Which is the largest three digit number which when divided by 6 leaves the remainder 5 and when divided by 5 leaves the remainder 3?
What I did:
On division by 6 leaves remainder 5
So numbers are 6, 11, 17, 23
On division by 5 leaves remainder 3
3,8,13,18,23
So common number between the two is 23. Largest three digit number divisible by 23 is 989
But answer is 983. How?
This is a gmat exam question.
Best Answer
You don't want "divisible by $23$." $46$ is divisible by $23$ but it doesn't have the property you want.
You want a number which can be written $30k+23$, where $30=6\cdot 5$.
The general way to do this problem is called the Chinese Remainder Theorem.