Which of the following numbers is divisible by

Solution

In order to be divisible by 33, a number should be divisible be both '3' and '11'. Divisibility rule of 3 = Sum of digits should be divisible by '3'. Divisibility rule of 11 = Difference between sum of digits at odd places and even places must be either '0' or a multiple of '11'. For option 'A' = 2 + 8 + 7 + 8 + 1 + 2 = 28 {Since 28 is not divisible by '3', we may discard this option.} For option 'B' = 4 + 8 + 9 + 4 + 6 + 7 = 38 {Since 38 is not divisible by '3', we may discard this option} For option 'C' = 1 + 4 + 3 + 8 + 8 + 9 = 33 {Since, 33 is divisible by 3, this is a potential answer.} Now divisibility check for 11 = (1 + 3 + 8) - (4 + 8 + 9) = 9 {Since, '9' is not divisible by '11', we may discard this option} For option 'D' = 1 + 4 + 9 + 3 + 5 + 8 = 30 {Since, 33 is divisible by 3, this is a potential answer.} Now divisibility check for 11 = (1 + 9 + 5) - (4 + 3 + 8) = 0 So, option 'D' is divisible by 11.