Question

Find the least positive value of $x$ such that $67+x\equiv 1\left(mod4\right)$.

• A. 2

Answer 1

The correct option is A 2
Given: $67+x\equiv 1\left(mod4\right)$
$\Rightarrow 67+x-1=4n$
(for some integer n)
$\Rightarrow 66+x=4n$
$\therefore$ $66+x$ is a multiple of 4.

Therefore, the least positive value of $x$ must be 2, since 68 is the nearest multiple of 4 more than 66.