2024 · Q26
What is the value of x, (0 < x < 8) if (100⁹⁷ + 100⁵⁴ + x + 1) leaves a remainder 0 when divided by 9?
Elementary MathematicsNumber System
- A8
- B6
- C4
- D1
Explanation
100 ≡ 1 (mod 9), so 100^97 + 100^54 + x + 1 ≡ 1 + 1 + x + 1 = x+3 (mod 9). For divisibility by 9, x+3 ≡ 0 (mod 9); with 0 < x < 8 this forces x = 6. This is option B.