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

 It is currently 21 May 2019, 11:58

### 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

# There are 2 circles, 1 big circle and 1 small circle, and they meet at

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7354
GMAT 1: 760 Q51 V42
GPA: 3.82
There are 2 circles, 1 big circle and 1 small circle, and they meet at  [#permalink]

### Show Tags

02 Aug 2017, 01:01
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:19) correct 16% (01:21) wrong based on 47 sessions

### HideShow timer Statistics

Attachment:

8.2.png [ 12.19 KiB | Viewed 1500 times ]

There are 2 circles, 1 big circle and 1 small circle, and they meet at one point. The diameter of the small circle is equal to the radius of the big circle, and the area of the big circle is $$14π$$. What is the area of the small circle?

$$A. 3π$$
$$B. 3.5π$$
$$C. 4π$$
$$D. 4.5π$$
$$E. 7π$$

_________________
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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 04 Dec 2015 Posts: 750 Location: India Concentration: Technology, Strategy WE: Information Technology (Consulting) Re: There are 2 circles, 1 big circle and 1 small circle, and they meet at [#permalink] ### Show Tags 02 Aug 2017, 01:29 1 MathRevolution wrote: Attachment: 8.2.png There are 2 circles, 1 big circle and 1 small circle, and they meet at one point. The diameter of the small circle is equal to the radius of the big circle, and the area of the big circle is $$14π$$. What is the area of the small circle? $$A. 3π$$ $$B. 3.5π$$ $$C. 4π$$ $$D. 4.5π$$ $$E. 7π$$ Given Area of big circle $$= 14π$$ Let the radius of big circle be $$= R$$ $$\pi$$$$R^2 = 14π$$ $$R^2 = 14$$ $$R = \sqrt{14}$$ Given diameter of small circle is equal to radius of big circle. Let the radius of small circle be $$= r$$ Therefore $$R = 2r$$ $$r = \frac{R}{2}$$ $$= \frac{\sqrt{14}}{ 2}$$ Area of small circle $$= \pi r^2 = \pi * \frac{\sqrt{14}}{ 2} * \frac{\sqrt{14}}{ 2} = \pi * \frac{14}{4} = \frac{7}{2} \pi = 3.5\pi$$ Answer (B)... _________________ Please Press "+1 Kudos" to appreciate. Director Affiliations: IIT Dhanbad Joined: 13 Mar 2017 Posts: 724 Location: India Concentration: General Management, Entrepreneurship GPA: 3.8 WE: Engineering (Energy and Utilities) Re: There are 2 circles, 1 big circle and 1 small circle, and they meet at [#permalink] ### Show Tags 02 Aug 2017, 02:08 MathRevolution wrote: Attachment: 8.2.png There are 2 circles, 1 big circle and 1 small circle, and they meet at one point. The diameter of the small circle is equal to the radius of the big circle, and the area of the big circle is $$14π$$. What is the area of the small circle? $$A. 3π$$ $$B. 3.5π$$ $$C. 4π$$ $$D. 4.5π$$ $$E. 7π$$ Let the radius of bigger circle be R & radius of smaller circle be r. So, r = R/2 $$πR^2 = 14π$$ $$R = \sqrt{14}$$ $$r = \sqrt{14}/2$$[/m] Area of smaller circle $$= πr^2 = π(R/2)^2= πR^2 /4$$ $$=14π/4 = 3.5π$$ _________________ CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler UPSC Aspirants : Get my app UPSC Important News Reader from Play store. MBA Social Network : WebMaggu Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish". Intern Joined: 15 Oct 2016 Posts: 29 There are 2 circles, 1 big circle and 1 small circle, and they meet at [#permalink] ### Show Tags 02 Aug 2017, 02:14 MathRevolution wrote: Attachment: 8.2.png There are 2 circles, 1 big circle and 1 small circle, and they meet at one point. The diameter of the small circle is equal to the radius of the big circle, and the area of the big circle is $$14π$$. What is the area of the small circle? $$A. 3π$$ $$B. 3.5π$$ $$C. 4π$$ $$D. 4.5π$$ $$E. 7π$$ The ratio of areas of two circles is the same as the ratio of the squares of their respective Radii / Diameters. Hence the correct answer should be 1/4 of the area of the bigger circle. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7354 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: There are 2 circles, 1 big circle and 1 small circle, and they meet at [#permalink] ### Show Tags 04 Aug 2017, 02:23 ==> Ratio of length^2=Ratio of area, and since the ratio of the length is 2, the ratio of the area becomes 4, so you get $$\frac{14π}{4}=3.5π$$. The answer is B. Answer: B _________________ 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"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: There are 2 circles, 1 big circle and 1 small circle, and they meet at   [#permalink] 04 Aug 2017, 02:23
Display posts from previous: Sort by