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HKIMO 2026 Grade 8 National Preliminary Set 02

Question 1

A two-digit number $\overline{AB}$ is divisible by 7. Reversing its digits increases it by 9. Find $A+B$.
  1. 11
  2. 10
  3. 9
  4. 12

Question 2

A store sells cupcakes for 2 dollars and muffins for 3 dollars. It sells 100 cakes in a day and collects 260 dollars. How many muffins did it sell?
  1. 40
  2. 60
  3. 20
  4. 100

Question 3

Peter travels 45 km southeast, then 46 km southwest, then 22 km northeast. How far is he from his starting point?
  1. 25 km
  2. 51 km
  3. 24 km
  4. 21 km

Question 4

Given $A:B=5:6$, $B:C=6:7$ and $A+B+C=54$, find $A$.
  1. 18
  2. 16
  3. 15
  4. 21

Question 5

A train travels at 80 km/h and a car at 40 km/h in the opposite direction. The car takes 30 seconds to pass the train completely. Find the train length in metres.

Editorial convention: neglect the car’s length and treat it as a moving point.
  1. 1000 m
  2. 800 m
  3. 1100 m
  4. 1200 m

Question 6

Find $x$ if $(15-x)+(x-12)=7-(-5+x)$.
  1. -9
  2. 8
  3. -8
  4. 9

Question 7

Given $a+b=9$ and $a^2+b^2=45$, find $|b-a|$.
  1. 3
  2. 6
  3. 2
  4. 1

Question 8

How many positive integers $x$ satisfy $8<\frac{3x-2}{4}<11$?
  1. 5
  2. 2
  3. 3
  4. 4

Question 9

Given $x^2+y^2+4x-2y+5=0$, find $(x+y)^{2021}$.

Editorial domain convention: x and y are real numbers.
  1. 2
  2. 0
  3. 1
  4. -1

Question 10

The sum of the first n natural numbers, starting at 1, is 66. Find n.
  1. 12
  2. 11
  3. 10
  4. 13

Question 11

How many three-digit numbers are divisible by 6?
  1. 149
  2. 102
  3. 150
  4. 250

Question 13

How many positive factors does 2020 have?
  1. 12
  2. 18
  3. 14
  4. 20

Question 14

A three-digit number leaves remainder 1 when divided by either 4 or 6. Find its greatest possible value.
  1. 999
  2. 997
  3. 996
  4. 998

Question 15

Given $A=20!=1\times2\times\cdots\times19\times20$, how many trailing zeros does $A$ have?
  1. 2
  2. 4
  3. 3
  4. 5

Question 16

A right-angled triangle has area $30\ \mathrm{cm}^2$ and shortest side 5 cm. Find its hypotenuse.
  1. 10 cm
  2. 14 cm
  3. 13 cm
  4. 15 cm

Question 17

Find the sum of the interior angles of a regular eighteen-sided polygon.
  1. $3240^\circ$
  2. $2700^\circ$
  3. $2880^\circ$
  4. $3060^\circ$

Question 18

Combine 2015 squares of side 1 cm to form a rectangle. Find the minimum perimeter of the rectangle.

Editorial convention: tile without gaps or overlaps, with the square edges parallel to the rectangle edges.
  1. 192
  2. 166
  3. 408
  4. 96

Question 19

One jar of paint covers all faces of the cube in Figure 1. At least how many jars are needed to cover all faces of the solid in Figure 2?

Editorial convention: read the pictured solid as complete, without additional wholly hidden cubes. Use identical unit cubes and uniform paint coverage, include the underside, and count whole jars.

Figure 1

Question illustration

Figure 2

Question illustration
  1. 5
  2. 4
  3. 26
  4. 8

Question 20

In the figure, AFEC is a rectangle. If $AB:BC=1:1$, $AG:GD=3:1$, $AC=8$ and $CE=12$, find the area of triangle GDE.

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