question from Princeton Online Practice test

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charmingirl8: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Sat Jun 16, 2007 7:47 am

question from Princeton Online Practice test

by charmingirl8 » Mon Sep 03, 2007 5:36 pm

Can anyone solve this? The answer makes no sense to me...Thanks!

If circle A has 3 times the area of circle B, and circle B has one-sixth of the area of square WXYZ, what is the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A?

A- PI/ 12

B- PI/6

C- PI/2

D- 2/PI

E- 12PI

Quote

Source: Beat The GMAT — Problem Solving | Mon Sep 03, 2007 5:36 pm

jaspreet.sharma: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Wed Aug 22, 2007 4:49 pm; Thanked: 3 times

Re: question from Princeton Online Practice test

by jaspreet.sharma » Mon Sep 03, 2007 10:31 pm

charmingirl8 wrote:Can anyone solve this? The answer makes no sense to me...Thanks!

If circle A has 3 times the area of circle B, and circle B has one-sixth of the area of square WXYZ, what is the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A?

A- PI/ 12

B- PI/6

C- PI/2

D- 2/PI

Answer is C

Take some time to understand wat i wrote....couldnt put it in more simpler words........i hope this explanation will help u understand the ques

Soln

Area of Circle A = Pi sq(R)

Area of Circle B = Pi sq(r)

Area Of Square = sq (a) [let ‘a’ is side of square ]

Area Of Circle inscribed in Square = Pi sq (a/2)

As
circle B has one-sixth of the area of square WXYZ

Pi sq(r) = 1/6 sq (a)

sq (a)= 6 Pi sq (r)

ATQ
ratio of the area of a circle inscribed within WXYZ to that of the area of circle A = [Pi * 6 Pi sq (r)] / 4* Pi sq(R)
As circle A has 3 times the area of circle B
So ratio = Pi /2

As Pi sq(R) = 3 * Pi sq(r)

E- 12PI

Quote

ratindasgupta: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Jun 11, 2007 10:32 pm; Location: Mumbai

Re: question from Princeton Online Practice test

by ratindasgupta » Tue Sep 04, 2007 1:09 am

charmingirl8 wrote:Can anyone solve this? The answer makes no sense to me...Thanks!

If circle A has 3 times the area of circle B, and circle B has one-sixth of the area of square WXYZ, what is the ratio of the area of a circle inscribed within WXYZ to that of the area of circle A?

A- PI/ 12

B- PI/6

C- PI/2

D- 2/PI

E- 12PI

Let circle B have area = x

Circle A area = 3x

Square WXYZ area = 6x

So (Square WXYZ)/(Circle A) = 6x/3x = 2/1

Area of circle inscribed inside square = Pi/4(area of square)

So if (Square WXYZ)/(Circle A) = 2/1
(Area of circle inscribed inside squareWXYZ)/(Circle A) = Pi/4 * 2/1 = Pi/2

Answer is C