Question

$\text{If}9\equiv 3\left(mod6\right)\text{and}14\equiv 2\left(mod6\right)$, then $-5\equiv y\left(mod6\right)$. Find y.

• A. 6
• B. 5
• C. 1
• D. -1

Answer 1

The correct option is C 1

Given:$-5\equiv y\left(mod6\right)$

By the theorem on modulo operations, if a, b, c and d are integers and m is a positive integer such that if $a\equiv b\left(modm\right)$ and $c\equiv d\left(modm\right)$ , then
(i) $(a-c)\equiv (b-d)\left(modm\right)$

Given, $9\equiv 3\left(mod6\right)\text{and}14\equiv 2\left(mod6\right)$
Hence, from the (i) theorem,
$(9-14)\equiv (3-2)\left(mod6\right)$
$\Rightarrow$ $-5\equiv 1\left(mod6\right)$
By comparing the above expression with the given one, we get y = 1.