Question 84

Which of the following numbers is completely divisible by 99?

Solution

For a number to be divisible by 99, it must be divisible by 9 and 11
Divisibility rule of 9: Sum of the digits must be divisible by 9.
Divisibility rule of 11: Absolute value of (Sum of digits in even positions - Sum of digits in odd positions) = 0 or 11

(A) : 57717 = 5 + 7 + 7 + 1 + 7 = 27 which is divisible by 9 and also by 11

(B) : 57627 = 5 + 7 + 6 + 2 + 7 = 27 which is divisible by 9 but not by 11

(C) : 55162 = 5 + 5 + 1 + 6 + 2 = 19 which is not divisible by 9

(D) : 56982 = 5 + 6 + 9 + 8 + 2 = 30 which is not divisible by 9

Thus, only option (A) is divisible by 99


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