold on the first day. On the second day, 3 fewer books than two thirds of the remaining stock were sold. Finally, 9 books were left. How many books were there originally?
  1. 28
  2. 76
  3. 40
  4. 58

Question 4

Alice needs 60 days to finish a project. Peter needs 15 days to finish the same project. If they work together, how many days will they need?
  1. 75
  2. 12
  3. 45
  4. 20

Question 5

A bag contains 10 blue balls, 18 red balls and 5 green balls. At least how many balls must be drawn at random to guarantee 3 balls of each color?
  1. 31
  2. 26
  3. 33
  4. 18

Question 7

Find $\left(\frac32+\frac34+\frac36+\frac38\right)\div\left(\frac95+\frac9{10}+\frac9{15}+\frac9{20}\right)$.
  1. $\frac{25}{8}$
  2. $\frac{15}{4}$
  3. $\frac45$
  4. $\frac56$

Question 8

Find $200\div4+400\div8+600\div12+800\div16$.
  1. 200
  2. 250
  3. 240
  4. 150

Question 9

Find $34\times34-8\times32$.
  1. 900
  2. 1412
  3. 1156
  4. 256

Question 10

Find $\frac12+\frac14+\frac18+\cdots+\frac1{512}+\frac1{1024}$.
  1. $\frac{1015}{1024}$
  2. $\frac{511}{512}$
  3. $\frac{1023}{1024}$
  4. $\frac{127}{188}$

Question 11

If the 10-digit number $\overline{201905139B}$ is divisible by 12, find digit $B$.
  1. 2
  2. 6
  3. 4
  4. 8

Question 12

Find the last four digits of $141\times144\times147\times\cdots\times186\times189\times192$.
  1. 4000
  2. 2800
  3. 0900
  4. 0000

Question 13

Define $a\oplus b=3a-2b$. Find $11\oplus(6\oplus4)$.
  1. 13
  2. 8
  3. 33
  4. 55

Question 14

A teacher gives candies to students. Giving 9 candies to each leaves 2; giving 7 to each leaves 18. How many candies does the teacher have?
  1. 56
  2. 72
  3. 74
  4. 90

Question 15

How many 3-digit numbers are divisible by 4 and have units digit 2?
  1. 54
  2. 27
  3. 36
  4. 45

Question 16

How many rectangles are there in the figure below?

Question illustration
  1. 63
  2. 71
  3. 77
  4. 78

Question 17

A square is formed by 128 rectangles, each measuring 2 cm by 1 cm. Find the decrease in perimeter in cm after they are combined.
  1. 640
  2. 832
  3. 768
  4. 704

Question 18

22 small cubes of side 1 cm are stacked as shown. Find the total surface area in cm².

Question illustration
  1. 60
  2. 67
  3. 55
  4. 58

Question 19

Find the size of one angle of an equilateral triangle.
  1. 90°
  2. 60°
  3. 45°
  4. 30°

Question 20

$ABDF$ is a square. Triangles $FDE$ and $BDC$ are right isosceles triangles. Find the area of $ACDE$ given that $FE=BC=10$.

Question illustration
  1. 125
  2. 100
  3. 75
  4. 50