HKIMO 2026 Grade 6 National Preliminary Set 05

A and D are nonzero digits. $\overline{DA}=2(\overline{AD}-2)$, and $\overline{AD}$ is a square number. Find $\overline{AD}$.

There are chickens and rabbits in a cage. The number of chickens is twice the number of rabbits, and they have 352 legs altogether. How many rabbits are there?

Andy is three times as old as John now. In 12 years Andy will be twice as old as John. How old is Andy now?

A motorbike leaves a police station at 30 km/h. Twenty minutes later a car leaves the same station in pursuit at 50 km/h. How many minutes does the car need to catch the motorbike?

Six white, eight yellow and eleven brown chopsticks are mixed together. To obtain three pairs of chopsticks of the same colour in the dark, at least how many individual chopsticks must be taken out?

Find $222222222\div 9$.

Find $\frac 1{1\times 2\times 3}+\frac 1{2\times 3\times 4}+\cdots+\frac 1{7\times 8\times 9}+\frac 1{8\times 9\times 10}$.

Find $1\times 2+2\times 3+3\times 4+\cdots+20\times 21$.

Find $144-143+142-141+140-\cdots+4-3+2-1$.

Calculate $(2^1\times 2^2-2^3)\times 2^4$.

The nine-digit number $\overline{2 A 018901 B}$ is divisible by 11. Find $B-A$.

How many simplified fractions with denominator 80 are there?

How many three-digit numbers are divisible by 7 or 11?

A three-digit number leaves remainder 2 when divided by 3, 5 or 7. Find the largest such three-digit number.

Nine consecutive natural numbers have sum 126. Find the second largest.

How many rectangles are in the figure below?

A cuboid has volume 30 and positive integer side lengths. Find its minimum surface area.

Unit cubes are stacked according to the pattern below. If the solid has 11 layers, find its total surface area.

A square is formed from 722 rectangles measuring 1 cm by 2 cm. By how many centimetres does the total perimeter decrease after joining them?

A square has side 18.84 cm. A circle has the same perimeter as the square. Find the circle area, using $\pi=3.14$.