• Board contributors include instructors with "800" GMAT scores.
  • 95% of posts have replies within 24 hours.
  • Join for discounts with 800score, VeritasPrep and ManhattanGMAT


FAQ  - Register  - Search - Login 

All times are UTC - 7 hours




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: GMAT Geometry
PostPosted: Mon Apr 29, 2013 8:17 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 477
Image

In the figure above, ABCD is a rectangle inscribed in a circle. If the length of AB is three times the length of AD, then what is the ratio of the area of the rectangle to the area of the circle? (Figure not drawn to scale.)

A. 1:2
B. 3:2π
C. 2:5
D. 4:3π
E. 6:5π

(E) Let AD = x. AB = 3x. Area of the rectangle is (AD) × (AB) = x × (3x) = 3x².

Using the Pythagorean theorem, take AB and AD to get the diameter AC of the circle.
x² + (3x)² = AC²
x² + 9x² = AC²
10x² = AC²
AC = x√10 and the radius is [x√10] / 2.

The area of a circle is πr², so the area is π [(x√10) / 2]² = (10πx²)/4 = (5πx²)/2.

The ratio is:
3x² : (5πx²)/2 = 3 : 5π/2 = 6 : 5π

The correct answer is E.
----------
I was wondering why you couldn't assume that point O was the center of the circle. Does the question have to directly mention that fact, because I assumed that it was the center and therefore took OD and OA as being radii. Which ultimately gives you an answer of 3:π.
Top
 Profile  
 
 Post subject: Re: GMAT Geometry
PostPosted: Mon Apr 29, 2013 8:18 am 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 453
Quote:
I was wondering why you couldn't assume that point O was the center of the circle. Does the question have to directly mention that fact …
No, you cannot. Anything that is NOT stated by the question statement or specifically marked on graphics is considered unknown. (However basic facts, such as: lines, which look straight, are straight; how the points are notated, etc. can be assumed based on the graphics.)

But maybe you could prove (based on the given facts) that O is the center of the circle? Unfortunately no. There are no grounds for that.

Quote:
… , because I assumed that it was the center and therefore took OD and OA as being radii. Which ultimately gives you an answer of 3:π.
Even if O was the center of the circle, then 3:π would still NOT be the correct answer. OA and OD would be the radii indeed, but the triangle AOD would be just an isosceles one. And as the explanation shows, the radius differs from the length of AD, so AOD would NOT be an equilateral triangle.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC - 7 hours


Who is online

Users browsing this forum: No registered users and 2 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
Template made by DEVPPL -
phpBB SEO
 
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.