VTMO 2026 - Grade 5 - Semifinal - SET 6 - Self-study

An cycles to the market to buy vegetables for his mother. After travelling one quarter of the way, he meets Binh and stops to talk. He then cycles another 1.2 km to reach the market. How far is the market from An’s home, in kilometres?

A teacher writes all three-digit numbers whose three digits are different, whose digit product is 24, and whose digit sum is 11. How many numbers does the teacher write?

Pi has some sheets of paper. Each time, Pi chooses any one sheet and cuts it into four smaller sheets. After seven such cuts, there are 30 sheets altogether. How many sheets were there at first?

A carpenter takes 20 minutes to cut a 1 m wooden bar into pieces 20 cm long. How many minutes are needed to cut a 2 m bar into 20 cm pieces?

For this practice question, assume each cut takes the same time and pieces are not stacked for cutting.

Vinh has 10 more sweets than Quang. If Vinh gives Nam two sweets, Nam will have as many as Vinh has left. How many more sweets does Nam initially have than Quang?

Rectangle $PQRS$ has side $PS=2$ cm, and square $JKLM$ has side 8 cm. Find the total shaded area in the diagram.

Find $P$.

$11+12+13+14+15+16+17+18+19=9\times P$.

A father is now 36 years old and his child is 6. In how many years will the father be three times as old as his child?

The chart shows the membership of a school’s Music, Modern Dance, Football and Basketball clubs. The horizontal gridlines are equally spaced. One club has 33 members, and it is not the club with the fewest members. How many members does the Music club have?

Which expression has an even value?

Fold the cardboard net into a cube. Which three faces meet at vertex $P$?

The operation $\odot$ is defined by the rule illustrated here: $8\odot5=8\times5+8+5=53$. Find $9\odot3$.

Find $N$.

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

What is the value of the circle in the equations shown? Each occurrence of the same shape has the same value.

Figures I, II and III are squares. Square I has perimeter 12 and square II has perimeter 24. What is the perimeter of square III?

During a Black Friday sale, Hai’s mother wants to buy him a watch. At 40% off, she would have 16 money units left. At the regular price, she would be 4 money units short. What is the regular price, in the same money units?

IQ5 is a Grade 5 mathematical-thinking class. No two girls in the class were born on the same day of the week, and no two boys were born in the same month. Adding any one more boy or any one more girl would make the corresponding condition fail. How many pupils are in IQ5? Explain your reasoning.

Two old rulers are each 15 cm long and were marked from 0 cm to 15 cm. All centimetre marks have faded except the 3 cm and 4 cm marks. The rulers overlap as shown, with a 3 cm mark on one ruler aligned with a 4 cm mark on the other. Find the total end-to-end length $L$, in centimetres.

The fifth Titan Mathematics Olympiad semifinal has multiple-choice and fill-in-answer sections. The multiple-choice section has ten questions. Each correct answer earns 2 points, each wrong answer loses 1 point, and an unanswered question earns 0 points. Van scores 12 points in this section and remembers leaving exactly one question unanswered. How many questions did Van answer correctly?

Anh and Binh leave city A for city B at the same time that Chau and Duy leave B for A. Anh meets Chau after one hour, then meets Duy 12 minutes later. Binh meets Chau two hours after starting. How many minutes after starting does Binh meet Duy?

For this practice question, assume everyone travels continuously at a constant individual speed along the same route.