Hi shibsriz,
While I agree with Brent that this question doesn't have the "feel" of a GMAT question (Where are the answer choices? Those answers would likely give you a hint as to the possibilities.), there are some Number Properties that would help you to answer it (and answer it quicker, if you spot the larger pattern).
The crux of this question is in how the functions work and what you "end up with" (and how this info allows you to work "backwards")
You have to run the function 5 times and at each level...
If x = even, then divide by 2
If x= odd, then add 5
After the 5th run, total = 19
Ending with a total of 19 limits your options.
You can only get to 19 if the prior number was 38 (since 38 is even, you'd divide by 2 to get 19).
You CAN'T get to 19 if the prior number is 14 (14 is even, so you'd divide by 2; you WOULDN'T add 5).
This means that when you're looking at an odd number, there's ONLY 1 way to get to it (by dividing by 2 from the previous number).
If, however, you're looking at an even number, there are 2 ways:
If you're trying to get to 38, then you can get there with....
76 (even, so divide by 2) = 38
33 (odd, so add 5) = 38
By working backwards, you can quickly map out each step. To help you continue on, think about....
how to get to 76
how to get to 33
Then continue on from there.
In the end, you should have 8 answers. And for the super-nerds out there, if you look closely, you'll see the beginning of a Fibonacci sequence, but that's not necessary to solve this question.
GMAT assassins aren't born, they're made,
Rich
