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VTMO 2026 - Grade 4 - Semifinal - SET 10 - Self-study

Question 1

We can write 8 as a product of natural numbers whose sum is also 8. For example, $8=1\times1\times2\times4$ and $8=1+1+2+4$. How many ways can we write 12 as a product of natural numbers whose sum is also 12?

Practice convention: use at least two positive integer factors. Changing their order does not give a new way.

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

Question 2

In the table, each letter represents a number. Each number in the rightmost column is the sum of the letters in its row. Each number in the bottom row is the sum of the letters in its column. Find $T\times M\times O$.

Question illustration
  1. 65
  2. 50
  3. 60
  4. 80
  5. 70

Question 3

Which of the following numbers is divisible by 9?

Question illustration
  1. 2012
  2. 2013
  3. 2014
  4. 2015
  5. 2016

Question 4

Bình buys a bag of 48 M&M candies: 20 red, 10 yellow and 18 brown. She draws candies without looking. What is the smallest number she must draw to be certain of getting 12 candies of the same colour?

Question illustration
  1. 33
  2. 34
  3. 35
  4. 31
  5. 30

Question 5

Giang uses five identical sheets with $4\times4$ grids and shades the five figures shown below. Which figure has the greatest shaded area?

Question illustration
  1. Figure A
  2. Figure B
  3. Figure C
  4. Figure D
  5. Figure E

Question 6

In a strange village, the villagers dislike the digit 3 so much that they never use any number containing it. The houses on the right side of a road are numbered with the remaining odd numbers in increasing order. The first house is numbered 1, the second 5, and so on. What is the number of the fifteenth house on that side?

Question illustration
  1. 29
  2. 41
  3. 49
  4. 45
  5. 47

Question 7

The length of a rectangle is increased by 3 m while its width stays the same. Its area increases by $12\text{ m}^2$. What is its width, in metres?

Question illustration
  1. 3
  2. 4
  3. 6
  4. 9
  5. 12

Question 8

Thanh chooses three numbers from the $3\times3$ table, exactly one from each row and exactly one from each column. He multiplies them together. What is the greatest possible product?

Question illustration
  1. 45
  2. 162
  3. 168
  4. 105
  5. 504

Question 9

Calculate $4\times2023+2\times2023+4\times2023$.

Question illustration
  1. 20230
  2. 8092
  3. 2023
  4. 16184
  5. 2239

Question 10

There are 60 equally spaced trees around a circular lake. Khang runs exactly one lap in 8 minutes, then walks exactly one lap in 25 minutes. The number of metres he runs per minute, the number he walks per minute, and the distance in metres between consecutive trees are all natural numbers. The circumference of the lake is greater than 1500 m and less than 2000 m. How many metres apart are consecutive trees?

Question illustration
  1. 27
  2. 25
  3. 30
  4. 40
  5. 32

Question 11

Bình initially has some marbles. He gives Hạnh half of them. Next, he gives Khang $\frac13$ of the remaining marbles and 2 more. Finally, he gives Nam $\frac14$ of the marbles then remaining and 6 more, leaving him with none. How many marbles did Bình have initially?

Question illustration
  1. 30
  2. 28
  3. 26
  4. 32
  5. 34

Question 12

The road in front of a school is 27 m long. The headteacher plans to plant trees 3 m apart along one side of the road, including a tree at each end. How many trees will be planted?

Question illustration
  1. 9
  2. 11
  3. 10
  4. 8
  5. 12

Question 13

How many two-digit numbers are divisible by 5?

Question illustration
  1. 17
  2. 18
  3. 19
  4. 20
  5. 21

Question 14

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

Question illustration
  1. $20+2+2$
  2. $20+2\times2$
  3. $20\times2\times2$
  4. $2\times0+22$
  5. $20\times22$

Question 15

Find $N=(15+20+25+30+35+40)-(10+15+20+25+30+35)$.

Question illustration
  1. 10
  2. 20
  3. 30
  4. 35
  5. 40

Question 16

How many squares are there altogether in the figure?

Question illustration
  1. 8
  2. 9
  3. 10
  4. 11
  5. 12

Question 17

Each face of a cube is painted one colour. What is the smallest number of colours needed so that no two adjacent faces have the same colour?

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

Question 18

Rectangle PQRS has side $PS=2$ cm. JKLM is a square with side length 8 cm. Find the total shaded area.

Question illustration
  1. $16\text{ cm}^2$
  2. $32\text{ cm}^2$
  3. $48\text{ cm}^2$
  4. $56\text{ cm}^2$
  5. $62\text{ cm}^2$

Question 19

A father is now 36 years old. His age 10 years ago equals the sum of his two children’s current ages. The older child is 6 years older than the younger child. How old is the older child now?

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

Question 20

A standard six-faced die is rolled twice in succession. In how many different ways can the two top faces have a total of 7 spots?

Question illustration