If the 5-digit number 676xy is divisible by 3, 7 and 11, then what is the value of (3x - 5y)?

Question: If the 5-digit number 676xy is divisible by 3, 7 and 11, then what is the value of (3x - 5y)?Solution:When 676xy is divisible by 3, 7 &11, it will also be divisible by the LCM of 3, 7 &11. Dividend = Divisor × Quotient + Remainder LCM (3, 7, 11) = 231 By taking the largest 5-digit number 67699 and divide it by 231. ∵ 67699 = 231 × 293 + 16 ⇒ 67699 = 67683 + 16 ⇒ 67699 - 16 = 67683 (completely divisible by 231) ∴ 67683 = 676xy (where x = 8, y = 3)(3x - 5y) = 3 × 8 - 5 × 3 = 24 - 15 = 9 ∴ The required result = 9