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

 It is currently 17 Feb 2019, 20:33

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

# In the figure above, the five circles have points in common as shown

Author Message
TAGS:

### Hide Tags

Moderator
Joined: 21 Jun 2014
Posts: 1113
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
In the figure above, the five circles have points in common as shown  [#permalink]

### Show Tags

20 Nov 2018, 08:21
1
4
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:41) correct 33% (01:51) wrong based on 81 sessions

### HideShow timer Statistics

In the figure above, the five circles have points in common as shown. P is the center of the largest circle, Q and R are centers of the medium-sized circles, and Q, P, and R are points on a straight line. What fraction of the largest circular region is shaded?

(A) $$\frac{1}{16}$$
(B) $$\frac{1}{8}$$
(C) $$\frac{3}{16}$$
(D) $$\frac{1}{4}$$
(E) $$\frac{1}{2}$$

Project PS Butler : Question #30

Attachment:

Circles.JPG [ 15.13 KiB | Viewed 790 times ]

_________________

---------------------------------------------------------------
Target - 720-740
Project PS Butler - https://gmatclub.com/forum/project-ps-butler-practice-everyday-280904.html
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

VP
Joined: 09 Mar 2016
Posts: 1286
In the figure above, the five circles have points in common as shown  [#permalink]

### Show Tags

20 Nov 2018, 10:05
have no idea if my solution is correct how is it possble to find fraction if i dont know radius

anyway i assigned some random values

let diamertre of large circle be 12, so radius is 6

hence diametre of smaller circle be 6 and radius is 3

Area of large circle 36
Area of two smaller circles is 18

so $$\frac{18}{36}$$ i.e. = $$\frac{1}{2}$$

IMO: E
Manager
Joined: 14 Jun 2018
Posts: 223
In the figure above, the five circles have points in common as shown  [#permalink]

### Show Tags

Updated on: 20 Nov 2018, 10:56
let radius of largest circle be 8
Radius of largest = diameter of Medium circle = 8 ; radius of medium = 4
Radius of smallest will be 2
ratio = 2 x π x 2^2 / π x 8^2 = 1/8

Originally posted by pandeyashwin on 20 Nov 2018, 10:55.
Last edited by pandeyashwin on 20 Nov 2018, 10:56, edited 1 time in total.
Manager
Joined: 09 Jun 2018
Posts: 189
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
Re: In the figure above, the five circles have points in common as shown  [#permalink]

### Show Tags

20 Nov 2018, 10:56
Let the larger circle have radius R.

So, QP = R/2 which is the diameter of the smaller circle.

So radius of smaller circle = 0.5*R/2 = R/4

Hence area of 2 smaller circles = 2* (pi*$$R^2$$/16) = pi*$$R^2$$/8

Ratio = (pi*$$R^2$$/8)/pi*$$R^2$$ = 1/8

Hence Option B
_________________

If you found this relevant and useful, please Smash that Kudos button!

VP
Joined: 09 Mar 2016
Posts: 1286
Re: In the figure above, the five circles have points in common as shown  [#permalink]

### Show Tags

20 Nov 2018, 11:08
pandeyashwin wrote:
let radius of largest circle be 8
Radius of largest = diameter of Medium circle = 8 ; radius of medium = 4
Radius of smallest will be 2
ratio = 2 x π x 2^2 / π x 8^2 = 1/8

pandeyashwin then whats wrong with my solution ?
VP
Joined: 09 Mar 2016
Posts: 1286
In the figure above, the five circles have points in common as shown  [#permalink]

### Show Tags

20 Nov 2018, 11:36
okay I got it, missed medium sized circles and assigned inconvenient radius number initially because if radius of large circle is 6, medium sized 3 and then smallest is 1.5
Intern
Joined: 30 Jan 2018
Posts: 2
Re: In the figure above, the five circles have points in common as shown  [#permalink]

### Show Tags

20 Nov 2018, 13:22
the region of the largest circle is πr^2
the region of the shaded circles is: 2 * π(1/4r)^2
=> 1/8 (B)
Director
Joined: 09 Mar 2018
Posts: 967
Location: India
Re: In the figure above, the five circles have points in common as shown  [#permalink]

### Show Tags

09 Feb 2019, 04:12
HKD1710 wrote:

In the figure above, the five circles have points in common as shown. P is the center of the largest circle, Q and R are centers of the medium-sized circles, and Q, P, and R are points on a straight line. What fraction of the largest circular region is shaded?

(A) $$\frac{1}{16}$$
(B) $$\frac{1}{8}$$
(C) $$\frac{3}{16}$$
(D) $$\frac{1}{4}$$
(E) $$\frac{1}{2}$$

Let the radius of bigger circle = 8
radius of smallest circle = 4

Area of a largest circle = 64
Area of shaded circles = 8

8/64

1/8

B
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Intern
Joined: 05 Sep 2015
Posts: 2
Re: In the figure above, the five circles have points in common as shown  [#permalink]

### Show Tags

09 Feb 2019, 18:24
Let the radius of the bugger circle= 2R
Hence, radius of the medium circle = R
and radius of the smaller circle = R/2
Required Ratio = {π(R/2)^2 + π(R/2)^2}/ π(2R)^2 = 1/8
Re: In the figure above, the five circles have points in common as shown   [#permalink] 09 Feb 2019, 18:24
Display posts from previous: Sort by