VTMO 2026 - Grade 4 - Final - SET 3 - Self-study

Given the notation $\otimes5=5+4+3+2+1$, calculate $\otimes10-\otimes9$.

At the starting station, buses A and B have 70 passengers altogether. Passengers get on and off during the journey. At the last station A has 5 more passengers than at the start, while B has 4 fewer. At that point B has 7 more passengers than A. How many passengers were on each bus at the start? Show your reasoning.

Class IQ4A has 15 pupils. After their good end-of-term results, the teacher gives sweets to every pupil. Seven pupils receive more than 1 sweet; five receive more than 2; three receive more than 3; one receives 5; and nobody receives more than 5. How many sweets does the teacher give out altogether? Show your reasoning.

Dũng’s father packs his apples into small and large boxes. Either 10 small boxes and 8 large boxes, or 5 small boxes and 10 large boxes, hold exactly all the apples. If he uses only small boxes, how many does he need to hold exactly all the apples?

A stationery shop offers these pencil prices: 1 pencil for 3 000 đồng, 2 pencils for 5 000 đồng, and 5 pencils for 9 000 đồng. What is the greatest number of pencils Pi can buy with 53 000 đồng?

An uses exactly 50 matchsticks to make digits with the shapes shown, then adds the values of all the digits. What is the largest possible sum?

Class IQ4 TiTan has 15 pupils, including 12 boys. After some girls join the class, the number of girls is exactly half the total number of pupils. How many pupils are then in the class? Show your reasoning.

There are 13 flowers: 5 roses and the rest chrysanthemums. Six flowers are white and the rest are red. What is the smallest possible number of red chrysanthemums?

A 4-by-6 grid contains the numbers 1 to 24 as shown. How many square subgrids have a sum divisible by 3? Do not count 1-by-1 squares.

A division has quotient 10 and remainder 4. Find the smallest possible dividend.

At the beginning of the semester, the ratio of boys to girls in Titan’s maths club is 3:4. During the semester, 2 boys leave and 2 girls join. The ratio becomes 2:5. How many pupils are in the club at the end?

Việt has 64 identical small cubes. First he assembles a 4×4×4 cube, paints its outside surface, and takes it apart. He then assembles another 4×4×4 cube using the same small cubes, paints the outside surface again, and takes it apart. What is the greatest possible number of small cubes with exactly 3 painted faces after the two rounds?

The number $A=20242024\ldots2024$ has 2024 digits. What is the greatest number of digits that can be deleted so that the remaining number has digit sum 2028?