Question

If $77 \equiv 88x \pmod{5}$, then x is equal to

• A. $4$
• B. $61$
• C. $59$
• D. $48$

Hint:

Modular arithmetic: find the multiplicative inverse modulo 5.

Answer 1

The Correct Option is B

Step 1: $77 \equiv 2 \pmod{5}$, $88 \equiv 3 \pmod{5}$. So $2 \equiv 3x \pmod{5}$.}
Step 2: Multiply by inverse of 3 mod 5 (which is 2): $4 \equiv x \pmod{5}$. So $x = 5k+4$.}
Step 3: Among options, $61 = 5 \times 12 + 1$? Actually $61 \equiv 1 \pmod{5}$, not 4. $59 \equiv 4 \pmod{5}$, so $x=59$ is correct.}