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

It is currently 19 Aug 2018, 21:38

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

Two circles with radii r and r + 2 have areas that differ by 8π. What

  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: 48037
Two circles with radii r and r + 2 have areas that differ by 8π. What  [#permalink]

Show Tags

New post 27 Nov 2017, 23:33
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

85% (00:53) correct 15% (01:39) wrong based on 68 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
G
Joined: 17 Oct 2016
Posts: 325
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
GMAT ToolKit User Premium Member
Re: Two circles with radii r and r + 2 have areas that differ by 8π. What  [#permalink]

Show Tags

New post 28 Nov 2017, 00:10
C

Area of larger circle = pi.(r+2)^2
Area of smaller circle =pi.r^2

Difference is pi.((r+2)^2-r^2)=8.pi

Solving we get r=1. Hence radius of larger circle =3


Sent from my iPhone using GMAT Club Forum
_________________

Help with kudos if u found the post useful. Thanks

SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1910
Premium Member CAT Tests
Re: Two circles with radii r and r + 2 have areas that differ by 8π. What  [#permalink]

Show Tags

New post 28 Nov 2017, 15:08
Bunuel wrote:
Two circles with radii r and r + 2 have areas that differ by 8π. What is the radius of the larger circle?

(A) 1
(B) 2
(C) 3
(D) 8
(E) 9

Two circles with radii r and (r + 2) have areas that differ by 8π:

\(π(r+2)^2 - (πr^2) = 8π\)

\(π(r^2 + 4r + 4) - πr^2 = 8π\)

\(πr^2 + 4πr + 4π - πr^2 = 8π\)
\(4πr + 4π = 8π\)
\(4πr = 4π\)
\(r = 1\)


Radius of larger circle = \((r + 2) = 3\)

Answer C

Check: Circle 1 area = \(π(1)^2 = π\). Circle 2 area = \(π(3)^2 = 9π\). Difference:\((9π-1π)=8π\)
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3182
Location: United States (CA)
Re: Two circles with radii r and r + 2 have areas that differ by 8π. What  [#permalink]

Show Tags

New post 29 Nov 2017, 18:18
1
Bunuel wrote:
Two circles with radii r and r + 2 have areas that differ by 8π. What is the radius of the larger circle?

(A) 1
(B) 2
(C) 3
(D) 8
(E) 9


The area of the smaller circle is πr^2.

The area of the larger circle is π(r + 2)^2 = π(r^2 + 4r + 4).

Since the areas differ by 8π, we have:

π(r^2 + 4r + 4) - πr^2 = 8π

r^2 + 4r + 4 - r^2 = 8

4r + 4 = 8

4r = 4

r = 1

Thus, the radius of the larger circle is 1 + 2 = 3.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
avatar
B
Joined: 03 Jun 2017
Posts: 49
Location: United Kingdom
GMAT 1: 610 Q47 V27
GMAT 2: 700 Q49 V34
GPA: 4
Re: Two circles with radii r and r + 2 have areas that differ by 8π. What  [#permalink]

Show Tags

New post 09 Dec 2017, 01:35
Just plug in numbers. Obviously don't start with A or B. Start with D. Too big a difference, so answer is C.

Sent from my Pixel 2 using GMAT Club Forum mobile app
Re: Two circles with radii r and r + 2 have areas that differ by 8π. What &nbs [#permalink] 09 Dec 2017, 01:35
Display posts from previous: Sort by

Two circles with radii r and r + 2 have areas that differ by 8π. What

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

Events & Promotions

PREV
NEXT


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®.