VTMO 2026 - Grade 4 - Final - SET 8 - Self-study

Initially An, Bình and Châu have marbles in the ratio 4:5:6. After giving marbles to one another, their amounts are in the ratio 2:4:3. The child whose amount decreases the most has 15 fewer marbles than at first. How many marbles did An have initially? Show your reasoning.

Among birth years from 1900 through 2021, how many have the property that the person’s age equals the sum of the digits of their birth year? Use age = 2021 − birth year.

Mr Thanh cuts a 4 m log into equal pieces 20 cm long. Each cut takes 10 minutes. He starts at 7:00 in the morning. At what time does he finish? Show your reasoning.

Whole numbers are arranged according to the pattern in the grid. For example, 1 is in row 1, column 1, and 6 is in row 3, column 2. What number is in row 10, column 10?

Tí wants to watch a film lasting 117 minutes. It starts at 7:30 p.m. He needs to arrive 15 minutes early to buy a ticket, and the journey from home to the cinema takes 20 minutes. What is the latest time he can leave home without being late for the film?

In the multiplication shown, different letters represent different digits. Find the four-digit number SEED: $\overline{BEE}\times4=\overline{SEED}$.

How many two-digit numbers have a digit sum of 9?

The sequence of circle figures is shown below. Find the difference between the number of grey circles and the number of white circles in Figure 10.

The figure is made by joining two large squares of side 7 cm and four small squares of side 3 cm, as shown. Find the area of the shaded square in cm².

A cinema has 10 rows of seats. The first row has 10 seats. The second row has 3 more seats than the first, the third has 3 more than the second, and this pattern continues to the last row. How many seats are there altogether?

The Number Kingdom is shaped like a square. Its numbers lie on the sides, with some at the vertices. The sums of the numbers on the four sides, including the vertices, are 5, 7, 13 and 14. The sum of all the numbers in the kingdom is 31. Find the sum of the numbers at the four vertices.

The year 2012 was a leap year with 366 days, equal to 52 weeks and 2 days. In 2012 there were more Sundays than Saturdays and more Mondays than Fridays. What day of the week was 1 January 2016? Explain your reasoning.

Four teams A, B, C and D take part in a game competition. Each match is between two teams. A win earns 3 points and a loss earns 0 points; in a draw, each team earns 1 point. All four teams play the same number of matches. The number of matches with a winner and a loser equals the number of drawn matches. The teams score 100 points altogether. Team A scores 42 points and loses no matches. How many matches does A win? Explain your reasoning.