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

It is currently 18 Mar 2019, 16:49

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.

Close

Request Expert Reply

Confirm Cancel

Consider a circle with area 81π . An arc on this circle is such that i

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53657
Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 02 Jul 2015, 01:44
1
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (01:47) correct 38% (01:45) wrong based on 56 sessions

HideShow timer Statistics

Image
If angle ABC is 40 degrees (see figure), and the area of the circle is \(81\pi\), how long is arc AXC? (CB is a diameter of the circle)

A. \(\frac{\pi}{2}\)
B. \(\pi\)
C. \(2\pi\)
D. \(4\pi\)
E. \(8\pi\)


Kudos for a correct solution.

Attachment:
2015-07-02_1243.png
2015-07-02_1243.png [ 7.27 KiB | Viewed 4340 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
Status: Perspiring
Joined: 15 Feb 2012
Posts: 86
Concentration: Marketing, Strategy
GPA: 3.6
WE: Engineering (Computer Software)
GMAT ToolKit User
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 02 Jul 2015, 03:04
1
1
Concept: Length of an arc =[ø/360]*2*pi*r --------------- (1)
ø - is the central angle say COA, where O is the center of the circle!

Now central ∟COA = 2*∟CAB = 80 degrees ---------------- (2)

Area of circle = π*r*r = 81*π
Therefore r*r = 81
r = 9 -------------- (3)

From 1, 2 & 3
Length of arc AXC = (80/360)*2*π*9 = 4π

Hence D !!
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2829
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 02 Jul 2015, 03:57
Bunuel wrote:
Image
If angle ABC is 40 degrees (see figure), and the area of the circle is \(81\pi\), how long is arc AXC? (CB is a diameter of the circle)

A. \(\frac{\pi}{2}\)
B. \(\pi\)
C. \(2\pi\)
D. \(4\pi\)
E. \(8\pi\)


Kudos for a correct solution.

Attachment:
2015-07-02_1243.png


Property-1: Length of the Arc = (Angle/360)*2*π*r

So we need to calculate the angle made by Arc AXC at the centre of the Circle

Property-2: Angle made at the centre by any arc is always twice the angle made at the circumference by the same arc

i.e. Since Arc AXC makes an angle of 40 degrees at the circumference so
i.e. Arc AXC will make an angle of 2*40 = 80 degrees at the Centre of the circle

i.e. Length of the Arc AXC = (80/360)*2*π*9 [Area = πr^2 = 81π i.e. Radius = 8]

i.e. Length of the Arc AXC = 4π

Answer: Option D
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
avatar
Joined: 27 Jul 2014
Posts: 242
Schools: ISB '15
GMAT 1: 660 Q49 V30
GPA: 3.76
GMAT ToolKit User Reviews Badge
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 02 Jul 2015, 04:14
1
IMO D is correct
Length of arc AXC= angle subtended at centre/360 * 2 *pi*radius
Angle at centre=2 * angle at circumference=80
Radius
Area=pi* r^2=81pi
Radius=9
Length of arc= 80/360 * 2* pi* 9= 4pi
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2624
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 02 Jul 2015, 04:32
1
Bunuel wrote:
Image
If angle ABC is 40 degrees (see figure), and the area of the circle is \(81\pi\), how long is arc AXC? (CB is a diameter of the circle)

A. \(\frac{\pi}{2}\)
B. \(\pi\)
C. \(2\pi\)
D. \(4\pi\)
E. \(8\pi\)


Kudos for a correct solution.

Attachment:
2015-07-02_1243.png


GIven area of the circle = 81*\(\pi\)

Thus, \(\pi\)\(r^2\) = 81*\(\pi\)
r=9

NOw, as any angle subtended by an arc on the circumference is half the angle subtended by the same arc at the center of the circle, thus the angle subtended by arc AXC at the center of the circle is 2*40 deg.= 80 deg.

For the complete circumference, 2\(\pi\) or 360 is subtended by 2\(\pi\) r of the circumference. 80 deg will thus subtend = 80/360 * 2\(\pi\) r = 4\(\pi\). thus D is the answer.
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 163
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 02 Jul 2015, 06:13
So in other words the central angle is twice the size of an arc angle?
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2624
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 02 Jul 2015, 07:06
2
noTh1ng wrote:
So in other words the central angle is twice the size of an arc angle?


Yes, the angle made by the arc is half the angle made by the SAME arc at the center.

In the attached figure, the same arc is minor arc AB.
Attachments

Central Angle Theorem.jpg
Central Angle Theorem.jpg [ 15.13 KiB | Viewed 3442 times ]

Manager
Manager
User avatar
G
Joined: 13 Oct 2013
Posts: 136
Concentration: Strategy, Entrepreneurship
GMAT ToolKit User Premium Member CAT Tests
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 02 Jul 2015, 09:41
1
Area =81 pi
R=9
Arch AXC forms the angle at the center =twice the angle formed at circumference= 2*40 =80 degree
Length of Arc AXC=Angle formed at center/360 * 2 pi * R

80/360*2.Pi.9=4.pi

Ans is D
_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way :)

Manager
Manager
User avatar
Joined: 18 Mar 2014
Posts: 227
Location: India
Concentration: Operations, Strategy
GMAT 1: 670 Q48 V35
GPA: 3.19
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 03 Jul 2015, 09:10
does this mean ... whenever we are calculating length of arc we need to know angle subtended by it at centre ... not at circumference ..
Right ?
I calculated it as 2*pi
_________________

Press +1 Kudos if you find this Post helpful :)

CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2624
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 03 Jul 2015, 09:23
2
adityadon wrote:
does this mean ... whenever we are calculating length of arc we need to know angle subtended by it at centre ... not at circumference ..
Right ?
I calculated it as 2*pi


Yes, the angle always has to be the one that the arc subtends at the center of the circle.

the direct formula for calculating the length of any arc of a circle = l = \(r*\theta\) , where \(\theta\) is the angle measure at the center of the circle in RADIANS and not in degrees and r is the radius of the circle.

\(2\pi\) radians equal 360 degrees.

In the question above, 80 degrees will be equal to \((80/360) * 2\pi\) radians. Radius, r = 9.

Thus the length of the minor arc = \(r*\theta\) = \(9*(80/360) * 2\pi\) = \(4\pi\)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53657
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 06 Jul 2015, 04:34
Bunuel wrote:
Image
If angle ABC is 40 degrees (see figure), and the area of the circle is \(81\pi\), how long is arc AXC? (CB is a diameter of the circle)

A. \(\frac{\pi}{2}\)
B. \(\pi\)
C. \(2\pi\)
D. \(4\pi\)
E. \(8\pi\)


Kudos for a correct solution.

Attachment:
2015-07-02_1243.png


MANHATTAN GMAT OFFICIAL SOLUTION:

If the area of the circle is \(81\pi\), then the radius of the circle is 9 (\(A = \pi r^2\)). Therefore, the total circumference of the circle is \(18\pi\) (\(C = 2\pi r\)). Angle ABC, an inscribed angle of 40°, corresponds to a central angle of 80°. Thus, arc AXC is equal to 80/360 = 2/9 of the total circumference:

\(\frac{2}{9}*18\pi = 4\pi\).

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 24 May 2013
Posts: 79
GMAT ToolKit User
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 25 Mar 2016, 23:01
If angle ABC is 40 degrees (see figure), and the area of the circle is 81π, how long is arc AXC? (CB is a diameter of the circle)

pi*r^2 =81 pi
r=9
Angle at the center of the arc can be found as shown in fig...

for 80degree arc
Total perimeter*80/360
2pi*r*80/360
4pi
Attachments

Circle.png
Circle.png [ 27.99 KiB | Viewed 2688 times ]

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7415
Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 01 Apr 2016, 20:15
Chiragjordan wrote:
Consider a circle with area 81π.An arc on this circle is such that it makes a 40 degree inscribed angle with a point P on the circle. What is the length of this arc?
[A] 2π

[C] 8π
[D] 12π
[E] Cannot be determined


Hi,

[b]A GOOD Q.. +1kudos
Difficulty level should 600-700...

1) first, since we are talking of arc length, lets change the Area to Perimeter..
\(A=81π=π*r^2\)
so r=9 and P= 18π

2) Next would be to find the angle that this arc makes at center..
Since the ARC makes 40 degree angle at a point on the circumference, ARC will make 2*40 at the center..

3) Finally lets correlate the angle and perimeter to find length of ARC..
360 degree makes the perimeter or 18π..
so 1 degree will make \(\frac{18π}{360}\), and
2*40 or 80 degree will make\(\frac{18π}{360} * 80 = 4π\)
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 10130
Premium Member
Re: Consider a circle with area 81π . An arc on this circle is such that i  [#permalink]

Show Tags

New post 09 Mar 2019, 14:55
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: Consider a circle with area 81π . An arc on this circle is such that i   [#permalink] 09 Mar 2019, 14:55
Display posts from previous: Sort by

Consider a circle with area 81π . An arc on this circle is such that i

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.