Last visit was: 30 Apr 2026, 18:40 It is currently 30 Apr 2026, 18:40
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
555-605 (Medium)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 30 Apr 2026
Posts: 110,017
Own Kudos:
812,163
 [5]
Given Kudos: 105,962
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: 110,017
Kudos: 812,163
 [5]
The radius of Circle Q is 8. If the length of arc ABC is greater than 23 Jun 2020, 06:19
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

69% (02:05) correct 31% (02:07) wrong based on 85 sessions

History

Date
Time
Result
Not Attempted Yet

The radius of Circle Q is 8. If the length of arc ABC is greater than 26, which of the following could be the value of the sums of angles AQB and BQC ?

I. 180°
II. 240°
III. 270°

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Show Spoiler
Attachment:
1.jpg
1.jpg [ 24.36 KiB | Viewed 3334 times ]
ShowHide Answer
Official Answer
D
avatar
cakyoel
avatar
Joined: 23 Jun 2020
Last visit: 25 Jun 2020
Posts: 1
Posts: 1
Kudos: 0
The radius of Circle Q is 8. If the length of arc ABC is greater than 23 Jun 2020, 06:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
D is the answer. The angle must be greater than 180 degree.

Posted from my mobile device
User avatar
yashikaaggarwal
User avatar
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 29 Mar 2026
Posts: 3,088
Own Kudos:
3,158
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Schools: Cranfield (A) Warwick MiM "23 (M)
Posts: 3,088
Kudos: 3,158
The radius of Circle Q is 8. If the length of arc ABC is greater than 23 Jun 2020, 06:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Length of arc ABC > 26

Length of arc = Π/360*2πr
Where Π is the sum of angle of AQB and BQC

Let length of arc be 26.1
Therefore,
27 = Π/360*2*22/7*8
Π = 186.85 or 187° is the least sum of angle AQB and BQC

Therefore The sum of AQB+BQC satisfy all two values of B and C

IMO D

Posted from my mobile device
User avatar
VERBAL1
User avatar
Joined: 18 Jun 2020
Last visit: 10 Jul 2022
Posts: 174
Own Kudos:
162
Given Kudos: 151
Location: India
Concentration: Marketing, Sustainability
Schools: Cass '21 LBS '22 Cambridge '22
Schools: Cass '21 LBS '22 Cambridge '22
Posts: 174
Kudos: 162
The radius of Circle Q is 8. If the length of arc ABC is greater than 23 Jun 2020, 22:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
@yashikaagggarwal : can you please explain

27 = Π/360*2*22/7*8... what does the *2 signify ? where did you get the *2 from?
User avatar
yashikaaggarwal
User avatar
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 29 Mar 2026
Posts: 3,088
Own Kudos:
3,158
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Schools: Cranfield (A) Warwick MiM "23 (M)
Posts: 3,088
Kudos: 3,158
The radius of Circle Q is 8. If the length of arc ABC is greater than 23 Jun 2020, 22:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VERBAL1
@yashikaagggarwal : can you please explain

27 = Π/360*2*22/7*8... what does the *2 signify ? where did you get the *2 from?
Show more

In (Π/360)*2*22/7*8
Π is the angle, AQC
2*22/7*8 = circumference formula.
Which is in multiplication, to get the value of arc we multiply theta/360 to circumference to draw out value of the arc.

Hope that helps

Posted from my mobile device
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 30 Apr 2026
Posts: 6,991
Own Kudos:
16,941
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,991
Kudos: 16,941
The radius of Circle Q is 8. If the length of arc ABC is greater than 23 Jun 2020, 22:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

The radius of Circle Q is 8. If the length of arc ABC is greater than 26, which of the following could be the value of the sums of angles AQB and BQC ?

I. 180°
II. 240°
III. 270°

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Show Spoiler
Attachment:
1.jpg
Show more

ANgle AQB + Angle BQC = Angle AQC

Angle AQC is drawn by arc ABC at the center

Length of Arc \(= (\frac{ø}{360})*2πr\)

ie. Length of Arc ABC \(= (\frac{ø}{360})*2π*8\) > 26 (Given)

i.e. \(= (\frac{ø}{360})*2π*8 > 26\)

i.e. Angle (ø) > 186º



I. 180°
II. 240°
III. 270°

Answer: Option D

VERBAL1
User avatar
AnirudhaS
User avatar
LBS Moderator
Joined: 30 Oct 2019
Last visit: 25 Jun 2024
Posts: 777
Own Kudos:
887
 [1]
Given Kudos: 1,575
Posts: 777
Kudos: 887
 [1]
The radius of Circle Q is 8. If the length of arc ABC is greater than 23 Jun 2020, 23:06
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Circumference of the circle (radius =8) =\( 2 \pi r = 2*3.14*8 \approx48\)
So semi-circumference (or arc subtended by the diameter) \(\approx24\) <26
Angle at the centre of the sem-circumference = \(180^{\circ}\)
So the angle must be greater than \(180^{\circ}\)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,011
Own Kudos:
1,122
Posts: 39,011
Kudos: 1,122
The radius of Circle Q is 8. If the length of arc ABC is greater than 20 Mar 2023, 12:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
110017 posts
Krunaal
Tuck School Moderator
852 posts