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Question
f(f(f(k))) = 27. What is the sum of the digits of k ?
f(f(f(k))) = 27. What is the sum of the digits of k ?
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Solution
The correct option is B 6
Option (b)
Since k is odd then f(f(f(k))) =27
=> f(f(k+3)) = 27------------(1) since k is odd , k+3 will be even.
Hence, expanding (1) we get, 
--------------(2)
Here 
can either be even or odd
Case 1: let is even
Then (2) reduces to 
here sum of digits is 6
Case 2: let is odd
Then (2) reduces to 
=> k = 45
Substituting in it comes to be 24 which is not odd hence there is a contradiction hence
k = 105 here sum of digits is 6 is the only solution.
Hence, choice (b) is the correct answer.
Option (b)
Since k is odd then f(f(f(k))) =27
=> f(f(k+3)) = 27------------(1) since k is odd , k+3 will be even.
Hence, expanding (1) we get, --------------(2)
Here can either be even or odd
Case 1: let is even
Then (2) reduces to here sum of digits is 6
Case 2: let is odd
Then (2) reduces to => k = 45
Substituting in it comes to be 24 which is not odd hence there is a contradiction hence
k = 105 here sum of digits is 6 is the only solution.
Hence, choice (b) is the correct answer.
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