• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

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

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 416
Joined: 01 Mar 2018
Followed by:1 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2094
Joined: 04 Dec 2012
Thanked: 1443 times
Followed by:242 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.
Image

Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education


Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 4813
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:22 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
scott@targettestprep.com

Image

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

ImageImage