A function `f` from integers to integers is defined as `f(x)={n+3, n in od d n/2,n in e v e n` suppose `k in ` odd 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`