Question

Find the greatest number of five digits which when divided by $4,6,14$ and $20$ leaves respectively $1,3,11$ and $17$ as remainders.

• A. $99930$
• B. $99960$
• C. $99997$
• D. $99957$

Answer 1

The correct option is D $99957$

$4=2\times 2$
$6=2\times 3$
$14=2\times 7$
$20=2\times 2\times 5$
LCM of $4,6,14,20=2\times 2\times 3\times 7\times 5=420$
The greatest number of 5 digit$=99999$
When $99999$ is divided by $420$, it leaves reminder $39$
$\therefore 99999-39=99960$
According to the question, the difference of the divisor and their reminder is $3$.
$\therefore$ Required number $=99960-3=99957$.