Question

A value of x satisfying $150x\equiv 35$ (Mod 31) is ____.

• A. 14
• B. 22
• C. 24
• D. 12

Answer 1

Answer: (C)

24

$a\equiv b($ Mode $n)$

Means $a-b$ is divisible by $n$

So, $150x\equiv 35($ Mode 31$)$

$\Rightarrow 150x-35$ is divisible by 31

$\Rightarrow 5(30x-7)$ is divisible by 31

$30x-7=31k$, where $k$ is any natural number \

$\Rightarrow x=\frac{31k+7}{30}=\frac{30k+(k+7)}{30}=k+\frac{k+7}{30}$

so smallest positive value of $x$ , $k=23$

which given $x=23+1=24$