VTMO 2026 - Grade 4 - Final - SET 7 - Self-study

Along one side of a road, trees are planted 12 m apart. There are 40 trees, including a tree at each end. Along the same road there are 27 equally spaced lamp posts, also including one at each end. How many metres apart are consecutive lamp posts?

An older sibling has 6 more sweets than the younger sibling. Their mother gives 2 more sweets to the older child and 5 to the younger child. They then have 31 sweets altogether. How many sweets did the younger child have at first?

An and Bình play bowling. Each game score is a whole number.
(a) An scores 108 and 125 in his first two games. His average for games 3 and 4 is 122. What must he score in game 5 for his five-game average to be 120?
(b) Bình’s average for his first three games is 113. His scores in games 4 and 5 are equal. Can his five-game average be 120? Explain.

Pi writes a four-digit number with four different digits. Its thousands digit is twice its tens digit; its hundreds digit is 2 less than its thousands digit; its units digit is not 0; and the sum of its digits is 12. What is the number?

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?

Calculate $39\times15+20\times17+20\times18+35\times19$.

A large rectangle is divided into four smaller rectangles. Three of their areas are shown in the diagram. What is the perimeter of the shaded rectangle, in centimetres? Explain your reasoning.
Clarification: No side length or further shape condition is supplied in the original question. Decide whether the perimeter can be uniquely determined from the given information.

Initially Bình and Châu have cards in the ratio 2:3. Their mother gives each some cards, and their new totals are still in the ratio 2:3. (For example, mother gives Bình 10 cards and Châu 11 cards.) If the two gifts are exchanged, Bình instead has 12 more cards than Châu. (With the exchange, mother gives Bình 11 cards and Châu 10 cards.) Find the difference between the total number of cards given by mother and the total number the children had initially. Show your reasoning.
Clarification: The parenthetical 10/11 examples illustrate only exchanging the recipients, not the actual gift amounts satisfying the stated ratios.

The total age of all members of a family this year is 96 years. In 6 years their total age will be 120 years. The number of family members does not change. How many people are in the family? Show your reasoning.

Class 4A’s football team has 10 members. Each match has two 20-minute halves. All members play for the same amount of time. Exactly 7 players are on the pitch at any time, and substitutions are unrestricted. How many minutes does each member play in a match?

Mother shares 17 sweets among An, Bình and Châu. An has the most sweets and twice as many as Châu. Bình has more sweets than Châu. How many sweets does Bình have?

Five identical small rectangles are placed inside a large rectangle measuring 24 cm by 18 cm, as shown. Find the area of one small rectangle, in square centimetres.

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?