Question

Find the least positive value of $x$ such that $147$ $\equiv$ $(x+5)\left(\text{mod}7\right)$.

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is A $2$

$147$ $\equiv$ $(x+5)\left(\text{mod}7\right)$
$⟹147-(x+5)=7n$, for some integer $n$
$⟹142-x=7n$
$(142-x)$ is a multiple of $7$.
$\therefore$ The least positive value of $x$ must be $2$ as $142-2=140$, which is the nearest multiple of $7$ less than $142$.