VTMO 2026 - Grade 4 - Final - SET 9 - Self-study

Minh has five boxes: one red, two blue and two yellow. Minh stacks them with these rules: boxes of the same colour are not adjacent; the top box is not yellow; the middle (third) box is not red; a yellow box is immediately below the red box; and the bottom box is not yellow. Give the colours of the boxes in order from bottom to top.

A class of 30 pupils takes a mathematics test. The average score of pupils numbered 1 to 10 is 89, the average of pupils numbered 11 to 30 is 80, and the average of pupils numbered 1 to 20 is 85. Find the average score of pupils numbered 21 to 30. Explain your reasoning.

A supermarket sells three kinds of rice bags: a 5 kg bag costs 80 thousand đồng, a 10 kg bag costs 153 thousand đồng, and a 15 kg bag costs 210 thousand đồng. Hạnh buys at least one bag of each kind. The average cost per kilogram of all the rice is 15 thousand đồng. What is the smallest possible total number of bags she buys? Explain your reasoning.

Tom writes a sequence of consecutive two-digit odd numbers, containing more than one term. Their sum is 161. What is the middle term?

An has one large box containing 4 medium boxes. Each medium box contains 5 small boxes. How many boxes does An have altogether, counting large, medium and small boxes?

The difference between two three-digit numbers is 328. What is the greatest possible sum of the two numbers?

Châu washes glasses at a café. She earns 2 thousand đồng for each glass washed. If she breaks a glass, she receives no washing payment for that glass and must pay the café owner 25 thousand đồng. In one week she is given 812 glasses and receives a net 1 408 thousand đồng. How many glasses does she break?

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.

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

What is the hundreds digit of $1\times2\times3\times4\times5\times6\times7\times8\times9\times10$?

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?

An uses small equilateral triangular cards of side 1 cm to make the first sequence. Bình uses small square cards of side 1 cm to make the second sequence. The first four figures in each sequence contain 1, 4, 9 and 16 cards, as shown. Each child chooses one figure from their own sequence. The sum of the two perimeters is 50 cm. What is the greatest possible number of cards in An’s figure?

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.