VTMO 2026 - Grade 3 - Final - SET 6 - Self-study

Mother has 6 identical square cakes. She cuts every cake into the same number of equal pieces so that all the cake can be shared equally among 8 children. What is the smallest possible number of pieces per cake?

Which piece of card cannot be folded to make a cube?

An is queuing to buy a cinema ticket. An is 7th from the front and 8th from the back. How many people are in the queue?

An and Bình initially have equal numbers of marbles. An buys 24 more and Bình buys 6 more. Bình then has one third of their combined total. How many marbles did An have at first?

The diagram shows a net of a cube. Which numbered face is opposite face 2?

Minh wants to buy a book but is 15,000 đồng short. Khoa wants the same book but is 19,000 đồng short. Together their money is exactly enough for one copy. How much does the book cost?

Five teams play in a volleyball tournament, where no match is drawn. The table shows the results so far. How many matches has team E won?

The sum of An’s, Bình’s and Châu’s ages is 24 years. In how many years will the sum be 30 years?

Four pupils guess their teacher’s age as 24, 29, 35 and 37 years. The teacher says their guesses differ from his true age by 1, 5, 6 and 7 years, in some order. How old is the teacher?

Some pupils stand in a line. Pi is in the exact middle of the line and is also halfway between An and Bình. An is 3rd from the front. Bình is 8 positions after An. How many pupils are in the line?

There are 660 passengers on ships A and B altogether. If 30 passengers move from A to B and 70 move from B to A, the ships then have equal numbers. How many passengers were on each ship at first? Show your working.

An older brother has 6 more candies than his younger brother. Mother gives the older brother 2 more candies and the younger brother 5 more. They then have 31 candies altogether. How many candies did the younger brother have at first?

Mai has the piece of card shown, with equally spaced points marked around its boundary. She makes one straight cut joining two marked points, dividing the card into two pieces with equal perimeters. How many different cuts are possible?

The Fibonacci sequence begins $1,1,2,3,5,8,13,21,34,\ldots$, with each later term the sum of the previous two. How many of its first 100 terms are odd?

Each shape has a fixed value. The number below each panel is the sum of the shapes in it. Find the value of the square marked by the question mark.

An cuts rectangular cards measuring 4 cm by 3 cm from a sheet measuring 36 cm by 27 cm. What is the greatest number of cards she can cut?

A father is 33 years old, and his two children are 3 and 7. In how many years will the sum of the children’s ages equal the father’s age?

Việt writes the positive even numbers less than 102 in increasing order. Dũng writes the positive odd numbers less than 101 in increasing order. In each column, Nam writes the product of Việt’s and Dũng’s numbers, as shown. How many different numbers divisible by 5 have the three boys written altogether? Count each value only once.

Different shapes represent different digits in the subtraction shown. Find the sum of the star digit and the heart digit.

Đức has marbles numbered 1, 3, 5, 7, 9. Hải has marbles numbered 0, 2, 4, 6, 8. Nhi takes one marble from each boy and adds their numbers. How many different sums can she obtain?