Question

If $r$ is the remainder when each of the numbers $1059$, $1417$ and $2312$ is divided by $d$. where $d$ is an integer greater then one, $d-r$ equals

• A. $1$
• B. $15$
• C. $179$
• D. $d-15$

Answer 1

Answer: (B)

$15$

The Greatest number that will divide $x,y$ and $z$ leaving the same remainder in each case is the $HCF$ of $(x-y),(y-z)$ and $(z-x)$.

Here, $d$ is the number which divides $1059,1417$ and $2312$ leaves the same remainder $r$.

When $1059,1417$ and $2312$ is divided by $179$ we get the same remainder $164$ in each case.

So, $d=179$ and $r=164$

$\therefore d-r=179-164=15$ (Option B)