I like the quiz idea, but think the scale you think of is too big compared to the other gates.
Just make it similar to the dance-GATE where you have 4 x 4 dancemoves, just in this case, 4 x 4 questions and the difficulty increases between each set of 4.

As for how it works: I think it would be better to have 2 buttons on screen for O and X (like the "throw me off"-button in A11), otherwise you can just follow the crowd and interact with the right symbol based on that.