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

Question 1

There are nine cards on a table, numbered 1, 2, 3, 4, 5, 6, 7, 8 and 9. Việt removes one card, leaving a sum divisible by 5. Nam then removes two more cards, and the remaining sum is still divisible by 5. The product of the three removed numbers is odd. What is their sum?

Question illustration
  1. 15
  2. 10
  3. 5
  4. 12
  5. 20

Question 2

How many squares are there in the figure?

Question illustration
  1. 4
  2. 5
  3. 6
  4. 11
  5. 12

Question 3

If Minh buys 3 notebooks, he has 5,000 đồng left. If he buys 5 notebooks, he is 19,000 đồng short. How many thousand đồng does one notebook cost?

Question illustration
  1. 5 000
  2. 10 000
  3. 12 000
  4. 19 000
  5. 24 000

Question 4

Mr Tom writes $1+2+3+4+5+\cdots+19+20$ on the board. Jerry successively replaces the sum of any two numbers by their difference. Which of the following cannot be his result?

Question illustration
  1. 18
  2. 19
  3. 20
  4. 10
  5. 0

Question 5

Find the missing number in the last triangle.

Question illustration
  1. 11
  2. 22
  3. 44
  4. 54
  5. 64

Question 6

Calculate $10+9+8+\cdots+1+0+1+2+\cdots+9+10$.

Question illustration
  1. 110
  2. 55
  3. 45
  4. 90
  5. 100

Question 7

A bag of candies can be shared equally among 3, 4 or 5 children with no candies left over. What is the smallest possible number of candies in the bag?

Question illustration
  1. 50
  2. 48
  3. 24
  4. 30
  5. 60

Question 8

A box contains four balls of different colours: red, yellow, blue and black. The red ball is heavier than the yellow ball but lighter than the blue ball. The black ball is lighter than the red ball but heavier than the yellow ball. Arrange the balls from heaviest to lightest.

Question illustration
  1. Blue - red - yellow - black
  2. Yellow - black - red - blue
  3. Black - yellow - red - blue
  4. Blue - red - black - yellow
  5. Yellow - red - black - blue

Question 9

A rectangle has perimeter 42 cm and width 4 cm. What is its length in centimetres?

Question illustration
  1. 17
  2. 19
  3. 21
  4. 34
  5. 38

Question 10

Each small square has area $1\text{ cm}^2$. Find the area of the shaded shape.

Question illustration
  1. 12
  2. 13
  3. 14
  4. 15
  5. 16

Question 11

A $6\times6$ square grid is shown. Each small square has area $2\text{ cm}^2$. Find the shaded area.

Question illustration
  1. 48 cm²
  2. 28 cm²
  3. 12 cm²
  4. 24 cm²
  5. 26 cm²

Question 12

If the five-digit number $2212A$ is divisible by 9, what is the digit $A$?

Question illustration
  1. 5
  2. 3
  3. 9
  4. 0
  5. 2

Question 13

A teacher has 90 notebooks. She gives An 5 notebooks, then gives Bình, Châu and Dũng 10 notebooks each. She distributes all the remaining notebooks among the other pupils in the class so that each of those pupils receives a positive, different number of notebooks. What is the greatest possible number of pupils in An’s class?

Question illustration
  1. 11
  2. 14
  3. 15
  4. 16
  5. 20

Question 14

The numbers from 1 to 32 are placed in order at equal intervals around a circle. Straight lines through the centre pair opposite numbers. Which number is paired with 12?

Question illustration
  1. 28
  2. 27
  3. 23
  4. 25
  5. 29

Question 15

Twenty people stand in a queue. Châu is fifth from the front and Minh is tenth from the back. How many people stand between Châu and Minh?

Question illustration
  1. 3
  2. 4
  3. 5
  4. 6
  5. 7

Question 16

An buys 120 candies altogether: strawberry, orange and milk candies. There are twice as many strawberry candies as orange candies. There are 4 more orange candies than milk candies. How many orange candies does An have?

Question illustration
  1. 31
  2. 32
  3. 33
  4. 34
  5. 35

Question 17

A pet shop has 30 white and grey animals altogether. Of the 20 white animals, 7 are rabbits. Among the grey animals, 8 are not rabbits. How many rabbits are there in the shop?

Question illustration
  1. 7
  2. 9
  3. 10
  4. 12
  5. 15

Question 18

Pi colours the letters in TITAN EDUCATION. Different letters must have different colours, and repeated copies of the same letter must have the same colour. How many colours does Pi need?

Question illustration
  1. 7
  2. 8
  3. 9
  4. 10
  5. 11

Question 19

In the magic square below, the numbers from 2 to 10 are placed one in each cell so that every row, column and diagonal has the same sum. Find $x$.

Question illustration

Question 20

Châu has 40 cards numbered from 1 to 40, one of each number. She draws 2 cards. In how many different ways can she draw them so that their sum is divisible by 3? Drawing cards 10 and 2 is the same as drawing 2 and 10.

Question illustration