VTMO 2017 — Grade 5 — final

Evaluate $80 \times 3 - 70 \times 4 + 60 \times 5 - 50 \times 6 + 40 \times 7 - 30 \times 8 + 20 \times 9$.

An has three times Binh’s candies, and Chau $4$ more than Binh. Their total is $29$. Find An’s count.

Each $2 \times 2$ square pattern represents a digit. Rows $A , B , C , D$ encode $913 , 895 , 628 , 238$ in unknown order as shown. Find $B$.

Two four-digit numbers differ by $6789$. What is their greatest possible sum?

A road has $28$ trees $20 m$ apart, including endpoints, and $13$ equally spaced lamp posts including endpoints. Find lamp spacing.

The rectilinear shape below has black area $A$ and perimeter $P$. Find $A + P$ from the marked lengths.

A year has more Sundays than Tuesdays and more Saturdays than Thursdays. What weekday is December $17$?

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?

Dividing $162$ candies equally among $5$ A leaves $6$; $345$ is $6$ short of equal shares; $273$ divides exactly. What is the greatest possible class size?

A shop receives $\frac{2}{7}$ of an apple order in delivery $1$ and $55 \,\mathrm{kg}$ in delivery $2$. After both, received: remaining $= 3 : 5$. How many kilograms have arrived?

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?