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M is the largest three digit number which when divided by 6 and 5 leaves remainder 5 and 3 respectively. What will be the remainder when M is divided by 11?
- A1
- B2
- C3
- D4
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CCommunity
Lcm of (6, 5) = 30
Let’s assume the number be "30K + constant", where Constant is the remainder.
let that number be ‘M’
⇒ M/6 = 5 (remainder)
M could be 5, 11, 17, 23, 30, ...
⇒ M/5 = 3 (remainder)
M could be 3, 8, 13, 18, 23, 28, ...
The very first number common in both term is 23.
⇒ M is 23 i.e. a constant term
⇒ 30K + constant = 30K + 23
The largest three digit number comes when K is 32
⇒ 30 (32) + 23 = 983
∴ When 983 is divided by 11, leaves the remainder 4.
Let’s assume the number be "30K + constant", where Constant is the remainder.
let that number be ‘M’
⇒ M/6 = 5 (remainder)
M could be 5, 11, 17, 23, 30, ...
⇒ M/5 = 3 (remainder)
M could be 3, 8, 13, 18, 23, 28, ...
The very first number common in both term is 23.
⇒ M is 23 i.e. a constant term
⇒ 30K + constant = 30K + 23
The largest three digit number comes when K is 32
⇒ 30 (32) + 23 = 983
∴ When 983 is divided by 11, leaves the remainder 4.