CAT 2008 — QA Question 9
Prime and Composite NumbersEasy
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?
Answer & solution
Correct answer: 55
- A
39
- B
72
- C
81
- D
108
55
Solution
Sum of the digits of multiples of 9 is always 9.
∴ Seed of any number will be 9 if and only if it is a multiple of 9.
There are 55 multiples of 9 which are less than 500 (as 500/9 = 55.555)
∴ There are 55 positive integers which will have seed = 9
Hence, option (e).