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

Question 1

How many squares are in the figure below?

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

Question 2

The figure is made of small rectangles whose length is twice their width. In how many ways can one small rectangle be removed without changing the perimeter of the remaining figure?

1. 2
2. 4
3. 1
4. 3
5. 0

Question 3

Different letters stand for different digits in the addition below. What is the value of $B$?

1. 5
2. 6
3. 7
4. 8
5. 9

Question 4

Which expression below has value 7?

1. $4\times5+6\times3$
2. $4\times5+6\div3$
3. $6\div3+5\times4$
4. $3\times4\div6+5$
5. $3+4\times5\times6$

Question 5

A rectangle has area $48\text{ cm}^2$ and perimeter 32 cm. Its side lengths are natural numbers in centimetres. Find the difference between its length and width.

1. 4
2. 6
3. 8
4. 10
5. 12

Question 6

The digit sum of 123 is $1+2+3=6$. How many three-digit numbers have digit sum 6?

1. 12
2. 16
3. 17
4. 18
5. 21

Question 7

The average of five natural numbers is 60. Replacing the smallest number with 80 changes the average to 65. What number was replaced?

1. 45
2. 48
3. 50
4. 55
5. 60

Question 8

Class 5A has 12 more pupils than class 5B. How many pupils must move from 5A to 5B so that 5A has exactly 4 more pupils than 5B?

1. 2
2. 3
3. 4
4. 6
5. 8

Question 9

In the year 2021, the difference between a mother’s birth year and her age is 1961. How old is she in that year?

1. 25
2. 30
3. 32
4. 35
5. 60

Question 10

Pi buys three toys. For the first, Pi spends half the money plus 10,000 đồng. For the second, Pi spends half the remaining money plus 20,000 đồng. For the last, Pi spends half the money then remaining plus 30,000 đồng. How much money did Pi have initially? Practice clarification: no money remains after the third purchase.

1. 374 000
2. 140 000
3. 180 000
4. 300 000
5. 340 000

Question 11

The three scales below are balanced. One circle has the same weight as how many squares?

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

Question 12

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 in decreasing order of weight.

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 13

How many decimal numbers less than 100 have exactly two decimal places? Note: trailing zeros in the decimal part do not count. For example, 2.20 is regarded as having only one decimal place. Practice clarification: count nonnegative numbers.

1. 9 900
2. 8 910
3. 10 000
4. 8 900
5. 9 000

Question 14

Four friends An, Bình, Châu and Dũng talk about their candies. An says, “I have 12 more than the average of the other three.” Bình says, “I have 15 fewer than An.” Châu says, “I have 3 fewer than An.” If they pool all their candies and share them equally, how will Dũng’s number change?

1. Increase by 9
2. Increase by 6
3. Increase by 12
4. Decrease by 6
5. Increase by 15

Question 15

The $3\times3$ table below has the same sum in each row, column and diagonal. What is $A$?

1. 22
2. 56
3. 31
4. 39
5. 47

Question 16

Evaluate $80\times3-70\times4+60\times5-50\times6+40\times7-30\times8+20\times9$.

Question 17

A group of children has average age 11. If 17-year-old Nam joins, the average becomes 12. How many children were originally in the group?

Question 18

A teacher has one bag of blue candies and one bag of red candies, with equal numbers in the two bags. Each pupil chooses either option 1: 2 blue and 2 red candies, or option 2: 1 blue and 3 red candies. After everyone chooses, only 20 blue candies remain. How many pupils chose option 2?

Question 19

Nine balls are numbered 1 to 9. An, Bình, Châu and Dũng each take two balls in turn. An’s two numbers sum to 10; Bình’s differ by 1; Châu’s product is 24; and Dũng’s larger number divided by the smaller is 3. What number is on the remaining ball? Explain.

Question 20

A worker takes 20 hours to paint a room, including its four walls and ceiling. At the same work rate, painting another room with twice the width, twice the length and the same height takes 50 hours. How many hours are needed to paint the original ceiling?