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

 It is currently 20 Nov 2018, 19:59

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

Events & Promotions

Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• Free lesson on number properties

November 23, 2018

November 23, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

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

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50711
Two circles with radii r and r + 2 have areas that differ by 8π. What  [#permalink]

Show Tags

27 Nov 2017, 22:33
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:17) correct 16% (01:51) wrong based on 82 sessions

HideShow timer Statistics

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

_________________
Senior Manager
Joined: 17 Oct 2016
Posts: 321
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: Two circles with radii r and r + 2 have areas that differ by 8π. What  [#permalink]

Show Tags

27 Nov 2017, 23:10
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

Senior SC Moderator
Joined: 22 May 2016
Posts: 2117
Re: Two circles with radii r and r + 2 have areas that differ by 8π. What  [#permalink]

Show Tags

28 Nov 2017, 14:08
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 = $$(r + 2) = 3$$

Check: Circle 1 area = $$π(1)^2 = π$$. Circle 2 area = $$π(3)^2 = 9π$$. Difference:$$(9π-1π)=8π$$
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: Two circles with radii r and r + 2 have areas that differ by 8π. What  [#permalink]

Show Tags

29 Nov 2017, 17:18
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.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Intern
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

09 Dec 2017, 00:35

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, 00:35
Display posts from previous: Sort by