VTMO 2014 — Grade 4 — final

Clocks $A , B , C$ are all set to $8$ a.m. A gains $30$ seconds per hour relative to $B$; $B$ loses $30$ seconds per hour relative to $C$. When $C$ shows noon, what time does A show (hours, minutes, seconds)?

Find a and $b$ using the triangle pattern shown below.

Using digits $1 , 2 , 3 , 4 , 5 , 6$, how many three-digit numbers have distinct digits and an even digit sum? For example, $123$.

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

A cinema has $10$ rows. The first has $10$ seats, and each later row has $3$ more than the previous one. How many seats are there?

Buses $A$ and $B$ initially carry $70$ passengers in total. By the end A gains $5$ and $B$ loses $4$; $B$ then has $7$ more than $A$. Find each initial count.

A family’s ages sum to $96$ now and will sum to $120$ in $6$ years. The member count stays fixed. How many people are there?

A father, Tuan and Lan walk to school. For every $3$ father’s steps Tuan takes $5$; for every $3$ Tuan’s steps Lan takes $5$. Tuan and Lan take $400$ steps combined. How many does the father take?