SAT Question Everyone Got Wrong

[jte]

I didn’t get a chance to watch the video yet, but my way of looking at this is to first have a rotating reference frame, as if the two circles are on fixed axles (keeping the centers of the circles and the point of contact all at fixed positions). It’s then intuitive that the ratio of circumferences determines the number of times the smaller circle rotates (to the one turn of the larger). Then one can rotate the reference frame to get the one additional turn.