If the center of a circle lies on a smaller circle...

This topic has expert replies
Moderator
Posts: 1988
Joined: 15 Oct 2017
Followed by:6 members
Image

If the center of a circle lies on a smaller circle, as shown above, what portion of the area of the larger circle is shaded?

A. 5/8
B. 2/3
C. 11/16
D. 3/4
E. 7/9

The OA is D.

I get the solution to this PS question as follow,

Radius of smaller circle = r2.

Radius of bigger circle = r1.

r1 = 2r2.

Portion of the area of the shaded region: pir2^2.

pi(2r2)^2 - pi r2^2 = 3/4 pi r1^2.

What portion of the area of the larger circle is shaded?

(3/4 pi r1^2)/(pi r1^2) = 3/4. Option C.

Experts, any suggestion? Thanks!

User avatar
GMAT Instructor
Posts: 15533
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1900 members
GMAT Score:790

by GMATGuruNY » Thu Mar 15, 2018 4:07 pm
LUANDATO wrote:Image

If the center of a circle lies on a smaller circle, as shown above, what portion of the area of the larger circle is shaded?

A. 5/8
B. 2/3
C. 11/16
D. 3/4
E. 7/9
Let the diameter of the larger circle = 4, implying that the diameter of the smaller circle = 2.
Area of the larger circle = πr² = π(2)² = 4π.
Area of the smaller circle πr² = π(1)² = π.
Area of the unshaded portion = larger circle - smaller circle = 4π - π = 3π.
Thus:
(unshaded portion)/(larger circle) = (3Ï€)/(4Ï€) = 3/4.

The correct answer is D.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 6362
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:26 members

by [email protected] » Fri May 24, 2019 3:14 pm
BTGmoderatorLU wrote:Image

If the center of a circle lies on a smaller circle, as shown above, what portion of the area of the larger circle is shaded?

A. 5/8
B. 2/3
C. 11/16
D. 3/4
E. 7/9

We can let the radius of the smaller circle = 1 and thus the radius of the larger circle = the diameter of the smaller circle = 2. The area of the smaller circle is π and the area of the larger circle is 4π. Therefore, the area of the shaded region is 4π - π = 3π and hence the area of the shaded region is 3π/4π = 3/4 of the area of the larger 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