A function f : Z → Z is defined as f n = n + 1 n ∈ odd integer n 2 n ∈ even integer . If k ∈ odd integer and f f f k = 33 , then the sum of the digits of k is

Step-by-step solution

∵   k ∈ o d d   integer f k = k + 1 which is even ∴ f f k = k + 1 2 If k + 1 2 is odd ⇒ 33 = k + 1 2 + 1 ⇒ k = 63 not possible (because k + 1 2 is even) If k + 1 2 is even ⇒ 33 = k + 1 2 2 ⇒ 33 = k + 1 4 ⇒ k = 131 Sum of digits = 5