If these are the only requirements of the app, its cost depends on who will build the app.
Keep in mind that you need both a designer and an engineer. The proper selection of the people who will build the app is crucial for the app success. If you have a solid business model for your app, you'd better hire a good team to do it. Otherwise, you can give it to an undergraduate student and get it for almost free.
As a technical person, I can tell you that not much work is required. However, the process most creative professionals adopt is the following:
- First of all, they need to know you and your business
- Secondly, they need to understand what is the unique feature of your app and what value are you bringing to the market
- Then, they propose 1-3 different design approaches, based on your business values
- Finally, they design and code the app according to your specifications
A good professional will also let you know the strengths and weaknesses of each approach. For example, having 100 questions is a single scrolling page may not be the best solution for the problem you are trying to solve.
For example, in my company we do not take projects for less than four-figure numbers, since anything lower than this would not worth our time, meeting sessions, roadmapping sessions, technical support, and more.
Keep in mind that, most of the times, you get what you pay for. Your budget is an investment for your business success. You can spend 100 bucks and get your app in the AppStore, but 1,000 bucks may guarantee better support, future improvements, immediate bug fixes, etc.
To sum up, the first question you need to ask is "how this app will help my business". Then, try to find out whether the professionals who'll build the app will bring you a return of your investment or not.