The SAT Question Everyone Got Wrong

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Huge thanks to Dr. Doug Jungreis for taking the time to speak with us about this SAT question.

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Directed by Emily Zhang
Written by Emily Zhang and Gregor Čavlović
Edited by Peter Nelson
Animated by Ivy Tello and Fabio Albertelli
Filmed by Derek Muller
Produced by Emily Zhang, Han Evans, Gregor Čavlović, and Derek Muller

Thumbnail by Ren Hurley
Additional video/photos supplied by Getty Images and Pond5
Music from Epidemic Sound

[KevinJDildonik]

To all the 1st posters: YouTube takes up to 15 minutes to gather data on a video before showing stats. Everyone in the first 15 minutes all think they're first.

[MadMovieMakers]

This was a mentally challenging video to watch first thing in the morning. I'm awake now

[NCore_._]

I don't like math, but any visual explanation like this makes me engross in it for hours, replaying multiple sections to fully understand it and appreciate the fact, that how amazing it is.

[JClayJohnsonOfficial]

What makes it intuitively easiest for me to understand is to think about it this way: if the circumference of Circle B were 0 (i.e., a dot) then rotating Circle A around it would result in one revolution. So any addition to the circumference of Circle B would simply add on to the starting number of 1 rotation needed.

[duckyfam]

“I was amazed how badly it’s worded, ” literally half of the SAT problems.

[NoraOlson-ctnr]

Having the small circle rotating 3 times with the camera rotating is the best intuitive explanation of what's going on I've ever seen for something like this

[-ADOI-]

I was so confused because of the word "revolution, " "1" is what I thought the answer was because of that

[SuperJm]

Good job, very clear. My professor in computer science used to say that if you are a good programmer and you have an error in your code chances are you are usually off by 1 somewhere.

[felixp]

That part about the circle rotating around the triangle was mind-blowing. You instantly understand why it's not the same if the circle rolls on a flat line or rolls on a curved line

[forkmonkey]

Another fun way to conceptualize the N+1 is to ask what happens if the circumference of B is 0. A still has to rotate around that point, one time. Great video.

[markrittman]

I took the SAT in 1982 and scored a 780 in the math section, indicating that I likely missed just one math question. When faced with this question, I initially thought that it needed to roll around three times and then once more, leading me to select 4 as my answer. However, upon realizing that 4 was not provided as an option, I doubted myself and ultimately chose 9/2. As I doubt that I would have chosen 3, this is probably the question I missed.

[LGTVQHD]

as soon as Dr. Doug drew it on the white board with dots, it instantly clicked that the point touching the circles is moving 3r but the center of smaller circle moves 4r
wow
such simple yet mindblowing question.

[Shepard-Thomas]

In college, I took a poetry class and once had an answer marked wrong on a test. Confident in my response, I reached out to the poet themselves, who affirmed I was right and even communicated this to my professor. Despite not being a fan of poetry, that moment made me quite proud!

[Spondre]

I loved the "I hope so" answer from Doug at the end. It highlights the most important lesson I learned during my education: "I might be wrong."

[brucelade]

Excellent video. Thank you !!! This is possibly the best STEM video I have seen. The link to sidereal time etc is brilliant! To see practical application of "tricky maths" is how people learn. Well done! And thank you again

[littlezombie]

Mathematically it‘s actually really easy to calculate.

1) Calculate the distance d that point A has to travel. If you think about it, that‘s not the circumference of circle B, but the circumference of the radius B plus the radius of A, creating a third circle C around point B with point A now on it‘s outline. The circumference of this new circle C is now the distance d that point A has to travel to get back to its starting position.
Formula for circle circumference: 2 * r * PI
Now we know that r = rB + rA and rB = 3 * rA
-> d = 2 * (4 * rA) * PI
= 8 * rA * PI

2) Calculate the distance dRev that circle A covers with one revolution, which is equals the circumference of circle A. Again we use the formula for circumference, this time on circle A.
-> dRev = 2 * rA * PI

3) Lastly, calculating the number of revolutions needed, we divide the total distance point A has to travel on d ( = circumference of circle C) by dRev (the circumference of A).
-> R = d / dRev = (8 * rA * PI) / ( 2 * rA * PI)
rA and PI cancel each other out.
-> R = 8 / 2 = 4

[TupperWallace]

The 1872 novel “Around the World in Eighty Days” had a plot that depended on this kind of situation. Phileas Fogg traveled around the world eastward, against the earth’s rotation. Though initially he thought he’d missed the 80 day deadline by some hours, in fact only 79 days had passed in London. One extra rotation had passed beneath his feet. He won the prize, married the girl and lived happily ever after.

[ElectroBOOM]

This was a great video! Blew my mind when I realized how I was wrong!! Good to know question wordings can be so important, eh?! 😁😉

[parv]

It's revolutions, not rotation. So the logical answer is 1.😁

[pikastudios]

Here’s my guess, if the wheel A is revolving like a wheel then you divide both the circles circumference. Circle A has a radius of X and circle B has a radius of 3X, to find the circumference we multiply the radius by two and then times PI, making Circle A have a circumference of 2XPi and circle B having a circumference of 6X PI, so it should be 3