BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

In the figure above, what fraction of the circle with center

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pm
Thanked: 1443 times
Followed by:247 members

by ceilidh.erickson » Tue Jun 11, 2019 11:50 am
Angles opposite one another have the same measurement. Thus, both non-shaded regions measure 45 degrees from the center of the circle, for a total of 90 degrees.

A circle is 360 degrees, so 90 degrees is 1/4 of the circle that is unshaded. That leaves 3/4 of the circle shaded.

The answer is D.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Tue Jun 11, 2019 7:15 pm
Gmat_mission wrote:Image
In the figure above, what fraction of the circle with center O is shaded?

A. 1/8
B. 1/4
C. 2/3
D. 3/4
E. 5/6

[spoiler]OA=D[/spoiler]

Source: Princeton Review
Since the central angle of each white region is 45 degrees, the central angle of each shaded region is 180 - 45 = 135. Thus, (135 + 135)/360 = 270/360 = 3/4 is shaded.

Alternate Solution:

A sector corresponding to 45° will have an area which is 1/8 of the complete circle. The unshaded region consists of two such sectors; therefore, the unshaded region is 1/8 + 1/8 = 1/4 of the whole circle. Thus, the shaded region is 1 - 1/4 = 3/4 of the whole circle.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1