Last visit was: 21 Apr 2026, 05:16 It is currently 21 Apr 2026, 05:16
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
Sub 505 (Easy)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 Apr 2026
Posts: 109,720
Own Kudos:
810,375
 [1]
Given Kudos: 105,796
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,720
Kudos: 810,375
 [1]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 20 Nov 2020, 01:15
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

91% (02:16) correct 9% (02:20) wrong based on 102 sessions

History

Date
Time
Result
Not Attempted Yet

In the figure shown, the arc of the quarter circle has length \(6\pi\). The rectangle has perimeter 60. What is the perimeter of the shaded region?

A. \(36 + \pi\)
B. \(36 + 2\pi\)
C. \(36 + 3\pi\)
D. \(36 + 4\pi\)
E. \(36 + 6\pi\)


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS


Show Spoiler
Attachment:
2020-10-27_14-10-11.png
2020-10-27_14-10-11.png [ 92.16 KiB | Viewed 3895 times ]
ShowHide Answer
Official Answer
E
User avatar
rajatchopra1994
User avatar
Joined: 16 Feb 2015
Last visit: 22 Jun 2024
Posts: 1,052
Own Kudos:
1,305
 [1]
Given Kudos: 30
Location: United States
Posts: 1,052
Kudos: 1,305
 [1]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 20 Nov 2020, 01:31
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Explanation:

Arc of length = 2πr(90/360) = πr/2
6π = πr/2
r = 12 which is Breadth of Rectangle

Perimeter of rectanglle = 2(L+B) = 60
L+B = 30
L = 30 - 12 = 18.

Perimeter of shaded region = 12 + 18 + 6 + 6π = 36 + 6π

IMO-E
User avatar
mdsaddamforgmat
User avatar
Joined: 05 Dec 2019
Last visit: 20 Oct 2024
Posts: 108
Own Kudos:
158
 [2]
Given Kudos: 155
Location: Nepal
Schools: Tuck '23
GMAT 1: 420 Q33 V15
GMAT 2: 650 Q48 V31
GMAT 3: 640 Q47 V31
Schools: Tuck '23
GMAT 3: 640 Q47 V31
Posts: 108
Kudos: 158
 [2]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 20 Nov 2020, 03:08
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO: E
Since, arc length is of Quarter circle... Radius of Circle = 6Pi x 360 /(90 x Pi X 2) = 12
Also, Length of Rectangle = (60/2)-breadth = 18
From Diagram it follows that perimeter of shaded region = Quarter circle’s arc length + Length of Rectangle + Breadth of Rectangle + (Length of Rectangle – Radius of Circle) = 36 + 6 Pi
avatar
Akp880
avatar
Joined: 24 Mar 2019
Last visit: 08 Nov 2021
Posts: 192
Own Kudos:
151
 [1]
Given Kudos: 196
Location: India
Concentration: Marketing, Operations
Schools: IIMA PGPX'23 IIM
WE:Operations (Aerospace and Defense)
Schools: IIMA PGPX'23 IIM
Posts: 192
Kudos: 151
 [1]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 20 Nov 2020, 07:00
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Explanation:

As the length of arc=6π

so 2πr/4=6π

r=12 units i.e width of rectangle

Given perimeter of rectangle=60

thus perimeter of shaded area=2*width +2*length

60=2*12+2*length
length=36/2=18 units

so perimeter of shaded area= width+ arc length + length +(length-radial distance)
=12 + 6π + 18 + (18-12)
=36+ 6π

Hence E is the correct answer.
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,904
Own Kudos:
5,446
 [1]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,904
Kudos: 5,446
 [1]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 20 Nov 2020, 07:38
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

In the figure shown, the arc of the quarter circle has length \(6\pi\). The rectangle has perimeter 60. What is the perimeter of the shaded region?

A. \(36 + \pi\)
B. \(36 + 2\pi\)
C. \(36 + 3\pi\)
D. \(36 + 4\pi\)
E. \(36 + 6\pi\)


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS


Show Spoiler
Attachment:
2020-10-27_14-10-11.png
Show more

\(\frac{2πr}{4} = 6π\)

So, \(r = 12\)

\(2(12 + l) = 60\)

So, \(l = 18\)

Perimeter of the shaded region is \(18 + 12 + 6 +6π = 36 + 6\pi\), Answer must be (E)
User avatar
Pankaj0901
User avatar
Joined: 18 Dec 2018
Last visit: 17 Dec 2022
Posts: 406
Own Kudos:
53
 [1]
Given Kudos: 737
Location: India
WE:Account Management (Hospitality and Tourism)
Posts: 406
Kudos: 53
 [1]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 21 Nov 2020, 00:30
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ANSWER IMO-E
Arc of length = 2πr(90/360) = πr/2
6π = πr/2
r = 12 which is Breadth of Rectangle

Perimeter of rectanglle = 60
L = 30 - 12 = 18.

Required Perimeter = 36 + 6π



Bunuel

In the figure shown, the arc of the quarter circle has length \(6\pi\). The rectangle has perimeter 60. What is the perimeter of the shaded region?

A. \(36 + \pi\)
B. \(36 + 2\pi\)
C. \(36 + 3\pi\)
D. \(36 + 4\pi\)
E. \(36 + 6\pi\)


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS


Show Spoiler
Attachment:
2020-10-27_14-10-11.png
Show more
avatar
GCMEMBER
avatar
Joined: 09 Dec 2019
Last visit: 03 Jun 2021
Posts: 123
Own Kudos:
176
 [1]
Given Kudos: 5
Posts: 123
Kudos: 176
 [1]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 21 Nov 2020, 00:59
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Arc length = (90/360)*2πr = πr/2
6π = πr/2
r = 12 = Rectangle's Breadth = B

Rectangle's Perimeter = 60
2(L+B) = 60
L + B = 30
L = 18

Shaded Region Perimeter = L + B + (L-B) + (πr/2)
= 18 + 12 + 6 + 6π
= 36 + 6π

Option E
User avatar
karnavora1
User avatar
Joined: 29 Feb 2020
Last visit: 07 Sep 2025
Posts: 77
Own Kudos:
102
 [1]
Given Kudos: 13
Location: India
Concentration: Marketing, International Business
Schools: Rotman '22 ISB'22 Goizueta "23
GMAT 1: 600 Q42 V31
Products:
My Reviews
Schools: Rotman '22 ISB'22 Goizueta "23
GMAT 1: 600 Q42 V31
Posts: 77
Kudos: 102
 [1]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 21 Nov 2020, 09:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Option E.

The keyword here is "Quarter".
Since we know that the Quarter length of the circle is 6π, we can find out the Radius of the circle with the formula of circumference.
2πr/4=6π, upon solving we will get radius as 12.

Since the Radius is the breadth of the rectangle we can find the length of the rectangle.
Perimeter of Rectangle = 2 (L+B)
60 = 2 (L+12)
30 = L + 12
L = 18

Perimeter of the shaded region then becomes 18+12+6π+(18-12) = 36 + 6π
User avatar
Harsh9676
User avatar
Joined: 18 Sep 2018
Last visit: 27 Feb 2023
Posts: 239
Own Kudos:
228
 [1]
Given Kudos: 322
Location: India
Concentration: Finance, International Business
GMAT 1: 690 Q49 V36
GPA: 3.72
WE:Investment Banking (Finance: Investment Banking)
Products:
My Reviews
GMAT 1: 690 Q49 V36
Posts: 239
Kudos: 228
 [1]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 22 Nov 2020, 05:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO E

So the Perimeter of the Shaded Region = Perimeter of the Rectangle -2 (Radius of the quarter circle) + Length of the Arc

Radius of the circle can be found using the relation

Central Angle / 360 = Length of Arc / Circumferece.

Therefore Radius = 90/360 = 6pi / 2 pi r >> r = 12

Then the Perimeter of the Shaded region = 60 - 2(12) + 6pi
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 20 Apr 2026
Posts: 22,268
Own Kudos:
26,522
 [1]
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,268
Kudos: 26,522
 [1]
In the figure shown, the arc of the quarter circle has length 6\pi. Th 28 Nov 2020, 10:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

In the figure shown, the arc of the quarter circle has length \(6\pi\). The rectangle has perimeter 60. What is the perimeter of the shaded region?

A. \(36 + \pi\)
B. \(36 + 2\pi\)
C. \(36 + 3\pi\)
D. \(36 + 4\pi\)
E. \(36 + 6\pi\)


Show more
Solution:

We see that the perimeter of the shaded region consists of the length (L) and width (W) of the rectangle, the arc (A) of the quarter circle and a length that is the difference between the length of the rectangle and the radius (R) of the quarter circle.

Since the arc of the quarter circle is given to be 6π, the circle’s circumference is 24π, and therefore its diameter and radius are 24 and 12, respectively. Notice that the radius of the quarter circle is also the width of the rectangle. Since we are given that the perimeter of the rectangle is 60, the length of the rectangle is (60 - 12 x 2)/2 = 36/2 = 18. Therefore, the perimeter of the shaded region is:

L + W + A + (L - R)

18 + 12 + 6π + (18 - 12)

36 + 6π

Answer: E
Moderators:
Bunuel
Math Expert
109720 posts
Krunaal
Tuck School Moderator
853 posts