Question

What is the sum of the digits of the least number which, when divided by $52$, leaves $33$ as remainder; when divided by $78$, leaves $59$ and when divided by $117$, leaves $98$ as remainder?

• A. $445$
• B. $448$
• C. $449$
• D. $441$

Answer 1

The correct option is C $449$

Given, $x$ mod $52$ $=33$

$x$ mod $78$ $=59$

and $x$ mod $117$ $=98$

In all of the three cases, if $19$ is added to the reminders, $x$ become divisible by the numbers given.

Thus we can say that $x+19$ is divisible by $52$, $78$ and $117$.

The lowest value of $x+119$ that is divisible by these numbers is equal to the LCM of $52,78$ and $117$.

LCM of$(52,78,117)=468$

Thus the minimum value of $x=468-19=449$.