The SAT Question Everyone Got Wrong

[billchao]

It would be the perfect video for @ChetlovesMer if only there was a white belt in it.

[boogielicious]

We had this problem in high school. If you visualize it, you will see how to respond to the question. Of course when I was in high school, we had to learn how to use a slide rule. 😜

[saevel25]

So, I am going to try to answer this before watching. 

R1 = 1/3 x R2

C1 = 2xPixR1
C2 = 2xPixR2

This should be just the ratio of the circumferences of the circles. One revolution is just traversing the circumference of the circle. So, how many times does it take the small circle to traverse the larger circle's circumference. 

A = C2/C1 = R2/R1. Since R1 = 1/3 x R2. Then A = 1 / (1/13) = 3

 

[iacas]

8 minutes ago, saevel25 said:

So, I am going to try to answer this before watching. 

Good on you for trying first. That's what most people would guess.

I knew the answer to this one because it had come up at some point in high school. I didn't know about the time with telescopes and all of that, but it makes sense.

Thanks for sharing this, @billchao.

[saevel25]

1 minute ago, iacas said:

Good on you for trying first. That's what most people would guess.

I knew the answer to this one because it had come up at some point in high school. I didn't know about the time with telescopes and all of that, but it makes sense.

Thanks for sharing this, @billchao.

The frustrating part was, when I was doing that math. I thought, wait the center of the small circle is traveling a circle that combines the two radii. I wish I explored that route a bit. 🤣

[billchao]

1 hour ago, saevel25 said:

The frustrating part was, when I was doing that math. I thought, wait the center of the small circle is traveling a circle that combines the two radii. I wish I explored that route a bit. 🤣

Yea I made that same mistake at first. It helped me to visualize it.

[ChetlovesMer]

7 hours ago, billchao said:

It would be the perfect video for @ChetlovesMer if only there was a white belt in it.

I remember when this happened. We learned about it in math class. Then I learned about it again in my prep-class for the SAT which was 1987 for me. So, I already knew this quite well. 

 

4 hours ago, iacas said:

Good on you for trying first. That's what most people would guess.

I knew the answer to this one because it had come up at some point in high school. I didn't know about the time with telescopes and all of that, but it makes sense.

Thanks for sharing this, @billchao.

Same for me. It was a kinda big story in 1983-84ish. Then when I took the SAT prep in 87 it was covered at nauseum. 

BTW - Thanks for posting, @billchao

[Yukari]

I love these type of problems where it seems so "straight forward" at a first glance, but when you actually think about it in detail, you realize the simple answer is not the right one.

[GolfLug]

This was so cool. I think one day somewhere out there, someone will come up with the  explanation of the 'golf paradox' too..😆

Whoever they are, I'm rootn for them.

Edited January 27, 2024 by GolfLug