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# A smaller circle is inscribed in a larger circle shown as above figure

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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A smaller circle is inscribed in a larger circle shown as above figure  [#permalink]

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03 Apr 2016, 03:06
1
1
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:26) correct 11% (01:36) wrong based on 90 sessions

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circle.jpg [ 3.97 KiB | Viewed 2684 times ]

A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle’s area?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6

* A solution will be posted in two days.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7587 Re: A smaller circle is inscribed in a larger circle shown as above figure [#permalink] ### Show Tags 03 Apr 2016, 03:33 MathRevolution wrote: Attachment: circle.jpg A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle’s area? A. 1/2 B. 2/3 C. 3/4 D. 4/5 E. 5/6 * A solution will be posted in two days. Hi, you will have to mention that the two circles meet at one point.. Area of larger circle =$$pi * r^2$$ for smaller circle, the diameter = r, so radius = r/2 Area of smaller circle = $$pi*(\frac{r}{2})^2$$ area of shaded region = $$pi * r^2$$ - $$pi*(\frac{r}{2})^2$$ = $$pi*(\frac{3}{4})*r^2$$ ratio= $$(pi*(\frac{3}{4})*r^2)/(pi * r^2)$$ = $$\frac{3}{4}$$ C _________________ Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4426 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: A smaller circle is inscribed in a larger circle shown as above figure [#permalink] ### Show Tags 03 Apr 2016, 04:10 1 MathRevolution wrote: Attachment: The attachment circle.jpg is no longer available A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle’s area? A. 1/2 B. 2/3 C. 3/4 D. 4/5 E. 5/6 * A solution will be posted in two days. IMHO the best and easiest approach will be plugging in some values as below - Attachment: Circle 1.png [ 6.65 KiB | Viewed 2630 times ] Area of the bigger circle will be π$$(4)^2$$ = 16π Area of the smaller circle will be π$$(2)^2$$ = 4π So, Area of the shaded region will be 16π - 4π = 12π We are required to find - Quote: the ratio of the region shaded to the larger circle’s area? The required ratio is 12π / 16π = 3/4 _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2908 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) Re: A smaller circle is inscribed in a larger circle shown as above figure [#permalink] ### Show Tags 03 Apr 2016, 06:22 MathRevolution wrote: Attachment: circle.jpg A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle’s area? A. 1/2 B. 2/3 C. 3/4 D. 4/5 E. 5/6 * A solution will be posted in two days. From Figure we see that radius of bigger circle = Diameter of smaller circle Let, Radius of Bigger circle = 2 = Diameter of smaller circle i.e. Radius of Smaller circle = 2/2 = 1 Area of Bigger circle = Pi 2^2 = 4 Pi Area of Smaller circle = Pi 1^2 = Pi Area of Shaded Region = Big circle - Small Circle = 4 Pi - Pi = 3Pi Shaded Area/Area of Big circle = 3Pi/4 Pi = 3/4 Answer: Option C _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Current Student Joined: 12 Aug 2015 Posts: 2613 Schools: Boston U '20 (M) GRE 1: Q169 V154 Re: A smaller circle is inscribed in a larger circle shown as above figure [#permalink] ### Show Tags 03 Apr 2016, 12:55 Nice Question.. here we just need to figure out that radius of the larger circle is the diameter of the smaller circle. Hence C as Shaded area => 3/4 of the larger area _________________ Intern Joined: 26 Nov 2015 Posts: 30 Re: A smaller circle is inscribed in a larger circle shown as above figure [#permalink] ### Show Tags 05 Apr 2016, 04:57 As we know that the smaller circle will have radius half to that of main circle So area of smaller circle = 1/4* area of larger circle Now as per question it asks us the ratio of shaded region to that of whole So shaded region = area of larger - area of smaller = 1- 1/4 = 3/4 So answer is C Sent from my Mi 4i using Tapatalk _________________ PS : I do mind kudos Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7245 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A smaller circle is inscribed in a larger circle shown as above figure [#permalink] ### Show Tags 05 Apr 2016, 05:58 A smaller circle is inscribed in a larger circle shown as above figure. If the smaller circle passes through a center of the larger circle,what is the ratio of the region shaded to the larger circle’s area? A. 1/2 B. 2/3 C. 3/4 D. 4/5 E. 5/6 -> As the ratio of the radius is 1:2, the ratio of the area is 1:4. If the area of the small circle is a, the shaded area is 3a. Thus, 3a/(a+3a)=3/4 and the answer is C. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: A smaller circle is inscribed in a larger circle shown as above figure  [#permalink]

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27 Jul 2017, 19:36
I have a small doubt in this question. If you consider the radius of the smaller circle to be 3 and the radius of the larger circle to be 5 then the area of the smaller is pi and the larger area is 25pi . Therefore the shaded part is 25pi-pi=16pi
16pi/25pi

So here i am missing out on the fact that the smaller circle passes through the center of the larger circle. Is that so? and in what circumstance does this method hold valid. Thank you
Re: A smaller circle is inscribed in a larger circle shown as above figure   [#permalink] 27 Jul 2017, 19:36
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