Question
If the 5-digit number 676pq is divisible by 3, 7 and 11,
then what is the value of (6p – 7q)?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 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 = 676pq (where p = 8, q = 3) (6p – 7q) = 6 × 8 - 7 × 3 ⇒ 48 - 21 = 27 ∴ The required result = 27
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