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

 It is currently 20 Apr 2019, 02:04

### 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

# If a point is arbitrarily selected inside a circle of radius

Author Message
TAGS:

### Hide Tags

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1070
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
If a point is arbitrarily selected inside a circle of radius  [#permalink]

### Show Tags

Updated on: 26 Oct 2012, 23:31
00:00

Difficulty:

25% (medium)

Question Stats:

71% (01:24) correct 29% (02:07) wrong based on 75 sessions

### HideShow timer Statistics

If a point is arbitrarily selected inside a circle of radius R, what is the probability that the distance from this point to the center of the circle will be greater than R/2 ?

A. 1/2
B. 3/4
C. 7/8
D. 1/4*R^2
E. 3/4*R^2

_________________

Originally posted by Marcab on 26 Oct 2012, 21:20.
Last edited by Marcab on 26 Oct 2012, 23:31, edited 1 time in total.
Intern
Joined: 02 Feb 2012
Posts: 25
GPA: 4
Re: If a point is arbitrarily selected inside a circle of radius  [#permalink]

### Show Tags

27 Oct 2012, 00:23
Area of circle with radius R, A1 = 2*pi*(R)^2
Area of circle with radius R/2, A2 = 2*pi*(R/2)^2

Implies, A1/A2 = 4/1

The area of the circle excluding the area of circle with radius R/2 is 3 times more..

Hence the probability will be 3/4
Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 587
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Re: If a point is arbitrarily selected inside a circle of radius  [#permalink]

### Show Tags

27 Oct 2012, 00:41
1
Marcab wrote:
sorry....its R/2.
its been corrected in the original post.

Great now it makes sense
Basically in the question we are looking for probability of point lying in Green region in the attached figure.

Since the radius of Grean Circle is R and radius of red circle is R/2. Hence the area of greeen region =
$$pi R^2 - pi (r/2)^2$$
$$= 3/4 pi R^2$$

Also area of circle with radius R$$= pi R^2$$
Hence probability of point lying in green region =$$3/4 pi R^2 / pi R^2$$
= 3/4

Hence Ans B it is.

Hope it helps.
Attachments

circles.png [ 15.76 KiB | Viewed 2201 times ]

_________________
Lets Kudos!!!
Black Friday Debrief
Non-Human User
Joined: 09 Sep 2013
Posts: 10558
Re: If a point is arbitrarily selected inside a circle of radius  [#permalink]

### Show Tags

15 Aug 2017, 20:11
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: If a point is arbitrarily selected inside a circle of radius   [#permalink] 15 Aug 2017, 20:11
Display posts from previous: Sort by