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# If a circle, regular hexagon and a regular octagon have the

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Manager
Joined: 02 Jan 2007
Posts: 208
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If a circle, regular hexagon and a regular octagon have the [#permalink]  22 Mar 2007, 06:11
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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
Senior Manager
Joined: 11 Feb 2007
Posts: 356
Followers: 1

Kudos [?]: 47 [0], given: 0

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:

h > o > c E

Director
Joined: 12 Jun 2006
Posts: 534
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Kudos [?]: 34 [0], given: 1

ricokevin wrote:
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:

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?
Senior Manager
Joined: 11 Feb 2007
Posts: 356
Followers: 1

Kudos [?]: 47 [0], given: 0

ggarr wrote:
ricokevin wrote:
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:

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
Manager
Joined: 12 Feb 2007
Posts: 167
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Kudos [?]: 1 [0], given: 0

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.
Director
Joined: 12 Jun 2006
Posts: 534
Followers: 1

Kudos [?]: 34 [0], given: 1

the better you do the more the challenge probs will come into play. some of us may never see the difficult probs.
Director
Joined: 12 Jun 2006
Posts: 534
Followers: 1

Kudos [?]: 34 [0], given: 1

ricokevin wrote:
ggarr wrote:
ricokevin wrote:
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:

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?
Senior Manager
Joined: 11 Feb 2007
Posts: 356
Followers: 1

Kudos [?]: 47 [0], given: 0

ggarr wrote:
ricokevin wrote:
ggarr wrote:
ricokevin wrote:
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:

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...

In this problem, area was fixed.
Manager
Joined: 02 Jan 2007
Posts: 208
Followers: 2

Kudos [?]: 5 [0], given: 0

ricokevin wrote:
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:

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
Manager
Joined: 02 Jan 2007
Posts: 208
Followers: 2

Kudos [?]: 5 [0], given: 0

Look Ma I can post links now!

Here's the one for the quiz from where I got this question.
http://free-quiz.4gmat.com/showquiz.php?quiz=29
Senior Manager
Joined: 29 Jan 2007
Posts: 450
Location: Earth
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Thats cool Vikramjit..you did it

That was a cool link. Those were tough ones, for me.

Got 7 correct in 20 minutes. 1 silly mistake in calculating and 2 plain wrong.

Lets put those for our friends here.
Senior Manager
Joined: 11 Feb 2007
Posts: 356
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kyatin wrote:
Thats cool Vikramjit..you did it

That was a cool link. Those were tough ones, for me.

Got 7 correct in 20 minutes. 1 silly mistake in calculating and 2 plain wrong.

Lets put those for our friends here.

So this is where u got that "13^7 + 14^7 + 15^7 + 16^7" problem from kyatin!

It's hard...
Senior Manager
Joined: 29 Jan 2007
Posts: 450
Location: Earth
Followers: 2

Kudos [?]: 45 [0], given: 0

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.
Director
Joined: 14 Jan 2007
Posts: 779
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Kudos [?]: 75 [0], given: 0

vikramjit_01 wrote:
Look Ma I can post links now!

Here's the one for the quiz from where I got this question.
http://free-quiz.4gmat.com/showquiz.php?quiz=29

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.
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