In the figure shown above, if the are of the shaded region

This topic has expert replies
Legendary Member
Posts: 2499
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Image

In the figure shown above, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

A. 4
B. 3
C. 2
D. \(\sqrt{3}\)
E. \(\sqrt{2}\)

The OA is C

Source: Official Guide
Source: — Problem Solving |

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Aug 14, 2019 10:48 am
swerve wrote:Image

In the figure shown above, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

A. 4
B. 3
C. 2
D. \(\sqrt{3}\)
E. \(\sqrt{2}\)
Smaller circle:
Let r=1.
Area = πr² = π(1²) = π
Circumference = 2Ï€r = 2Ï€(1) = 2Ï€

Since the area of the shaded region is 3 times the area of the smaller circle, the shaded region = 3Ï€.

Larger circle:
Area = (smaller circle) + (shaded region) = π + 3π = 4π.
Thus:
πr² = 4π
r = 2
Circumference = 2Ï€r = 2Ï€(2) = 4Ï€

The circumference of the larger circle is how many times the circumference of the smaller circle?
(larger circumference)/(smaller circumference) = 4Ï€/2Ï€ = 2

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

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 » Sun Aug 18, 2019 6:29 pm
swerve wrote:Image

In the figure shown above, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

A. 4
B. 3
C. 2
D. \(\sqrt{3}\)
E. \(\sqrt{2}\)

The OA is C

Source: Official Guide
We can let a = the radius of the entire figure (i.e, the larger circle), and b = the radius of the whtie circle (i.e., the smaller circle), and we have:

π(a^2 - b^2) = 3 * πb^2

a^2 - b^2 = 3b^2

a^2 = 4b^2

a = 2b

The circumference of the larger circle is 2Ï€a = 4Ï€b and the circumference of the smaller circle is 2Ï€b. Therefore, the circumference of the larger circle is twice that of the smaller circle.

Answer: C

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