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If a circle, regular hexagon and a regular octagon have the [#permalink]

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22 Mar 2007, 06:11

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E

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If a circle, regular hexagon and a regular octagon have the same area and
if the perimeter of the circle is represented by "c",
that of the hexagon by "h" and
that of the octagon by "o",
then which of the following is true?

A) c > o > h
B) c > h > o
C) h > c > o
D) o > h > c
E) h > o > c

I got this question from an online quiz but since I don't yet have 10 legit
posts I cant post the link so I'll be able to post the link in a day or two
I think.
The OA however is E

A known property of circle is that it has the greatest area given a certain perimeter. This can also mean that given a certain area, it has the least perimeter.

The more sides a polygon has, the closer it resembles a circle.
So in this regard, a regular octagon is closer to circle than a regular hexagon.

Therefore, with areas equal, the perimeters should be:

A known property of circle is that it has the greatest area given a certain perimeter. This can also mean that given a certain area, it has the least perimeter.

The more sides a polygon has, the closer it resembles a circle. So in this regard, a regular octagon is closer to circle than a regular hexagon.

Therefore, with areas equal, the perimeters should be:

h > o > c E

Is this an advanced question. I haven't read that in any of my GMAT materials. Perhaps this is something I should've picked up from my readings?

A known property of circle is that it has the greatest area given a certain perimeter. This can also mean that given a certain area, it has the least perimeter.

The more sides a polygon has, the closer it resembles a circle. So in this regard, a regular octagon is closer to circle than a regular hexagon.

Therefore, with areas equal, the perimeters should be:

h > o > c E

Is this an advanced question. I haven't read that in any of my GMAT materials. Perhaps this is something I should've picked up from my readings?

Maybe it's an "unknown property" just kidding
No, I didn't pick this up from my GMAT readings either...
I remember it from a geometry class that I took in tenth grade

I appreciate the challenges really trying to push the brain to think of solutions to the toughest problems. However, I wonder whether a good portion of the material, or the principles that need to be known to solve the problems, will ever show up on the GMAT.

A known property of circle is that it has the greatest area given a certain perimeter. This can also mean that given a certain area, it has the least perimeter.

The more sides a polygon has, the closer it resembles a circle. So in this regard, a regular octagon is closer to circle than a regular hexagon.

Therefore, with areas equal, the perimeters should be:

h > o > c E

Is this an advanced question. I haven't read that in any of my GMAT materials. Perhaps this is something I should've picked up from my readings?

Maybe it's an "unknown property" just kidding No, I didn't pick this up from my GMAT readings either... I remember it from a geometry class that I took in tenth grade

ricokevin, can we say the greater the area, the lesser the perimeter?

A known property of circle is that it has the greatest area given a certain perimeter. This can also mean that given a certain area, it has the least perimeter.

The more sides a polygon has, the closer it resembles a circle. So in this regard, a regular octagon is closer to circle than a regular hexagon.

Therefore, with areas equal, the perimeters should be:

h > o > c E

Is this an advanced question. I haven't read that in any of my GMAT materials. Perhaps this is something I should've picked up from my readings?

Maybe it's an "unknown property" just kidding No, I didn't pick this up from my GMAT readings either... I remember it from a geometry class that I took in tenth grade

ricokevin, can we say the greater the area, the lesser the perimeter?

No, I don't think so...

Can't think of any shape whose area gets bigger as it gets smaller...

You'll have to have one (either the area or the perimeter) fixed and then talk about the other...

A known property of circle is that it has the greatest area given a certain perimeter. This can also mean that given a certain area, it has the least perimeter.

The more sides a polygon has, the closer it resembles a circle. So in this regard, a regular octagon is closer to circle than a regular hexagon.

Therefore, with areas equal, the perimeters should be:

h > o > c E

And among other things, I even thought the OA was incorrect!

I divided the hexagon into 6 equal parts - 6 equilateral triangles and equated its area to the circle's and got

(pi)r^2 = 6 (1/2bh) (base & height of the 6 traingles)
from here I basically got nowhere
but now I know

Maybe its all those classes in school that I spent daydreaming, that ricokevin spent listening to his teacher's

To be honest I guessed that one. I just realised 13 +14 + 15 + 16 summed up tp 58. I just had a hunch that numerator can be split into (a+b+c+d)(some tems with varying powers)

I would love to know how to methodically solve this one. So I put it on new thread.

I took this quiz too. Got 9 out of 10 correct. But I knew two of them before taking this test. so effective score is 7 out of 10.
Can somebody explain the circle, hexagon answer.
I am not convinced with the answer of 13^7 +14^7 + 15^7 + 16^7....
what is the rule to solve such problems.