HKIMO 2026 Grade 8 National Preliminary Set 03

A two-digit number $\overline{AB}$ is divisible by 5. Reversing its digits increases it by 27. Find $A+B$.

A store sells vanilla ice creams for 3 dollars and chocolate ice creams for 5 dollars. It sells 80 ice creams in a day and collects 280 dollars. How many vanilla ice creams were sold?

Peter travels 5 km west and then 12 km south. How far is he from his starting point?

Given $A:B=5:2$, $B:C=1:2$ and $A+B+C=55$, find $B$.

A train travels at 40 km/h and a car at 60 km/h in the same direction. The car takes 90 seconds to pass the train completely. Find the train length in metres.

Editorial convention: neglect the car length and treat it as a moving point.

Find $x$ if $12x+26=(4x-5)-(2x-1)$.

Given $a+b=16$ and $a^2+b^2=160$, find $ab$.

How many positive integers $x$ satisfy $20<60-3x<32$?

Given $x^2+y^2+2x+1=0$, find $(x-y)^{2022}+(x+y)^{2023}$.

Editorial domain convention: x and y are real numbers.

The sum of the first n natural numbers, starting at 1, is 171. Find n.

How many four-digit numbers are divisible by 2 or 5?

Find the units digit of $9\times19\times29\times\cdots\times99\times109$.

How many positive factors does 360 have?

A four-digit number X leaves remainder 1 when divided by either 4 or 6. Find its largest possible value.

Given $A=1\times2\times3\times\cdots\times39\times40$, how many trailing zeros does A have?

A right-angled triangle has area $150\ \mathrm{cm}^2$ and shortest side 15 cm. Find its perimeter.

Find the sum of the interior angles of a regular twelve-sided polygon.

Ten distinct points lie on a circle. How many triangles can be formed using these points as vertices?

Kellie stacks nine identical cubes of side 2 cm to form the solid shown. Find its total surface area in $\mathrm{cm}^2$.

Editorial convention: the drawing depicts the complete solid; include all exposed faces, including the underside.

Four circles fit inside a square of perimeter 16 cm as shown. Find the shaded area in $\mathrm{cm}^2$.

Editorial interpretation of the symmetric drawing: the four circles are congruent; each is tangent to one square side at its midpoint and passes through the square centre.