Question

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

• A. 39
• B. 72
• C. 81
• D. 108
• E. 55

Answer 1

The correct option is E 55

Sol:

e. 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. $9\stackrel{\sim }{A}\_\_1=9$ and $9\stackrel{\sim }{A}\_\_55=495.$ Hence there are 55 such numbers.