ratio of geomatry

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alltimeacheiver: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Feb 09, 2011 3:08 am; Location: Delhi; Thanked: 1 times; Followed by:5 members

ratio of geomatry

by alltimeacheiver » Tue Apr 05, 2011 10:06 pm

If the area of square S and the area of circle C are equal, then the ratio of the perimeter of S to the circumference of C is closest to

I got ans 2/1 straight away. but the ans is 9/8. Is that the case that we need to consider Pie over here. but how

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Source: Beat The GMAT — Problem Solving | Tue Apr 05, 2011 10:06 pm

HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 am; Thanked: 47 times; Followed by:13 members; GMAT Score:640

by HSPA » Tue Apr 05, 2011 10:13 pm

s^2 = pi* r^2 --- stat 1
we need 4s in terms of 2*pi*r

Let us say pi = 3
From stat 1 we have s = sqrt3 * r

perimeter/circumf = 4*sqrt 3/ 6 = 2/sqrt3 = 2/1.7 ~ 2.2

First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.

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vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 am; Thanked: 156 times; Followed by:34 members; GMAT Score:720

by vineeshp » Tue Apr 05, 2011 10:16 pm

s^2 = Pi r^2 (s is side of square S, r is radius of the cirlce)
s = Root of (Pi * r^2) = r * Root(Pi)

We need to find ratio of perimeter to circumference.
4s / 2 Pi r

Vineesh,
Just telling you what I know and think. I am not the expert.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Tue Apr 05, 2011 10:17 pm

alltimeacheiver wrote:If the area of square S and the area of circle C are equal, then the ratio of the perimeter of S to the circumference of C is closest to

I got ans 2/1 straight away. but the ans is 9/8. Is that the case that we need to consider Pie over here. but how

If s is the side of square, then area of square = sÂ²
If r is the radius of circle, then area of circle = (pi)rÂ²
sÂ² = (pi)rÂ² implies s = râˆš(pi)
Perimeter of square = 4s = 4râˆš(pi)
Circumference of circle = 2(pi)r
So, Perimeter of square:Circumference of circle = 4râˆš(pi):2(pi)r = 2:âˆš(pi) = 2:1.8

Now we need to have the answer choices to answer this question. Can you please post the same?

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alltimeacheiver: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Feb 09, 2011 3:08 am; Location: Delhi; Thanked: 1 times; Followed by:5 members

by alltimeacheiver » Tue Apr 05, 2011 10:35 pm

A 7/9

B 8/9

C 9/8

D 4/3

E 2/1

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Tue Apr 05, 2011 10:37 pm

alltimeacheiver wrote:A 7/9

B 8/9

C 9/8

D 4/3

E 2/1

2:1.8 is closest to 9:8

The correct answer is C.

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force5: Legendary Member; Posts: 582; Joined: Tue Mar 08, 2011 12:48 am; Thanked: 61 times; Followed by:6 members; GMAT Score:740

by force5 » Wed Apr 06, 2011 12:18 am

hi Anurag.. can you please help us know how did you find out that 2:SqrtÏ€ was equal to 9/8 and not 4/3. I would have marked D in the exam.approx the value of Ï€ to 3.