HKIMO 2026 Grade 7 National Preliminary Set 01

A farmer has some chickens and rabbits. There are 60 eyes and 100 legs altogether. How many chickens are there?

Doug takes twice as long as Becky to complete a project. Together they can complete the project in 10 hours. How long will Doug take alone, in hours?

Terry cycles from home to school at 12 km/h. After 20 minutes, Sally sees his forgotten backpack and drives from home at 32 km/h to catch him. She catches him at the school gate. How long did Terry take from home to school?

A two-digit number has digit sum 11. Reversing its digits and subtracting the original number gives 45. Find the original number.

According to the pattern, find the missing number: $1;3;8;26;106;?;\ldots$.

Find $1+5+9+13+17+\cdots+45+49$.

Given $A:B=1:3$, $B:C=6:5$ and $A+B-C=9$, find $B$.

Convert $1.212121\ldots$ to a fraction in lowest terms.

How many integer values of $x$ satisfy $777>9x+25>-29$?

Find $1\times2+2\times3+3\times4+\cdots+25\times26$.

Find the units digit of $9^{2021}$.

The nine-digit number $\overline{20219A22B}$ is divisible by 18. Find the greatest value of $A\times B$.

Find the number of positive factors of 540.

How many digits “2” are used to number all pages of a 200-page book?

How many two-digit numbers are divisible by 3 but not by 9?

Anna combines one square of side 15 cm and two identical right-angled triangles into the trapezium below, of area $345\ \mathrm{cm}^2$. Find its perimeter.

Find the sum of all interior angles of a hexagon.

Tom divides an 88 m copper wire into two equal halves, bending one into a square and the other into a circle. What is the difference between their areas, in $\mathrm{m}^2$? Take $\pi=22/7$.

A cube has total surface area $384\ \mathrm{cm}^2$. Find its volume in $\mathrm{cm}^3$.

A square is divided into four congruent rectangles and a smaller square as shown. The small square has perimeter 16 cm and one-quarter of the area of the original square. Find the perimeter of the original square in cm.