Numbers-15 (CAT-2008)

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

Solution follows here:

Solution:

It is asked that the sum of digits of a number should be 9

=> it is nothing but the divisibility condition of 9

=> we need to find number of multiples of 9 below 500

=> 9,18,27,….495

=> 495 = 55*9 => there are 55 multiples of 9 below 500.

Answer(5)