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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # In the figure shown, if the area of the shaded region is 3 t  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 06 Feb 2010 Posts: 149 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, 11:24 6 13 00:00 Difficulty: 55% (hard) Question Stats: 64% (01:45) correct 36% (02:01) wrong based on 586 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 23096 times ] Attachment: Untitled2.png [ 13.24 KiB | Viewed 32431 times ] _________________ Practice Makes a Man Perfect. Practice. Practice. Practice......Perfectly Critical Reasoning: http://gmatclub.com/forum/best-critical-reasoning-shortcuts-notes-tips-91280.html Collections of MGMAT CAT: http://gmatclub.com/forum/collections-of-mgmat-cat-math-152750.html MGMAT SC SUMMARY: http://gmatclub.com/forum/mgmat-sc-summary-of-fourth-edition-152753.html Sentence Correction: http://gmatclub.com/forum/sentence-correction-strategies-and-notes-91218.html Arithmatic & Algebra: http://gmatclub.com/forum/arithmatic-algebra-93678.html Helpful Geometry formula sheet: http://gmatclub.com/forum/best-geometry-93676.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, 08:09. Last edited by Bunuel on 06 Dec 2017, 11:24, edited 2 times in total. Renamed the topic, edited the question and added the OA. ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: In the figure shown, if the area of the shaded region is 3 t [#permalink] ### Show Tags 11 Nov 2010, 08:27 3 8 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. _________________ ##### General Discussion Manager Joined: 30 Sep 2010 Posts: 55 Re: In the figure shown, if the area of the shaded region is 3 t [#permalink] ### Show Tags 11 Nov 2010, 08:27 1 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: 51218 Re: In the figure shown, if the area of the shaded region is 3 t [#permalink] ### Show Tags 06 Mar 2014, 01:27 Bumping for review and further discussion. GEOMETRY: Shaded Region Problems! _________________ SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1825 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, 03:10 2 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: 10 Mar 2014 Posts: 192 Re: In the figure shown, if the area of the shaded region is 3 t [#permalink] ### Show Tags 13 Apr 2014, 08:24 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: 51218 Re: In the figure shown, if the area of the shaded region is 3 t [#permalink] ### Show Tags 13 Apr 2014, 08:37 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: 2211 Re: In the figure shown, if the area of the shaded region is 3 t [#permalink] ### Show Tags 06 Dec 2017, 11:09 1 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 Algebraically Let 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 algebra Large circle's area: Small circle's area? Small circle's area = x Shaded region's area = 3x Large circle's area = 3x + x = 4x Large 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: $$R = 2r$$ Intern Joined: 09 Mar 2017 Posts: 49 Location: India GMAT 1: 650 Q45 V31 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, 02:19 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: 51218 Re: In the figure shown, if the area of the shaded region is 3 t [#permalink] ### Show Tags 25 Dec 2017, 02:24 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/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13087 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: In the figure shown, if the area of the shaded region is 3 t [#permalink] ### Show Tags 01 Feb 2018, 12:19 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 # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: In the figure shown, if the area of the shaded region is 3 t  [#permalink]

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27 Feb 2018, 23:03
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 $$\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2$$.

Hi Bunuel,

Can you share problems that are similar to this?

Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 51218
Re: In the figure shown, if the area of the shaded region is 3 t  [#permalink]

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27 Feb 2018, 23:15
1
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 $$\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2$$.

Hi Bunuel,

Can you share problems that are similar to this?

Thanks.

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Re: In the figure shown, if the area of the shaded region is 3 t  [#permalink]

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01 Mar 2018, 17:35
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.

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Re: In the figure shown, if the area of the shaded region is 3 t &nbs [#permalink] 01 Mar 2018, 17:35
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