HKIMO 2026 Grade 7 National Preliminary Set 03

The two-digit number $\overline{AB}$ is prime and the two-digit number $\overline{BA}$ is divisible by 5. Find the maximum value of $A+B$.

A farm has chickens and rabbits. There are 24 more chickens than rabbits, and 240 legs altogether. How many chickens are there?

According to the pattern, find the next term: $12,18,16,16,20,14,24,\ldots$.

A 52-card deck is divided equally into four suits: spades♠, hearts♥, diamonds♦ and clubs♣. Andy draws cards at random. What is the least number he must draw to guarantee two cards of different suits?

After a 30% discount, Alice pays 392 dollars for a dress. Find its marked price.

Given $A:B=3:4$, $B:C=7:5$ and $A+B-C=87$, find $A$.

Factorize $5 x^2+17 x-12$.

How many integer values of $x$ satisfy $-40\le 6 x+8\le 32$?

Convert $1.781818181\ldots$ into a fraction in simplest form.

How many even numbers are greater than 21 and smaller than 60?

The eight-digit number $\overline{160 A 457 B}$ is divisible by 18. Find the maximum of $A\times B$.

Find the units digit of $A=3\times 13\times 23\times 33\times\cdots\times 2013\times 2023$.

Find the number of positive factors of 180.

How many digits “5” are used to write all page numbers of a 300-page book?

How many three-digit numbers are divisible by 4 but not by 6?

Find the sum of all interior angles of the figure below, given that a triangle’s interior angles sum to $180^\circ$.

A rectangle has area $405\ \mathrm{cm}^2$. Increasing both its length and width by 3 cm gives area $540\ \mathrm{cm}^2$. Find the original perimeter.

A square has twice the perimeter of a circle of radius 14. Find the square’s area. Take $\pi=22/7$.

Andy stacks 15 identical cubes of side 2 cm to form the solid below. Find its total surface area in $\mathrm{cm}^2$.

A wheel has radius 35 cm. At least how many revolutions are needed to cover 484 m? Take $\pi=22/7$.