Question

When $31513$ ad $34369$ are divided by a certain three digit number, the remainders are equal, then the remainder is ______.

• A. $86$
• B. $97$
• C. $374$
• D. $113$

Answer 1

The correct option is B $97$

Let the divisor be $a$ and remainder be $r$

Let $31513=am+r$

and $34369=an+r$

Then, $a(n-m)=2856=24\times 119=12\times 238=8\times 357=6\times 476=4\times 714$

All three digit numbers give same remainder $=$ $97$