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

It is currently 18 Jan 2019, 03:44

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
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

In the circle above, three right angles have vertices at the center of

  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: 52279
In the circle above, three right angles have vertices at the center of  [#permalink]

Show Tags

New post 10 Jan 2019, 01:59
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

92% (01:00) correct 8% (00:51) wrong based on 25 sessions

HideShow timer Statistics

Image
In the circle above, three right angles have vertices at the center of the circle. If the radius of the circle is 8, what is the combined area of the shaded regions?


A. 8π
B. 9π
C. 12π
D. 13π
E. 16π

Attachment:
2019-01-10_1358.png
2019-01-10_1358.png [ 22.17 KiB | Viewed 277 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
avatar
B
Joined: 01 May 2017
Posts: 69
Location: India
CAT Tests
Re: In the circle above, three right angles have vertices at the center of  [#permalink]

Show Tags

New post 10 Jan 2019, 05:07
In the circle above, three right angles have vertices at the center of the circle. If the radius of the circle is 8, what is the combined area of the shaded regions?

total 360 degrees are included in the circle, and in the figure non-shaded region is \(3*90 = 270 degrees\)

Area of the shaded region = 90 degrees

Area of the sector = \((x/360)*Pi*r^2\)
= \((90/360)*Pi*8*8\) --- radius given as 8
= \(16*PI\)

Option E is correct
Manager
Manager
avatar
S
Joined: 09 Mar 2018
Posts: 196
Location: India
Re: In the circle above, three right angles have vertices at the center of  [#permalink]

Show Tags

New post 10 Jan 2019, 05:27
r = 8,

Area of shaded region will be 3 * \(\frac{theta}{360}\)* π \(r^2\) --------------------(1)

At the center of a circle, sum of the angles = \(360^o\)

Sum of remaining angles will be 360 - 270 = 90
So each shaded region will have an angle as\(\frac{90}{3}\)

Substituting this value in (1)
=\(\frac{3}{3}\)* \(\frac{90}{360}\)* π \(8^2\)

=16π

Answer E
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2455
Re: In the circle above, three right angles have vertices at the center of  [#permalink]

Show Tags

New post 10 Jan 2019, 05:51

Solution


Given:
    • A circle as shown in the figure
    • Radius = 8

To find:
    • The combined area of the shaded regions

Approach and Working:
    • Angle of each unshaded sector = 90 degrees
      o Thus, area of each unshaded sector = \(\frac{90}{360} * ᴨ * r^2 = ᴨ/4 * 8^2 = 16ᴨ\)

    • Area of all three unshaded sectors combined = 3 * 16ᴨ = 48ᴨ
    • Area of the circle = \(ᴨ * r^2 = 64ᴨ\)

Therefore, area of shaded region = 64ᴨ - 48ᴨ = 16ᴨ

Hence, the correct answer is Option E

Answer: E

Image

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

VP
VP
User avatar
G
Joined: 18 Aug 2017
Posts: 1195
Location: India
Concentration: Sustainability, Marketing
WE: Marketing (Energy and Utilities)
CAT Tests
Re: In the circle above, three right angles have vertices at the center of  [#permalink]

Show Tags

New post 10 Jan 2019, 06:18
Bunuel wrote:
Image
In the circle above, three right angles have vertices at the center of the circle. If the radius of the circle is 8, what is the combined area of the shaded regions?


A. 8π
B. 9π
C. 12π
D. 13π
E. 16π

Attachment:
2019-01-10_1358.png



total angle whose area is to be determined = 360-270 = 90
90/360 * 2 * pi * 8*8
= 16 pi
IMO E
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

GMAT Club Bot
Re: In the circle above, three right angles have vertices at the center of &nbs [#permalink] 10 Jan 2019, 06:18
Display posts from previous: Sort by

In the circle above, three right angles have vertices at the center of

  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®.