A10. The three-digit number $2 A 4$ is added to 329 to get $5 B 3$. What is the largest possible value of the digit $A$ if $5 B 3$ is divisible by 3?
(A) 7
(B) 8
(C) 4
(D) 1
(E) 9

# Seventh Regional Mathematics Competition for Students of Vocational Schools

April 4, 2007

## II. Part: LONGER PROBLEMS

Instruction: Solve problems B1 to B4 of the second part on the provided paper, where you write down the complete calculations. Read each problem carefully and answer the questions asked. The solution to each of these problems will be scored from 0 to 5 points.

Note that you have 90 minutes to solve the problems of the first and second parts.
A10. In the ternary number $2 A 4$, $A$ can have a maximum value of 4. Then the sum $244+329=573$ is divisible by 3. For divisibility by 3, the digit $A$ could be increased by 3, but then the sum $274+329=603$ would not have the form $5 B 3$.

## II. PART