GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 06 Apr 2020, 11:44

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

Circle P shown above is centered at P. If the length of arc ABC is 40,

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62553
Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

Show Tags

New post 06 Feb 2020, 07:16
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

77% (01:28) correct 23% (02:20) wrong based on 48 sessions

HideShow timer Statistics

GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4592
Location: Canada
GMAT 1: 770 Q49 V46
Re: Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

Show Tags

New post 06 Feb 2020, 07:42
Top Contributor
Bunuel wrote:
Image
Circle P shown above is centered at P. If the length of arc ABC is 40, what is the area of circle P?


A. \(\frac{10,000}{\pi^{2}}\)

B. \(\frac{10,000}{\pi}\)

C. 10,000

D. \(10000\pi\)

E. \(10,000\pi^{2}\)
Attachment:
T6140.png


Since the answer choices are very spread apart, we can use estimation to quickly arrived at the correct answer.

Useful property: On the GMAT, the geometric diagrams in Problem Solving questions are assumed to be drawn to scale unless stated otherwise.

If arc ABC = 40, then the radius is approximately 30 (eyeballing)

Area of a circle \(= {\pi}r^2\)
\(≈ {\pi}(30^2)\)
\(≈ (3.1)(900)\)
\(≈ 3000\)

When we check the answer choices, answer choice B is the only answer choice that is remotely close to 3000

Answer: B

RELATED VIDEO FROM MY COURSE

_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6014
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

Show Tags

New post 06 Feb 2020, 09:30
72/360 * 2*pi* r = 40
find r = 100/pi
area = \(\frac{10,000}{\pi}\)
IMO B

Bunuel wrote:
Image
Circle P shown above is centered at P. If the length of arc ABC is 40, what is the area of circle P?


A. \(\frac{10,000}{\pi^{2}}\)

B. \(\frac{10,000}{\pi}\)

C. 10,000

D. \(10000\pi\)

E. \(10,000\pi^{2}\)


Attachment:
T6140.png
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9972
Location: United States (CA)
Re: Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

Show Tags

New post 08 Feb 2020, 12:28
1
Bunuel wrote:
Image
Circle P shown above is centered at P. If the length of arc ABC is 40, what is the area of circle P?


A. \(\frac{10,000}{\pi^{2}}\)

B. \(\frac{10,000}{\pi}\)

C. 10,000

D. \(10000\pi\)

E. \(10,000\pi^{2}\)


Attachment:
T6140.png


We can determine the circumference of the circle using the proportion:

72/360 = 40/C

1/5 = 40/C

C = 200

Therefore, the circumference of the circle is 200. We can determine the radius of the circle using the equation:

2πr = 200

πr = 100

r = 100/π

Thus, the area of the circle is:

π(100/π)^2 = 10,000π/π^2 = 10,000/π

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
avatar
B
Joined: 14 Sep 2019
Posts: 220
Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

Show Tags

New post 09 Feb 2020, 03:05
Formula of Length of Arc = 2πr C/360 , where C = central angel
We are given, Length of Arc = 40
Central angel, C = 72
As per question, 2πr C/360 = 40
2πr 72/360 = 40
r = 100/π

Area, πr^2 = π(100/π)^2 = 10000/π
Answer: B
GMAT Club Bot
Circle P shown above is centered at P. If the length of arc ABC is 40,   [#permalink] 09 Feb 2020, 03:05
Display posts from previous: Sort by

Circle P shown above is centered at P. If the length of arc ABC is 40,

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





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