CAT Quant Practice Problems

Question: Suppose, the seed of any positive integer n is defined as follows:

\(seed\left( n \right) = \left\{ {\begin{array}{*{20}{c}}{n,\;if\;n < 10}\\{seed\left( {s\left( n \right)} \right),\;otherwise}\end{array}} \right.\)

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

Correct Option:5

For seed (n) = 9, all the numbers below 500 must have a digit sum of 9.

These numbers are all divisible by 9.

So total number of numbers below 500 and divisible by 9 is 55.


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