Multiple choice

N is the largest 3-digit number, which when divided by 11 and 9 leaves 9 and 7 as the respective remainders. The sum of the digits of N is

  1. 25

  2. 16

  3. 18

  4. 20

  5. 27
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A Correct answer
Explanation

N = 11a + 9 and N = 9b + 7. This means N + 2 is divisible by both 11 and 9 (LCM = 99). So N + 2 = 99k - 2. For the largest 3-digit number, 99*10 - 2 = 988. 988/11 = 89 rem 9, 988/9 = 109 rem 7. Sum of digits 9+8+8 = 25.

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