Q67 / 180 · COMEDK 2018 · Mathematics

If $3 x \equiv 5(\bmod 7)$, then

  • A
    $x \equiv 2(\bmod 7)$
  • B
    $x \equiv 3(\bmod 7)$
  • Correct answer
    C
    $x \equiv 4(\bmod 7)$
  • D
    None of these

Solution

Given, $3 x \equiv 5(\bmod 7)$ $$ \begin{array}{cc} \Rightarrow & 3 x-5=0(\bmod 7)=\frac{7}{3 x-5} \\ \Rightarrow & 3 x-5=7 P, \text { where } P \in Z \\ \Rightarrow & x \equiv 4(\bmod 7) \end{array} $$

Hence, the correct answer is option: 'C'.

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