two three options:
Keep the answers separate from the rest of the source code
If you want your code to be open source, however don't want the answers to be open source, then you open source the code for the application without the questions & answers, with the questions & answers being a separate closed source "plugin" or data file. Your Android app would bundle both of these together into a single app.
Put the answers in your source code
Alternatively, if you consider the questions and answers to be a core part of what you want open sourced then you should put the answers into the source code, preferably un-obfuscated so that others can read and modify them. Obfuscating source code so that it can't be understood and modified isn't really in keeping with the principles of open source code.
Put the answers on a server on the internet
With both of the above solutions it's possible for someone who has downloaded your app to find out the answers without playing your program in either case - no matter how you obfuscate / encrypt your answers, if your program can identify the answer without additional information, so can a human examining your compiled app.
If you really want to make sure that nobody can find out the answers then the only real option is not to give them the answers and have the app call a web service etc... whenever they want to know the answer. The app should send the answer that the user has entered and the web service should tell the app whether or not the answer is correct, that way the user has no way of telling what the answer is until after they already have the correct answer (short of brute-forcing the web service, which you can detect and protect against).
If you are looking for ways to obfuscate your answers the that suggests to me that you don't really want to open source your answers in the first place, so you should consider the first options.
If it's critical that the user not be able to find the answer in advance then the third option is your only real choice, however I'm struggling to think of a scenario where this would be worth the effort, not least because it prevents your users from using your app without an Internet connection.