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Which one of the following numbers is exactly divisible by 99?
1. 42767
2. 31781
3. 21187
4. 53658

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Correct Answer - Option 4 : 53658

Concept used 

Divisibility rule of 99 : Number should be divisible by 9 and 11 

Divisibility of 9 = sum of digit should be divisible by 9 

Divisibility of 11 = Difference in sum of even place digit and sum of odd place digit is 0 or multiple of 11

Calculation 

From option 

Now option (1) 42767

⇒ 42767 = 4 + 2 + 7 + 6 + 7 = 27 

27 is divisible by 9 

Now check for 11 

⇒ (4 + 7 + 7) - (2 + 6) = 10

10 is not divisible by 11 

So number is not divisible by 99

Now option (2) 31781 

⇒ 31781 = 3 + 7 + 1 + 8 + 1 = 20 

20 is not divisible by 9 

So number is not divisible by 99 

Now Option (3) 21187 

⇒ 21187 = 2 + 1 + 1 + 8 + 7 = 19 

19 is not divisible by 9 

So number is not divisible by 99 

Now option (4) 

⇒ 53658 = 5 + 3 + 6 + 5 + 8 = 27 

27 is divisible by 9 

Now check for divisibility of 11 

⇒ (5 + 6 + 8) - (3 + 5) = 11

So, number is divisible by 99 

∴ 53658 is divisible by 99 

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