VTMO 2026 - Grade 5 - Semifinal - SET 4 - Self-study

A boxing match has 12 rounds. Each round lasts 3 minutes, with a 1-minute rest between consecutive rounds. If all 12 rounds are played, how long does the match last?

Minh writes a natural number on the board. Hai appends one digit to its right, making a new number that is 2020 greater than Minh’s number. Which digit does Hai append?

A 6 cm by 7 cm rectangle is divided into smaller pieces as shown. Each small grid square measures 1 cm by 1 cm. How many of the pieces have perimeter 10 cm?

What is the area of the shaded figure?

Each face of a cube is painted one colour. What is the fewest colours needed so that no two faces sharing an edge have the same colour?

The sum of two consecutive even numbers is 102. What is their product?

Lam uses four of the five types of pieces shown to form the figure below. Each type may be used more than once. Which piece cannot be used?

The rectangle is divided into six smaller squares. The largest square has area 16 square centimetres. What is the sum, in centimetres, of the perimeters of all six squares?

Minh joins Titan Education’s “9-week challenge” programme. On an outing, Minh’s class 5B lines up in one row. Minh is 10th from the front and 6th from the back. How many students are in the row?

A “symmetric time pair” consists of two times whose hour hands and minute hands are mirror images across the vertical axis of the clock, as illustrated by the dashed lines. For example, 10:45 and 1:15 form a pair, as do 12:55 and 11:05. How many pairs within one day are exactly 5 hours 30 minutes apart?

Practice convention: count pairs of distinct time instants within one midnight-to-midnight 24-hour day. The same clock displays occurring at different times of day count as different pairs.

Calculate $180-175+175-170+170-165+\cdots+110-105+105-100$.

Today is Sunday, 26 November 2017. Phương’s birthday is 1 January. Her older brother Khang’s birthday is six days before Phương’s. On which weekday is Khang’s birthday this year?

Let $A=2022-(135+357+579+791+20\times2\times2)$. Which calculation has the same value as $A$?

Hoàng thinks of an integer and multiplies it by 8. Which of the following numbers cannot be the result?

Tuấn colours the hexagons in the figure. Two hexagons that share an edge must have different colours. What is the fewest colours he needs?

Place the numbers 1 to 8 in the eight circles, using each once. Two circles connected by a segment must not contain consecutive natural numbers. What is the sum of the numbers in the four grey circles?

Minh has five boxes: one red, two blue and two yellow. He 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.
• The bottom box is not yellow.
Which colour is the bottom box?
Answer codes: 0001 = Blue; 0002 = Yellow; 0003 = Red.

Teams A and B each have 10 workers. They must build a road and a bridge. Team A can build the road in 14 days and the bridge in 25 days. Team B can build the road in 18 days and the bridge in 15 days. A new team C consists of five workers from A and five from B. Team C builds the road first, then the bridge. How long does it take to finish both?

Practice clarification: workers within each original team work at equal, constant rates, and their rates add when they work together.

A rectangle is divided into 16 smaller rectangles as shown. The areas of some smaller rectangles are marked. How many times as large as the hatched rectangle is the dark-shaded rectangle?

Trees are planted along one side of a road, 20 m apart. There are 28 trees, including one at each end. Along the same road, 13 equally spaced lamp posts are installed, also with one at each end. What is the distance between consecutive lamp posts?