Question

When the positive integer $m$ is divided by $7$, the remainder is $4$. What is the remainder when $2m$ is divided by $7$?

• A. $9$
• B. $1$
• C. $4$
• D. $6$
• E. $8$

Answer 1

The correct option is B $1$

$m=7\times quotient+remainder$

$m=7n+42m=2\times 7n+2\times 4$

since remainder can not be greater than or equal to divisor

$=7\times \left(2n\right)+7+1$

$=7(2n+1)+1$

Remainder is 1