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# OT- Math question about a ratio from an old SAT exam

#### David_M

##### Hot Rolled
Give the answer in number of turns.

#### BoxcarPete

##### Stainless
Is this some kind of trick question? If there were a "4" as a choice I'd consider it because it goes around the circle for another "turn" but it's just 3 otherwise.

#### Booze Daily

##### Titanium
Well circumference is pi x dia, so if one dia is 3x larger the circumference will be 3x larger. So 3.

#### Mark Rand

##### Diamond
NOTA. As Pete says, it'll go round four times.

This is one of the features of epicyclic gears.

I would say 3

#### Demon69

##### Titanium
Its ok Bob, your secrets safe with me

I got 3.

#### David_M

##### Hot Rolled
BoxcarPete and Mark got it!

It wasn't intended to be a trick question. They just got it wrong. It's worth watching.

#### CarlBoyd

##### Hot Rolled
Well circumference is pi x dia, so if one dia is 3x larger the circumference will be 3x larger. So 3.

Bingo, correct answer and correct logic.

CarlBoyd

#### plastikdreams

##### Diamond
It's nine...if you divide 3 by 1 you get three, then multiply 3 by the answer and you get 9...nine divided by .33 (1/3) is 27.27...the square root of 27.27 is 5.222 multiply that by pi and get 16.405...tan(16.405) is .29, round up to .3 and multiply by 30 and bam 9.

#### Demon69

##### Titanium
Thats interesting. In a sense its a matter of where circle A is viewed from. Ie looking out from the centre of circle B or directly down over circle A.
Either way I blame Boozy D

#### plastikdreams

##### Diamond
Thats interesting. In a sense its a matter of where circle A is viewed from. Ie looking out from the centre of circle B or directly down over circle A.
Either way I blame Boozy D

You have to look at the circles not as circles but as lines bent into a circle...but not any circle, a perfect circle with no chords or defects. It's an object of such perfection that no other 2 circles are as perfect...nor will there ever be.

#### Demon69

##### Titanium
You have to look at the circles not as circles but as lines bent into a circle...but not any circle, a perfect circle with no chords or defects. It's an object of such perfection that no other 2 circles are as perfect...nor will there ever be.
And the Lord said "let there be lulz," and there was lulz.

#### beege

##### Stainless
So here's the logic I find in this If I were to roll the smaller circle on a line three times the length of the circumference of the smaller circle, the center of the circle travels the same length as the line. Three rotations. Now if I make the line into a circle, the center of the circle will travel 1 + 1/3 the circumference of the large circle, or 4/3. It's all about how far the center travels. 4 rotations.

#### EPAIII

##### Diamond
"OK, Lucy; you have some splaining to do."

This is not the first or only time the people who wrote those exams got it wrong. I can recall a number of times where I had to stop and think, now what were they thinking, in order to bet the desired answer and a better grade.

It's nine...if you divide 3 by 1 you get three, then multiply 3 by the answer and you get 9...nine divided by .33 (1/3) is 27.27...the square root of 27.27 is 5.222 multiply that by pi and get 16.405...tan(16.405) is .29, round up to .3 and multiply by 30 and bam 9.

#### metal-ica

##### Aluminum
I lurnt sumthin today

##### Titanium
Dang! That's actually quite interesting.

#### jim rozen

##### Diamond
Roll the big circle out flat, it's a rack and the small one a pinion. Length of rack is 3 times the circumference of the pinion.

##### Titanium
You didn't watch the video. No pi for you.

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