Question

Suppose the seed of any positive integer n is defined as follows:
Seed $\left(n\right)=n$ (if $n<10$), otherwise Seed $\left(n\right)=seed\left(s\right(n\left)\right)$, where $s\left(n\right)$ indicates the sum of digits of n.
For example, seed$\left(7\right)=7,$ seed$\left(248\right)=2+4+8=$ seed$\left(14\right)=$ seed $(1+4)=$ seed$\left(5\right)=5$, etc.
How many positive integers $n$ (n < 500) are there such that Seed(n) = 9?

• A. 39
• B. 72
• C. 81
• D. 55

Answer 1

The correct option is D 55

From the definition of 'seed', it is clear that we have to count number of integers between 1 and 500, which are divisible by 9. The smallest is 9 and the largest is 495. Multiples of 9 from 9 to 495 = $\frac{495-9}{9}+1$. Hence there are 55 such numbers.