GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2019, 12:13 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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Senior Manager  Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 442
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45 GPA: 2.9
WE: Information Technology (Consulting)
The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

14 00:00

Difficulty:   75% (hard)

Question Stats: 60% (02:12) correct 40% (02:24) wrong based on 294 sessions

HideShow 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

Attachment: Arcs.PNG [ 7.21 KiB | Viewed 21902 times ]

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

1
5
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.

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

Hope it helps.

Attachment: Arcs.PNG [ 7.21 KiB | Viewed 23966 times ]

_________________
General Discussion
Senior Manager  Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 442
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45 GPA: 2.9
WE: Information Technology (Consulting)
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

How did you get x+2x+6x=360 Bunuel?
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

enigma123 wrote:
How did you get x+2x+6x=360 Bunuel?

Circumference 360 degrees.
_________________
Manager  Status: Employed
Joined: 17 Nov 2011
Posts: 78
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40 GPA: 3.2
WE: Business Development (Internet and New Media)
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

1
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 $$40$$
_________________
"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

4
1
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
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern  Joined: 21 Oct 2011
Posts: 4
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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?
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern  Joined: 16 Dec 2011
Posts: 37
GMAT Date: 04-23-2012
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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*
Intern  Joined: 16 Dec 2011
Posts: 37
GMAT Date: 04-23-2012
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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
Intern  Joined: 10 May 2015
Posts: 24
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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.

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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.

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
_________________
Intern  Joined: 10 May 2015
Posts: 24
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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.

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
Senior Manager  Joined: 15 Sep 2011
Posts: 309
Location: United States
WE: Corporate Finance (Manufacturing)
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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,
Board of Directors P
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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.
Intern  Joined: 20 May 2017
Posts: 1
Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

[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.

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
Manager  S
Joined: 21 Apr 2018
Posts: 73
Location: India
GMAT 1: 710 Q50 V35 GMAT 2: 750 Q49 V42 Re: The length of minor arc AB is twice the length of minor arc  [#permalink]

Show Tags

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. Re: The length of minor arc AB is twice the length of minor arc   [#permalink] 11 Aug 2018, 08:36
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  