Question

When the positive integer $m$ is divided by $7$, the remainder is $4$. When $m+26$ is divided by $7$, find the remainder.

• A. $0$
• B. $2$
• C. $4$
• D. $5$
• E. $6$

Answer 1

The correct option is B $2$

If $m$ is divided by $7$, the remainder is $4$, that can be written as:
$m=7x+4$ for some integer $x$.
Then $m+26$ can be written as,
$(7x+4)+26$
$\Rightarrow$ $7x+30$
$\Rightarrow$ $7x+7\times 4+2$.
$\Rightarrow$ $7(x+4)+2$.
As you see, if the $m$ $+26$ is divided by $7$, then the $(x+7)$ is factor and the remainder is $2$.
Hence, option B is correct.