VTMO 2026 - Grade 5 - Semifinal - SET 8 - Self-study

An, Binh and Chau share a bookcase containing 20 books. An has read 19 of them, Binh 12 and Chau 11. What is the smallest possible number of books that all three have read?

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

The two smaller squares inside the large square have perimeters 4 cm and 24 cm, as shown. What is the shaded area, in square centimetres?

Machines A, B and C make the same product at different rates. While A makes 18 items, B makes 14; while B makes 10 items, C makes 8. How many items does C make while A makes 45?

Find the remainder when $A$ is divided by 9, where

$A=(20230801-1082023)+(20230219-19022023)+2023$.

Class IQ5A initially has 12 fewer pupils than class IQ5D. After two pupils transfer from IQ5D to IQ5A, IQ5A has half as many pupils as IQ5D. How many pupils does IQ5D have after the transfer?

In a village, no house number may contain the digit 3. The rule says that “odd digits” are used to number the houses on the right side of the road in increasing order: the first is 1 and the second is 5. What is the number of the fifteenth house on that side?

Practice clarification: the house numbers must be odd numbers; their individual digits, other than the forbidden 3, may be even.

An’s birthday falls on a Wednesday. Binh’s birthday is 17 days before An’s. On which day of the week does Binh’s birthday fall?

Hoang chooses a natural number and multiplies it by 8. Which of these cannot be the result?

A running track is 400 m long. Points A, B, C and D divide it into four equal-length sections. An starts at Start, halfway along section AB, and walks anticlockwise at 1.4 m/s. After 30 minutes, which marked point is he nearest to?

The four types of pieces shown are made from 1 cm by 1 cm squares. An must use every type and the same number of pieces of each type to assemble a square without gaps or overlaps. What is the perimeter of the smallest possible square?

In rectangle $ABCD$, P lies on diagonal DB. Lines through P parallel to the sides form four rectangles, as shown. Given $AM=10$ cm, $AH=5$ cm and $PN=4$ cm, find the perimeter of ABCD in centimetres.

Evaluate $\left(1+\frac12\right)\times\left(1+\frac13\right)\times\left(1+\frac14\right)\times\left(1+\frac15\right)$.

The ratio of the side lengths of two squares is $\frac23$. What is their area ratio in the same order?

A two-digit natural number N leaves remainder 9 when divided by 10 and remainder 8 when divided by 9. Find the sum of its digits.

A factory divides 2800 kg of rice equally among 800 bags. A family uses 0.25 kg each day. How many days does one bag last?

Nhi uses matchsticks to make 2021 as shown. She moves exactly three matchsticks, without adding or removing any, to make the largest possible four-digit number. What is it? Use the digit shapes shown.

In the multiplication shown, different letters stand for different digits. What is the final product? Each dash marks one digit.

Some three-digit numbers have digit sum 25 and digit product 567. What is the largest such number?

Tank A is full of water and tank B is empty. Water is poured from A into B until both water levels have the same height. The tank dimensions are shown in centimetres. Find the common water height, in centimetres.