Question
Download Solution PDFIf the 5-digit number 676xy is divisible by 3, 7 and 11, then what is the value of (3x - 5y)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
676xy is divisible by 3, 7 & 11
Concept:
When 676xy is divisible by 3, 7 &11, it will also be divisible by the LCM of 3, 7 &11.
Dividend = Divisor × Quotient + Remainder
Calculation:
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
Last updated on Jun 11, 2025
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