NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 18:13 It is currently 24 Apr 2024, 18:13
Decision Tracker
My Rewards
New posts
New comers' posts

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

The length of minor arc AB is twice the length of minor arc

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
enigma123
Senior Manager
Senior Manager
Joined: 25 Jun 2011
Status:Finally Done. Admitted in Kellogg for 2015 intake
Posts: 396
Own Kudos [?]: 16650 [31]
Given Kudos: 217
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
Send PM
The length of minor arc AB is twice the length of minor arc [#permalink] New post   11 Feb 2012, 14:55
2
Kudos
28
Bookmarks
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

61% (02:18) correct 39% (02:27) wrong based on 396 sessions
Hide Show timer Statistics

The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

A. 20
B. 40
C. 60
D. 80
E. 120

Show Spoiler
Attachment:
Arcs.PNG
Arcs.PNG [ 7.21 KiB | Viewed 35721 times ]
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618816 [10]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   11 Feb 2012, 15:18
3
Kudos
7
Bookmarks
Expert Reply
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?
A. 20
B. 40
C. 60
D. 80
E. 120


(arc AB) = 2*(arc BC) and (arc AC) = 3*(arc AB);

(arc BC)=x, (Arc AB)=2x, and (Arc AC)=3*2x=6x --> x+2x+6x=360 --> 9x=360 --> x=40 --> (arc AB)=2x=80 --> according to the central angle theorem the measure of inscribed angle (<BCA) is always half the measure of the central angle (<BOA, which is the minor arc AB), hence <BCA=80/2=40.

Answer: B.

Check Circles chapter of Math Book for more: math-circles-87957.html

Hope it helps.

Show Spoiler
Attachment:
Arcs.PNG
Arcs.PNG [ 7.21 KiB | Viewed 37681 times ]
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14817
Own Kudos [?]: 64902 [9]
Given Kudos: 426
Location: Pune, India
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   16 Feb 2012, 04:26
5
Kudos
3
Bookmarks
Expert Reply
enigma123 wrote:
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

A. 20
B. 40
C. 60
D. 80
E. 120
Attachment:
Arcs.PNG

Any idea how to solve this guys?


Given the ratio of minor arcs, their central angles and inscribed angles are in the same ratio.
arc BC: arc AB : arc AC = 1:2:6
So inscribed angles angle A : angle C : angle B = 1:2:6
Since these three angles form a triangle, their sum is 180 which means angle C = 40 degrees
General Discussion
User avatar
enigma123
Senior Manager
Senior Manager
Joined: 25 Jun 2011
Status:Finally Done. Admitted in Kellogg for 2015 intake
Posts: 396
Own Kudos [?]: 16650 [0]
Given Kudos: 217
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   11 Feb 2012, 15:26
How did you get x+2x+6x=360 Bunuel?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618816 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   11 Feb 2012, 15:27
Expert Reply
enigma123 wrote:
How did you get x+2x+6x=360 Bunuel?


Circumference 360 degrees.
User avatar
omerrauf
Manager
Manager
Joined: 17 Nov 2011
Status:Employed
Posts: 67
Own Kudos [?]: 433 [3]
Given Kudos: 10
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE:Business Development (Internet and New Media)
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   15 Feb 2012, 13:08
3
Kudos
Let BC \(=x\)
So AB \(=2x\)
So AC \(=6x\)

Now angle in question is opposite AB... and we know that Angles are in proportion to the length of the sides they are in front of..

We need to find \(2x\).....so ratio of this side(AB) \(=\frac{{2x}}{{9x}}=\frac{2}{9}\)

Sum of angles of triangle \(=180\)

So we can use ratios to setup an equation as follows:

\(\frac{{2x}}{{9x}}*180=40\)

Hence Angle is \(40\)
avatar
pavan1mpv
Intern
Intern
Joined: 21 Oct 2011
Posts: 2
Own Kudos [?]: 2 [1]
Given Kudos: 0
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   16 Feb 2012, 05:01
1
Bookmarks
lenght of the arc = (x/360)*2pir
Given AB=2BC; AC=3AB. If x is the angle of arc BC then AB=2x; AC=6x;
AB+BC+AC=360 --> x+2x+6x=360 --> 9x = 360 --> x = 40
Is this approach right? can someone help me please?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14817
Own Kudos [?]: 64902 [0]
Given Kudos: 426
Location: Pune, India
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   16 Feb 2012, 05:41
Expert Reply
pavan1mpv wrote:
lenght of the arc = (x/360)*2pir
Given AB=2BC; AC=3AB. If x is the angle of arc BC then AB=2x; AC=6x;
AB+BC+AC=360 --> x+2x+6x=360 --> 9x = 360 --> x = 40
Is this approach right? can someone help me please?


When you say, "If x is the angle of arc BC", you mean the central angle, right?
The sum of the central angles will be 360 so you get x = 40. But remember, this is the central angle subtended by arc BC. The central angle subtended by arc AB = 2x = 80.

But since we are interested in the inscribed angle (i.e. the angle on the circumference of the circle), we get angle BCA (inscribed angle of arc AB) = 80/2 = 40 degrees (since inscribed angle is half of central angle)
avatar
pbull78
Intern
Intern
Joined: 16 Dec 2011
Posts: 28
Own Kudos [?]: 19 [1]
Given Kudos: 12
GMAT Date: 04-23-2012
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   22 Feb 2012, 08:15
1
Kudos
as all arcs are given so we can add all arcs to find radius of the circle bcoz sum of all arcs is equal to circumference of the circle,

assume BC = X,
AB= 2X AND AC= 6X
implies 9X = 2pir
implies, r= 9X/2pi
now angle subtended by arc AB at the centre of circle is twice of the angle BCA.

arc AB = 2X = angle at centre of circle ( Q)/360 *2pir

implies 2X= Q/360*
avatar
pbull78
Intern
Intern
Joined: 16 Dec 2011
Posts: 28
Own Kudos [?]: 19 [0]
Given Kudos: 12
GMAT Date: 04-23-2012
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   22 Feb 2012, 08:18
sorry submitted uncompleted ,

2X= Q/360*2pi*9X/2PI
Gives us angle Q= 80
and angle BCA = 40 ( HALF OF THE ANGLE subtended at centre of circle)

answer B = 40 degrees
User avatar
davesinger786
Intern
Intern
Joined: 10 May 2015
Posts: 14
Own Kudos [?]: 8 [0]
Given Kudos: 268
Send PM
GMAT ToolKit User
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   03 Jul 2015, 01:36
Bunuel wrote:
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?
A. 20
B. 40
C. 60
D. 80
E. 120
Attachment:
Arcs.PNG

(arc AB) = 2*(arc BC) and (arc AC) = 3*(arc AB);

(arc BC)=x, (Arc AB)=2x, and (Arc AC)=3*2x=6x --> x+2x+6x=360 --> 9x=360 --> x=40 --> (arc AB)=2x=80 --> according to the central angle theorem the measure of inscribed angle (<BCA) is always half the measure of the central angle (<BOA, which is the minor arc AB), hence <BCA=80/2=40.

Answer: B.

Check Circles chapter of Math Book for more: math-circles-87957.html

Hope it helps.


Hi Bunuel,

I have a doubt here. If x =40, angle subtended by Arc Ac becomes 240.But how can arc AC subtend 240 at the center.If we join the center to A and C thereby making it a triangle, one angle itself exceeds 180 degrees.Please guide me where am I going wrong.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618816 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   03 Jul 2015, 02:17
Expert Reply
davesinger786 wrote:
Bunuel wrote:
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?
A. 20
B. 40
C. 60
D. 80
E. 120
Attachment:
Arcs.PNG

(arc AB) = 2*(arc BC) and (arc AC) = 3*(arc AB);

(arc BC)=x, (Arc AB)=2x, and (Arc AC)=3*2x=6x --> x+2x+6x=360 --> 9x=360 --> x=40 --> (arc AB)=2x=80 --> according to the central angle theorem the measure of inscribed angle (<BCA) is always half the measure of the central angle (<BOA, which is the minor arc AB), hence <BCA=80/2=40.

Answer: B.

Check Circles chapter of Math Book for more: math-circles-87957.html

Hope it helps.


Hi Bunuel,

I have a doubt here. If x =40, angle subtended by Arc Ac becomes 240.But how can arc AC subtend 240 at the center.If we join the center to A and C thereby making it a triangle, one angle itself exceeds 180 degrees.Please guide me where am I going wrong.


Check here: the-length-of-arc-axb-is-twice-the-length-of-arc-bzc-and-105748.html#p1235232 and here: the-length-of-arc-axb-is-twice-the-length-of-arc-bzc-and-105748.html#p1235414
User avatar
davesinger786
Intern
Intern
Joined: 10 May 2015
Posts: 14
Own Kudos [?]: 8 [1]
Given Kudos: 268
Send PM
GMAT ToolKit User
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   03 Jul 2015, 02:42
1
Kudos
Bunuel wrote:
davesinger786 wrote:
Bunuel wrote:
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?
A. 20
B. 40
C. 60
D. 80
E. 120
Attachment:
Arcs.PNG

(arc AB) = 2*(arc BC) and (arc AC) = 3*(arc AB);

(arc BC)=x, (Arc AB)=2x, and (Arc AC)=3*2x=6x --> x+2x+6x=360 --> 9x=360 --> x=40 --> (arc AB)=2x=80 --> according to the central angle theorem the measure of inscribed angle (<BCA) is always half the measure of the central angle (<BOA, which is the minor arc AB), hence <BCA=80/2=40.

Answer: B.

Check Circles chapter of Math Book for more: math-circles-87957.html

Hope it helps.


Hi Bunuel,

I have a doubt here. If x =40, angle subtended by Arc Ac becomes 240.But how can arc AC subtend 240 at the center.If we join the center to A and C thereby making it a triangle, one angle itself exceeds 180 degrees.Please guide me where am I going wrong.


Check here: the-length-of-arc-axb-is-twice-the-length-of-arc-bzc-and-105748.html#p1235232 and here: the-length-of-arc-axb-is-twice-the-length-of-arc-bzc-and-105748.html#p1235414


Thanks for that,Bunuel. So if I go by the logic that the diagram isn't accurate, arc AC subtends 240 at the center right? but in this question ,it's mentioned as the "minor arc AC" w.r.t to the calculations but going by the diagram in your article it looks like 240 is actually made by the major arc? Please help me get an idea of what are the angles subtended by the arcs ..getting confused here.Thanks in advance
User avatar
mejia401
Senior Manager
Senior Manager
Joined: 15 Sep 2011
Posts: 258
Own Kudos [?]: 1371 [0]
Given Kudos: 46
Location: United States
WE:Corporate Finance (Manufacturing)
Send PM
GMAT ToolKit User
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   03 Jul 2015, 11:39
davesinger786 wrote:
Bunuel wrote:
davesinger786 wrote:

Hi Bunuel,

I have a doubt here. If x =40, angle subtended by Arc Ac becomes 240.But how can arc AC subtend 240 at the center.If we join the center to A and C thereby making it a triangle, one angle itself exceeds 180 degrees.Please guide me where am I going wrong.


Check here: the-length-of-arc-axb-is-twice-the-length-of-arc-bzc-and-105748.html#p1235232 and here: the-length-of-arc-axb-is-twice-the-length-of-arc-bzc-and-105748.html#p1235414


Thanks for that,Bunuel. So if I go by the logic that the diagram isn't accurate, arc AC subtends 240 at the center right? but in this question ,it's mentioned as the "minor arc AC" w.r.t to the calculations but going by the diagram in your article it looks like 240 is actually made by the major arc? Please help me get an idea of what are the angles subtended by the arcs ..getting confused here.Thanks in advance




That's true. If AC is larger than the two other archs, AC cannot be described as a minor arch. The archs are 2x their inscribed angles, and therefore, divide the degree of the arch by 2 to arrive at your answer.

Thanks,
User avatar
P
mvictor
Board of Directors
Joined: 17 Jul 2014
Posts: 2163
Own Kudos [?]: 1180 [0]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Send PM
GMAT ToolKit User Reviews Badge
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   14 Dec 2016, 15:59
enigma123 wrote:
The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

A. 20
B. 40
C. 60
D. 80
E. 120
Attachment:
Arcs.PNG

Any idea how to solve this guys?


what a nice question!
i got to the answer the same way
9x=360
x=40
2x=80
and as explained, the answer is B.
avatar
mrmocker
Intern
Intern
Joined: 20 May 2017
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 1
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   26 Aug 2017, 10:46
[quote="davesinger786"][quote="Bunuel"]The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?
A. 20
B. 40
C. 60
D. 80
E. 120
Attachment:
Arcs.PNG

(arc AB) = 2*(arc BC) and (arc AC) = 3*(arc AB);

(arc BC)=x, (Arc AB)=2x, and (Arc AC)=3*2x=6x --> x+2x+6x=360 --> 9x=360 --> x=40 --> (arc AB)=2x=80 --> according to the central angle theorem the measure of inscribed angle (<BCA) is always half the measure of the central angle (<BOA, which is the minor arc AB), hence <BCA=80/2=40.

Answer: B.

Hi Bunuel,

I have a doubt here. If x =40, angle subtended by Arc Ac becomes 240.But how can arc AC subtend 240 at the center.If we join the center to A and C thereby making it a triangle, one angle itself exceeds 180 degrees.Please guide me where am I going wrong.



would be thankful if someone could explain the above quoted discrepancy in the problem
User avatar
S
Wonderwoman31
Manager
Manager
Joined: 21 Apr 2018
Posts: 60
Own Kudos [?]: 41 [0]
Given Kudos: 82
Location: India
Schools: Rotman '22 (A$) CBS '22 (D) Wharton '22 (D) INSEAD Jan'21 Intake (A)
GMAT 1: 710 Q50 V35
GMAT 2: 750 Q49 V42
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   11 Aug 2018, 08:36
I think this question in incorrect because of the following case :-

Case 1: - when triangle inscribes centre of the circle within it.

In that case, x + 2x + 6x = 360

and 6x = 240. The arc subtended by angle 6x cannot be a minor arc, which is a main assumption in the question. Hence, this approach is incorrect.

Case 2:- when triangle does not inscribe circle within.

In that case, x + 2x = 6x, which is not possible.

There isn't any third case for this question. Therefore, I believe this question is incorrect.
avatar
B
gauranggarg
Intern
Intern
Joined: 11 Aug 2016
Posts: 26
Own Kudos [?]: 8 [0]
Given Kudos: 32
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   30 Jul 2020, 10:31
Hi guys, I got the method to solve this question, but somehow I am messing up in the ratio and proportions part. Can someone correct me as to what exactly I am doing wrong:
Arc(AB)=2(Arc(BC) - equation 1 & Arc(AC)=3(Arc(AB)) - equation 2
I multiplied equation 1 by 3: 3Arc(AB)=6(Arc(BC) - equation 3
So the ratio I got by combining equations 2&3 was: Arc(AC)=3(Arc(AB))=6(Arc(BC), Which is AC:AB:BC=1:3:6
Cant seem to figure out where I am messing up. Help would be much appreciated. Thanks!!
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32655
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: The length of minor arc AB is twice the length of minor arc [#permalink] New post   26 Jan 2023, 18:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: The length of minor arc AB is twice the length of minor arc [#permalink]
26 Jan 2023, 18:08
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions