Hello,
I am bidding low because I am new to freelancer but I have two years of experience as android application developer in software companies. In my career I have build an android application which had same requirements as yours it was Ajman Ramadan App build for Ajman(UAE) Land and property department by Smonte Technology.(Google Play link: [login to view URL])
Its a quiz app and the question comes from the server by admin through GCM and a status bar notification is generated when new question arrives and on clicking on the notification the question of the day screen opens, it also had signin and signup screen.
As I will be using PHP/Mysql on server side and Android Java for the app so a real server would be needed to properly test the GCM.
You can trust me as GOLD developer as I have experience and here I want to get good rating on my profile and therefore I would try my best to meet up the deadlines and milestones.