VTMO 2026 - Grade 5 - Semifinal - SET 9 - Self-study

Each solid below is made of unit cubes with edges of 1 cm. Binh chooses some of the solids, using each at most once, and joins them to form the largest possible solid cube with no gaps. What is the edge length of that cube?

What value does A mark on the ruler below?

At 06:00, a cyclist travelling at 12 km/h and a car travelling at 68 km/h leave A for B. At 06:30, a motorcyclist travelling at 44 km/h also leaves A for B. At what time is the motorcyclist exactly halfway between the cyclist and the car on route AB?

Practice convention: all three maintain the stated speeds and are still travelling on AB at the requested moment.

Thirty-two people stand in a queue. The first person moves to the back, and the second person sits down, so the original third person is now the first standing person. Repeat this process: the first standing person moves to the back and the next sits down. When only one person remains standing, what was that person’s original position?

Binh writes the numbers from 1 to 999 on a sheet of paper, but skips all multiples of 10 and all multiples of 100. How many numbers does he write?

On the planet “Mathematics”, numbers live happily in a city called “Happy Numbers”. One special family consists of four-digit numbers whose hundreds digit is 0. Deleting the thousands and hundreds digits of each member produces a number equal to one three-hundred-and-first of the original number. How many members does this family have?

Hoang lives with his father, mother, younger sister, one dog, one cat, two parrots and four fish. How many legs do all the members of Hoang’s household have altogether?

Tien, Son and Dung each start with the same amount of money. At the bookstore, Tien buys 3 pencils and 4 notebooks and has 7 dollars left; Son buys 3 pencils and 3 notebooks and has 28 dollars left; Dung buys 1 pencil and 4 notebooks and has 21 dollars left. How much money did each friend have at first?

What is 30% of 40% of 50% of 200?

In the addition below, different shapes stand for different digits. What digit does the square represent?

Four black boxes and four white boxes are arranged as shown below. Each move swaps two adjacent boxes. What is the smallest number of moves An needs to make the black and white boxes alternate?

Jerry writes three digits on the board. Spike uses the three digits to make the largest possible three-digit number, and Tom uses them to make the smallest possible three-digit number. What is the greatest possible difference between their numbers?

At 3:47, the sum of the displayed digits is $3+4+7=14$. What is the smallest number of minutes that must pass before the sum of the digits shown on the clock is 20?

Which of the following numbers is the largest?

In the subtraction shown below, different letters stand for different digits. Find $A+B+C+D$.

The rectangle below measures 12 cm by 8 cm. Find the area of its striped region.

In a certain year, there are more Sundays than Tuesdays and more Saturdays than Thursdays. What day of the week is December 17 in that year?

Enter the day code: 0001 Monday; 0002 Tuesday; 0003 Wednesday; 0004 Thursday; 0005 Friday; 0006 Saturday; 0007 Sunday.

Drink A contains 45% pure fruit juice and drink B contains 60% pure fruit juice. The two drinks are mixed to make 21 litres containing 50% pure fruit juice. How many litres of drink A are used?

In the grid below, each symbol represents a different number. The total for each row is shown on its right. Find the value of the square.

A box contains seven cards numbered 1 to 7. The first person shakes the box and three cards fall out. The second person then shakes the same box and two more cards fall out. The first person says, “I know for certain that the sum of the numbers on your two cards is even.” What is the sum of the numbers on the first person’s three cards?