VTMO 2017 — Grade 4 — final

Evaluate $39\times15+20\times17+20\times18+35\times19$.

How many figures below have exactly $\frac13$ of their area shaded?

An, Binh, Chau have $29$ candies total. An has three times Binh’s amount; Chau has $4$ more than Binh. How many does Chau have?

Two three-digit numbers differ by $328$. What is their maximum sum?

Natural numbers follow the table pattern: $1$ is at row $1$, column $1$ and $6$ at row $3$, column $2$. What is at row $10$, column $10$?

The figure joins a square of perimeter $40 \,\mathrm{cm}$ and a rectangle of perimeter $70 \,\mathrm{cm}$ as shown. Find the combined perimeter.

One side of a road has $40$ trees including both ends, spaced $12 m$ apart. The same road has $27$ equally spaced lamp posts including both ends. What is the lamp spacing?

An, Binh, Chau all lie and each owns a blue or red stone. An: “Mine matches Binh’s”; Binh: “Mine matches Chau’s”; Chau: “Exactly two of us have red stones.” How many are true: An is blue; Binh is blue; Chau is red; An and Chau differ?

A three-digit number has digit sum $25$ and digit product $567$. What is the largest such number?

Distinct letters are distinct digits: $\overline{BEE}\times4=\overline{SEED}$. Find $SEED$.

Balls $1$ through $9$: An takes two summing to $10$; Binh takes two differing by $1$; Chau takes two with product $24$; Dung takes two with quotient $3$. Each ball is used once. Which ball remains?

Among $30$ pupils, the mean for numbers $1 \text{--} 10$ is $89 , 11 \text{--} 30$ is $80$, and $1 \text{--} 20$ is $85$. Find the mean for $21 \text{--} 30$.