HKIMO 2026 Grade 6 National Preliminary Set 04

A train travels at 72 km/h and crosses a 220-metre bridge in 17 seconds. Find the length of the train in metres.

Tap A alone fills a tank in 8 hours and tap B alone in 16 hours. Starting with an empty tank, A runs alone for 2 hours, then both taps are opened. How many hours does it take until the tank is full?

Find the tenth number in the pattern $1,2,5,10,17,\ldots$.

Find the missing number in the diagram according to the pattern.

An athlete shoots 30 bullets. Each hit earns 10 points and each miss loses 5 points. His final score is 105. How many shots hit the target?

Find $64^2-36^2$.

Find $\dfrac{1}{2-\dfrac{3}{4-\dfrac 56}}$.

Find $3+6+12+24+\cdots+3072$.

Find $P=1\times 2+2\times 3+3\times 4+\cdots+29\times 30$.

The letters M, A, T, H, K, I, O represent distinct digits in the addition below. Find H+K+I+M+O.

Find the number of positive factors of 2022.

How many three-digit numbers leave remainder 6 when divided by 7?

The ten-digit number $\overline{20212022 AB}$ is divisible by 18. Find the greatest possible $A\times B$.

Given $2\otimes 3=3\times 5$, $3\otimes 4=4\times 7\times 10$, and $4\otimes 5=5\times 9\times 13\times 17$, find $(3\otimes 6)\div(2\otimes 4)$.

Lucas writes $1,2,3,4,\ldots$ in order. What is the least number of terms needed so their sum is divisible by 33?

A right triangle has one side 20 cm and hypotenuse 29 cm. Find its area in square centimetres.

Ten small cubes, each of volume $27\ \mathrm{cm}^3$, form the solid below. Find its total surface area in $\mathrm{cm}^2$.

A rectangle has perimeter 34 cm and integer side lengths. How many different areas can it have?

The square below contains four identical quarter-circles. Their curved edges have total length 44. Find the area of the region enclosed between the curves. Use $\pi=22/7$.

Six identical rectangles form the figure below, whose perimeter is 110. Find its area.