Question

Find the greatest number of four digits which when divided by $8,9$ and $10$ leaves $5$ as remainder in each case.

• A. $9730$
• B. $9725$
• C. $9715$
• D. $9995$

Answer 1

The correct option is B $9725$

The LCM of $8,9$ and $10$ is $360$.
The greatest four-digit number $=9999$.

Divide $9999$ by $360$. The remainder is $279$.

The greatest four-digit number divisible by $360$ is $9999-279=9720$.

Now, the greatest four-digit number divisible by $360$ and leaving a remainder $5$ is $9720+5=9725$.