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CAT 2008 | Question: 25

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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 $n.$ 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. $55$

1 Answer

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2 2 votes
Question is equivalent to finding numbers of no <500 which are divisible by 9 as if any number is divisible by 9 if and only if it has sum of digits a multiple of 9.

495/9=55

 So ans is 55
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