Question

If $\frac{(x+2)}{7}$ is an integer greater than $2$, then the remainder, when $x$ is divided by $7$ is

• A. $2$
• B. $5$
• C. $8$
• D. $4$
• E. $3$

Answer 1

The correct option is B $5$

Let $\frac{x+2}{7}=k$ where $k$ is an integer greater than $2$.

Hence, $x+2=7k$

$\Rightarrow x=7k-2$

We now divide $x$ by $7$

$\Rightarrow \frac{x}{7}=\frac{(7k-2)}{7}$

$\Rightarrow \frac{x}{7}=k-\frac{2}{7}$

Since $x$ is an integer greater than $12$, the remainder of the division of $x$ by $7$ is $5$.