These scammers are after your money, identity, data, etc. The different things they could do are:
Identity Theft: They could use the information obtained from you to social engineer your cellphone provider to disconnect your mobile service or port your mobile service to another carrier. Once they have access to your number, they could impersonate you and would also have access to your two factor authentication codes (if you've used your number/SMS as your second factor). Based on the type of reconnaissance they've done, they could then gain access to your email, Twitter, iCloud and other accounts.
Data Theft: Based on the information you gave them, they could send targeted malware to your device by sending you SMS messages with links. Opening these links on your mobile browser would result in them being able to exploit a bug in your browser to gain access to your mobile device. They could do this using something like BeEF - The Browser Exploitation Framework Project.
Change your Phone Plan: They could convince the cellphone provider to change your plan, make calls that you would be charged for.
There are many other things that they can do. In summary, if you receive a call from a number not stored within your contacts or from Private Numbers, it's better not to answer the call.
Also be wary of missed calls that are made to your number. Scammers give missed calls from premium numbers to make you call back, after which, you're charged a hefty fee.