A function `f` from integers to integers is defined as `f(x)={(n+3, n "is odd"),(n/2 , n "is even"):}`. If `k` is an odd integer and `f(f(f(k)))=27` then the sum of digits of `k` is

Options

A. `3`
B. `6`
C. `9`
D. `12`

Answer

B

Explanation

`kepsilon` odd
`f(k)=k+3` even
`f(f(k))=(k+3)/2`
Case 1 if `(k+3)/2epsilon` odd
`27=(k+3)/2+3impliesk=45` (not possible)
Case 2 if `(k+3)/2 epsilon` even
`27=f(f(f(k)))=f((k+3)/2)=(k+3)/4`
`implies k=105`
sum digits `=6`