Groups primarily attract spammers and many fake users and they can drive you nuts.
Here's a method to authenticate members and even monetize a Facebook group.
Instead of asking simple questions which can easily be lied on, request a valid email address and mobile phone number, with the statement that periodical emails only from and about the group activities will be sent. Send an immediate email message to which they must reply to be confirmed.
Now you get primarily authentic members and secondly get to build a valid email and SMS database to which you can send periodic notices on the latest exciting group activities. The result is more member interaction and the opportunity to earn revenue from members who wish to place ads in the newsletters.