The video begins by introducing a problematic math question from the 1982 SAT, which involved the rotation of two circles.

• The question asked how many revolutions circle A (with a radius one third of circle B) would make when it rolls around circle B and returns to its original position.
• The options provided were 3/2, three, six, 9/2, and nine.
• The presenter initially thought the answer was three, based on the ratio of the circles' circumferences, but this was incorrect.

The video reveals that the correct answer to the SAT question was not among the provided options, leading to every student getting it wrong.

• The correct answer is four, based on the 'coin rotation paradox'.
• This paradox shows that when a circle rolls around another circle of the same size, it makes two rotations, not one.
• Therefore, when circle A, with a radius one third of circle B, rolls around circle B, it makes four rotations.

The video discusses the impact of the error in the SAT question, which led to it being scrapped and test scores being recalculated.

• The College Board, the entity that administers the SAT, admitted their mistake and nullified the question for all test takers.
• The rescoring process cost the College Board over $100,000 and affected students' scores by up to 10 points.
• Such a shift in scores could have significant implications for college admissions and scholarships that use strict minimum test score cutoffs.

The video delves deeper into the mathematics behind the SAT question, explaining how the rotation and revolution of a circle can result in different answers.

• To understand why the circle completes an extra rotation, the presenter uses a ribbon to represent the larger circle's circumference and shows how the smaller circle rolls along it three times.
• However, when the path becomes circular, the smaller circle makes an additional rotation, leading to the correct answer of four.
• The presenter also points out that from the perspective of circle B, circle A only appears to rotate three times, and from an astronomical perspective, it only revolves once.

The video explains how the mathematics of circle rotation and revolution are crucial in astronomy and timekeeping, using the example of Earth's rotation and revolution around the Sun.

• From an external observer's perspective, the Earth rotates 366.24 times in a year, while from the Earth's perspective, it rotates 365.24 times.
• The extra day is due to the Earth's circular path around the Sun.
• This difference between solar time (based on the Earth's rotation on its axis) and sidereal time (based on the Earth's revolution around the Sun) is crucial for tracking objects in space and operating geostationary satellites.

The video concludes by discussing the aftermath of the SAT question error and the future of standardized testing.

• Despite the College Board's efforts to correct the error, some students may have been affected by the shift in scores.
• The presenter notes that such errors and the shift towards test-optional admissions during COVID-19 are contributing to the decline of the SAT.
• However, the presenter also interviews one of the students who discovered the error, who went on to have a successful career in mathematics.