Suppose, the seed of any positive integer n is defined as follows:
seed(n) = n, if n < 10
= seed(s(n)), otherwise,
where s(n) indicates the sum of digits of n. For example,
seed(7) = 7, seed(248) = seed(2 + 4 + 8) = seed(14) = seed(1 + 4) = seed(5) = 5 etc. How many
positive integers n, such that n < 500, will have seed (n) = 9?
(1) 39 (2) 72 (3) 81 (4) 108 (5) 55[CAT08]

1) 1
2) 2
3) 3
4) 4
5) 5

• Answer is 55
  
  Since, if the sum of the digits of a no. is divisible by 9 then the no. is divisible by 9.
  So, there are 500 / 9 = (55) nos. which are divisible by 9.
  
  Lets take an example according to this question.
  
  lets take a no. (495) which is divisible by 9 and check whether it follows the specified rule given or not.
  
  => 4 + 9 + 5 = 9 + 9 = 18 => 1 + 8 = 9
  so, the no. (495) satisfies the give condition.
  
  Similarly every no. divisible by 9 will follow this same condition and will satisfy this.
  
  So, our ans is 55.
• 8 years agoHelpfull: Yes(1) No(0)