VTMO 2026 - Grade 5 - Semifinal - SET 10 - Self-study

The two diagonals of a $3\times3$ square grid pass through 5 small squares, as shown. How many small squares do the two diagonals of a $9\times9$ square grid pass through?

The average of three equally spaced even natural numbers is 2022. What is the largest possible number among the three? Here natural numbers include 0.

What should replace $\ast$ to make $1+1\ast1-2=100$ true? A replacement digit joins the adjacent digits to form one number.

A large cube is formed from 8 small cubes as shown. How many faces of the small cubes are in contact with other small cubes?

Việt has a special bicycle. The rear wheel has diameter 60 cm and the front wheel has diameter 50 cm. On a journey, the rear wheel makes 700 revolutions. How many revolutions does the front wheel make?

An buys 120 sweets in total: strawberry, orange and milk sweets. There are twice as many strawberry sweets as orange sweets, and 4 more orange sweets than milk sweets. How many orange sweets does An buy?

During the summer holiday, Khoa works part-time at KFC and earns 3 units of money for every 2 hours worked. He works 6 hours a day, 6 days a week, for 6 weeks. How much does he earn in total, in the same money units?

A teacher writes nine natural numbers in increasing order. In every three consecutive terms, the middle term is the average of the three. The largest term is 58. Which number below cannot be the smallest term?

Choose the figure in which the shaded area is half of the total area. The five choices are labelled A–E in the illustration.

Each different figure represents a different number. Find the product of the four-lobed figure and the circular button figure in the equations shown.

Convention for this question: each figure represents a distinct decimal digit; two adjacent figures form a two-digit number. Select the value from the supplied choices. Zero is allowed.

Việt has twenty 3 cm sticks and seven 2 cm sticks. What is the least number of additional 1 cm sticks he needs to arrange all the sticks end to end along the boundary of a rectangle with whole-number side lengths?

A digital clock displays every minute from 00:00 to 23:59. At how many times in one day do the two hour digits have sum 5 and the two minute digits also have sum 5? For example, 05:41 and 14:05 satisfy the conditions.

The first day of February 2014 is stated to be a Sunday. What weekday is the last day of that month?

Use the Sunday given in the question as a hypothetical starting weekday, rather than the real calendar.

Five identical rectangular bricks are joined to make the figure shown. Each brick has area $32\text{ cm}^2$. Find the perimeter of the whole figure.

The length of a rectangle is increased by 3 m while its width stays the same. Its area increases by $12\text{ m}^2$. What is the width, in metres?

Twenty-five points form the square grid shown. How many different squares have all their vertices among these points and have exactly two grid points on each side? Some examples are included in the illustration.

Fifty boys and girls hold hands in a circle. There are 14 more handholds between two boys than between two girls. How many boys are in the circle?

Three dice have faces numbered 1 to 6, as shown. Find the total number of dots on the faces that cannot be seen in this picture.

Some children go mushroom picking. If An gives Bình half of his mushrooms, all the children will have the same number. If instead An gives Châu all his mushrooms, Châu will have as many mushrooms as all the other children combined. How many children went mushroom picking? Explain your reasoning.

Convention for this practice question: the children collect a positive total number of mushrooms.

A hall has 12 rows of 10 seats each. There are 108 pupils seated in the hall. What is the largest number of rows that can be selected so that their numbers of seated pupils are all different?

A completely full row is allowed among the selected rows.