Everyone Got This SAT Math Question Wrong

Problem: Circle A has 1/3 the radius of circle B, and circle A rolls one trip around circle B. How many times will circle A revolve in total?

1982 SAT Question
In the figure above, the radius of circle A is one third the radius of circle B. Starting from position shown in figure, circle A rolls around circle B. At the end of how many revolutions of circle A will the center of circle A first reach its starting point?

(a) 3/2
(b) 3
(c) 6
(d) 9/2
(e) 9

Blog post summary: http://mindyourdecisions.com/blog/2015/07/05/everyone-got-this-sat-math-question-wrong-can-you-solve-it-sunday-puzzle/#.VZmO9flVhBc

Sources:
http://www.donaldsauter.com/rolling-circles.htm
http://www.nytimes.com/1982/05/25/us/error-found-in-sat-question.html

Also see the Coin Rotation Paradox
https://en.wikipedia.org/wiki/Coin_rotation_paradox

Update: some people have made really cool interactive worksheets at Geogebra. You should check these out!

Rolling Circles: http://tube.geogebra.org/m/787131
Rolling coin paradox: http://tube.geogebra.org/m/112822
A question about a rolling circle: http://tube.geogebra.org/m/107691

If you like my videos, you can support me at Patreon:
https://www.patreon.com/mindyourdecisions

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

My Blog: https://mindyourdecisions.com/blog/
Twitter: https://twitter.com/preshtalwalkar
Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965
Google+: https://plus.google.com/108336608566588374147/posts
Pinterest: https://www.pinterest.com/preshtalwalkar/
Tumblr: https://preshtalwalkar.tumblr.com/
Instagram: https://instagram.com/preshtalwalkar/
Patreon: https://www.patreon.com/mindyourdecisions

Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r

If you buy from the links below I may receive a commission for sales. This has no effect on the price for you.

My Books
"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.8/5 stars on 31 reviews)
http://amzn.to/1uQvA20

"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.6/5 stars on 3 reviews)
http://amzn.to/1o3FaAg

"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews.
http://amzn.to/1GhUUSH

"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews)
http://amzn.to/1NKbyCs

"Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 5 reviews)
http://amzn.to/1NKbGlp

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews)
http://amzn.to/1LOCI4U

"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews)
http://amzn.to/18maAdo

"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews)
http://amzn.to/XRm7M4

Видео Everyone Got This SAT Math Question Wrong канала MindYourDecisions