Jun 16 07:00 AM PDT  09:00 AM PDT Get personalized insights and an accurate assessment of your current quant score to achieve your Target Quant Score. Jun 16 09:00 PM PDT  10:00 PM PDT For a score of 4951 (from current actual score of 40+). AllInOne Standard & 700+ Level Questions (150 questions) Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jun 23 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 06 Feb 2010
Posts: 145
Concentration: Marketing, Leadership
Schools: University of Dhaka  Class of 2010
GPA: 3.63
WE: Business Development (Consumer Products)

In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
Updated on: 06 Dec 2017, 12:24
Question Stats:
62% (01:46) correct 38% (02:06) wrong based on 494 sessions
HideShow timer Statistics
In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle? A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\) Attachment:
1111220830.jpg [ 344.39 KiB  Viewed 27711 times ]
Attachment:
Untitled2.png [ 13.24 KiB  Viewed 38649 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Practice Makes a Man Perfect. Practice. Practice. Practice......Perfectly
Critical Reasoning: http://gmatclub.com/forum/bestcriticalreasoningshortcutsnotestips91280.html
Collections of MGMAT CAT: http://gmatclub.com/forum/collectionsofmgmatcatmath152750.html
MGMAT SC SUMMARY: http://gmatclub.com/forum/mgmatscsummaryoffourthedition152753.html
Sentence Correction: http://gmatclub.com/forum/sentencecorrectionstrategiesandnotes91218.html
Arithmatic & Algebra: http://gmatclub.com/forum/arithmaticalgebra93678.html
Helpful Geometry formula sheet: http://gmatclub.com/forum/bestgeometry93676.html
I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.
Originally posted by monirjewel on 11 Nov 2010, 09:09.
Last edited by Bunuel on 06 Dec 2017, 12:24, edited 2 times in total.
Renamed the topic, edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 55613

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
11 Nov 2010, 09:27
In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\) The area of the shaded region is \(area_{shaded}=\pi{R^2}\pi{r^2}\) and the area of the smaller circle is \(area_{small}=\pi{r^2}\). Given: \(\pi{R^2}\pi{r^2}=3\pi{r^2}\) > \(R^2=4r^2\) > \(R=2r\); Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \(\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2\). Answer: C.
_________________




SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1798
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
09 Mar 2014, 04:10
Let the area of small circle = x Area of shaded region = 3x Total Area = x+3x = 4x This means that Area of larger circle is 4 times Area of Small Circle; which also means radius of larger circle is 2 times radius of small circle & so the circumference So Answer = C = 2
_________________
Kindly press "+1 Kudos" to appreciate



Manager
Joined: 30 Sep 2010
Posts: 53

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
11 Nov 2010, 09:27
circular shaded region = area of large circle  area of small circle = 3 * area of small circle so area of large circle = 4 * area of small circle
that means radius oflarge circle = 2 * radius of small circle so the cicumference of large circle is 2 times that of the small circle Option C



Math Expert
Joined: 02 Sep 2009
Posts: 55613

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
28 Feb 2018, 00:15
shivamtibrewala wrote: Bunuel wrote: In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\) The area of the shaded region is \(area_{shaded}=\pi{R^2}\pi{r^2}\) and the area of the smaller circle is \(area_{small}=\pi{r^2}\). Given: \(\pi{R^2}\pi{r^2}=3\pi{r^2}\) > \(R^2=4r^2\) > \(R=2r\); Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \(\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2\). Answer: C. Hi Bunuel, Can you share problems that are similar to this? Thanks. Shaded Region Problems from our Special Questions Directory.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 55613

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
06 Mar 2014, 02:27
Bumping for review and further discussion.GEOMETRY: Shaded Region Problems!
_________________



Manager
Joined: 10 Mar 2014
Posts: 186

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
13 Apr 2014, 09:24
Bunuel wrote: In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\) The area of the shaded region is \(area_{shaded}=\pi{R^2}\pi{r^2}\) and the area of the smaller circle is \(area_{small}=\pi{r^2}\). Given: \(\pi{R^2}\pi{r^2}=3\pi{r^2}\) > \(R^2=4r^2\) > \(R=2r\); Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \(\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2\). Answer: C. HI Bunnel, Have one doubt on this as you have mentioned here R = 2r. Now we put this in the pi*rsquare then for both circles the are we got is 4pir square = pi r square. Now area is four times instead of 3 times. So please clarify this



Math Expert
Joined: 02 Sep 2009
Posts: 55613

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
13 Apr 2014, 09:37
pawankumargadiya wrote: Bunuel wrote: In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\) The area of the shaded region is \(area_{shaded}=\pi{R^2}\pi{r^2}\) and the area of the smaller circle is \(area_{small}=\pi{r^2}\). Given: \(\pi{R^2}\pi{r^2}=3\pi{r^2}\) > \(R^2=4r^2\) > \(R=2r\); Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \(\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2\). Answer: C. HI Bunnel, Have one doubt on this as you have mentioned here R = 2r. Now we put this in the pi*rsquare then for both circles the are we got is 4pir square = pi r square. Now area is four times instead of 3 times. So please clarify this The stem says that the area of the shaded region is 3 times the area of the smaller circular region, not that the area of the larger circular region is 3 times the area of the smaller circular region. Does this make sense?
_________________



Senior SC Moderator
Joined: 22 May 2016
Posts: 2888

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
06 Dec 2017, 12:09
monirjewel wrote: Attachment: Untitled2.png In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle? A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\) Attachment: 1111220830.jpg AlgebraicallyLet a = Small circle's area Let s = Shaded region's area Let A = Large circle's area \(s = 3a\) \(A = s + a\) \(A = 3a + a\) \(A = 4a\)
\(a = \pi r^2\) \(A = \pi R^2\)From above: \(A = 4a\) \(\pi R^2 = 4\pi r^2\) \(R^2 = 4r^2\) \(\sqrt{R^2}=\sqrt{4r^2}\) \(R = 2r\)* Circumference, Large and Small C = \(2\pi R\), and c = \(2\pi r\)\(R = 2r\), so \(\frac{C}{c}=\frac{2\pi (2r)}{2\pi r}= \frac{2r}{r}=2\)The large circle's circumference is two times the small circle's circumference. Answer C Numbers and algebraLarge circle's area: Small circle's area?Small circle's area = x Shaded region's area = 3x Large circle's area = 3x + x = 4xLarge circle circumference/ small circle's circumference?Let Small circle's radius \(r = 1\)Area of Small: \(\pi r^2 = \pi\)Area of Large = ( 4x) = \((4*\pi) = 4\pi\)Radius, R, of Large circle: \(4\pi =\pi R^2\) \(R = 2\)Circumference, Small: \(2 \pi r = 2 \pi\)Circumference, Large: \(2 \pi R = 4 \pi\)\(\frac{Large}{Small}=\frac{4\pi}{2\pi} = 2\) The large circle's circumference is two times the small circle's circumference. Answer C ** OR \(A = 3a + a\) \(A  3a = a\) AND \(A = \pi R^2\)
\(\pi R^2  3\pi r^2=\pi r^2\) \(\pi (R^2  3r^2)=\pi r^2\) \(R^2  3r^2 = r^2\) \(R^2 = 4r^2\) Take square roots: \(R = 2r\)
_________________
SC Butler has resumed!Get two SC questions to practice, whose links you can find by date, here.Tell me, what is it you plan to do with your one wild and precious life?  Mary Oliver



Intern
Joined: 09 Mar 2017
Posts: 44
Location: India
GPA: 4
WE: Marketing (Advertising and PR)

In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
25 Dec 2017, 03:19
Bunuel,
The area of the shaded region is areashaded=πR2−πr2areashaded=πR2−πr2 and the area of the smaller circle is areasmall=πr2areasmall=πr2.
I made a mistake here. I write this like: πR^2=3*πr^2 (as is say 3 times)
What mistake have I made?



Math Expert
Joined: 02 Sep 2009
Posts: 55613

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
25 Dec 2017, 03:24
amitpandey25 wrote: Bunuel,
The area of the shaded region is areashaded=πR2−πr2areashaded=πR2−πr2 and the area of the smaller circle is areasmall=πr2areasmall=πr2.
I made a mistake here. I write this like: πR^2=3*πr^2 (as is say 3 times)
What mistake have I made? I think it's addressed above. The stem says that the area of the shaded region is 3 times the area of the smaller circular region, not that the area of the larger circular region is 3 times the area of the smaller circular region.
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14338
Location: United States (CA)

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
01 Feb 2018, 13:19
Hi All, This question can be solved by TESTing VALUES. We're told that the area of the shaded region is 3 TIMES the area of the central circle... Area of center = 1 Area of shaded region = 3(1) = 3 Area of FULL CIRCLE = 1+3 = 4 With those values.... Radius of center = 1 Radius of FULL CIRCLE = 2 The question asks how many times the circumference of the full circle is to the smaller circle... Circumference of small circle = 2pi Circumference of full circle = 4pi Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



Intern
Joined: 02 Nov 2017
Posts: 17

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
28 Feb 2018, 00:03
Bunuel wrote: In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\) The area of the shaded region is \(area_{shaded}=\pi{R^2}\pi{r^2}\) and the area of the smaller circle is \(area_{small}=\pi{r^2}\). Given: \(\pi{R^2}\pi{r^2}=3\pi{r^2}\) > \(R^2=4r^2\) > \(R=2r\); Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \(\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2\). Answer: C. Hi Bunuel, Can you share problems that are similar to this? Thanks.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6521
Location: United States (CA)

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
01 Mar 2018, 18:35
monirjewel wrote: In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle? A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\) Attachment: 1111220830.jpg Attachment: Untitled2.png If we let A = the radius of the larger circle and B = the radius of the smaller circle, then we can create the equation: (A^2  B^2)π = area of shaded region Area of the smaller circle = πB^2; thus: (A^2  B^2)π = 3πB^2 A^2  B^2 = 3B^2 A^2 = 4B^2 A = 2B Since the radius of the larger circle can be expressed as 2B, the circumference of the larger circle is 4Bπ, and the circumference of the smaller circle is 2Bπ, so the circumference of the larger circle is twice that of the smaller circle. Answer: C
_________________
5star 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.



NonHuman User
Joined: 09 Sep 2013
Posts: 11364

Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
Show Tags
17 Mar 2019, 12:27
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.
_________________




Re: In the figure shown, if the area of the shaded region is 3 t
[#permalink]
17 Mar 2019, 12:27






