Question : What will be the greatest number $32 \mathrm{a} 78\mathrm{b}$, which is divisible by 3 but NOT divisible by 9? (Where a and b are single digit numbers).
Option 1: 329787
Option 2: 329784
Option 3: 329781
Option 4: None of these
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Correct Answer: 329784
Solution :
For option 1, the sum of the digits = $3 + 2 + 9 + 7 + 8 + 7 = 36$ (Divisible by 3 and 9)
For option 2, the sum of the digits = $3 + 2 + 9 + 7 + 8 + 4 = 33$ (Divisible by 3 but not divisible by 9)
For option 3, the sum of the digits = $3 + 2 + 9 + 7 + 8 + 1 = 30$ (Divisible by 3 but not divisible by 9)
So, $329784$ and $329781$ are divisible by 3 but not divisible by 9
The greatest number among them = $329784$
Hence, the correct answer is $329784$.
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