VTMO 2014 — Grade 3 — final

Transferring one pupil from class $3$ A to $3 B$ makes their sizes equal. Transferring one pupil from $3 B$ to $3 C$ makes $3 C$ have two more pupils than $3 B$. Which class was originally the largest?

How many two-digit numbers have digit sum $9$?

How many squares in the grid contain the letter $A$?

Eight cards are numbered $1$ through $8$. An, Binh and Chau each draw two cards.
• Binh: one card’s number is twice the other’s.
• Chau: the two numbers sum to $9$.
• An: the two numbers sum to $7$, but their difference is not $3$.
Which two cards remain?

An has three clocks $A , B$ and $C$. A gains $30$ seconds per hour compared with $B$. $B$ loses $30$ seconds per hour compared with $C$. All three are reset to $8$ a.m. What time does A show when $C$ shows noon? Give hours, minutes and seconds.

Two ships carry $660$ passengers in total. After transferring $30$ passengers from A to $B$ and $70$ from $B$ to $A$, the ships carry equal numbers. How many were originally on each ship?

The large square is tiled by four congruent rectangles and a small square of side $6 \,\mathrm{cm}$. The large square has side $14 \,\mathrm{cm}$. What is the length of each rectangle?