Correct Answer - Option 2 : 29
Calculation:
⇒ Sum of digits = 23
⇒ Remainder when N is divided by 9
⇒ N/9 = 5 {Remainder on division by 9 for any number is equal to the remainder of dividing the sum of the digits of the number by 9}
⇒ The remainder of N/3 = 2 {The number of the form 9k + 5 divided by 3 leaves a remainder 2}
⇒ N = 11k + 7
⇒ N = 3m + 2
⇒ 11k + 7 => Possible numbers are 7, 18, 29, 40, 51
⇒ 3m + 2 => Possible numbers are 2, 5, 8, 11, 14, 17, 20, 23, 26, 29
⇒ The number that is of the form 11k + 7 and 3m + 2 should be of the form 33b + 29.
⇒ The first natural number that satisfies both properties is 29.
⇒ Now, starting with 29, every 11th number is of the form 11k + 7, and every 3rd number is of form 3m + 2.
⇒ So, starting from 29, every 33rd number should be on both lists (33 is the LCM of 11 and 3).
⇒ Or, any number of the form 33b + 29 will be both of the form 11K + 7 and 3m + 2, where b, k, m are natural numbers.
⇒ The remainder when the said number is divided by 33 is 29.