2019 · Q4
Consider the multiplication 999 × abc = def132 in decimal notation, where a, b, c, d, e and f are digits. What are the values of a, b, c, d, e and f respectively?
Elementary MathematicsNumber System
- A6, 6, 8, 6, 8, 7
- B8, 6, 8, 6, 7, 8
- C6, 8, 8, 7, 8, 6
- D8, 6, 8, 8, 6, 7
Explanation
999n ends in 132, so 999n ≡ 132 (mod 1000) ⇒ −n ≡ 132 ⇒ n ≡ 868 (mod 1000). Thus abc = 868, and 999 × 868 = 867132, so def = 867. The digits are a,b,c,d,e,f = 8,6,8,8,6,7.