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

It is currently 21 Oct 2019, 11:49

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Circles X and Y are concentric. If the radius of circle X is three

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
Joined: 10 Apr 2012
Posts: 262
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
GMAT ToolKit User
Circles X and Y are concentric. If the radius of circle X is three  [#permalink]

Show Tags

New post Updated on: 26 Jun 2013, 03:26
1
6
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:37) correct 22% (01:46) wrong based on 136 sessions

HideShow timer Statistics

Circles X and Y are concentric. If the radius of circle X is three times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?

(A) 13

(B) \(\frac{\pi}{3}\)

(C) \(\frac{\pi}{2}\)

(D) 5/6

(E) 8/9

Originally posted by guerrero25 on 26 Jun 2013, 03:11.
Last edited by guerrero25 on 26 Jun 2013, 03:26, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58396
Circles X and Y are concentric. If the radius of circle X is three  [#permalink]

Show Tags

New post 26 Jun 2013, 03:18
1
guerrero25 wrote:
Circles X and Y are concentric. If the radius of circle X is three times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?

(A) 13

(B) \(\frac{\pi}{3}\)

(C) \(\frac{\pi}{2}\)

(D) 5/6

(E) 8/9


Say the radius of the smaller circle (Y) is 1, then the radius of the larger circle would be 3.

The area of X = \(\pi{R^2}=9\pi\);
The area of Y = \(\pi{r^2}=\pi\).

The probability = (Favorable)/(Total) = \(\frac{9\pi-\pi}{9\pi}=\frac{8}{9}\).

Answer: E.
_________________
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1747
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Circles X and Y are concentric. If the radius of circle X is three  [#permalink]

Show Tags

New post 14 Oct 2013, 01:54
Small circle radius = a, so area = PI a ^ 2

Large circle radius = 3a, so area = 9. PI a ^ 2

Area of shaded region = 9PI a^2 - PI a^2 = 8 PI a^2

So, probability = ( 8 PI a^2 ) / (9 PI a^2 )

= 8/9 = Answer = E
Attachments

circle.JPG
circle.JPG [ 7.89 KiB | Viewed 1689 times ]


_________________
Kindly press "+1 Kudos" to appreciate :)
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13384
Re: Circles X and Y are concentric. If the radius of circle X is three  [#permalink]

Show Tags

New post 20 Jan 2018, 08:58
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.
_________________
GMAT Club Bot
Re: Circles X and Y are concentric. If the radius of circle X is three   [#permalink] 20 Jan 2018, 08:58
Display posts from previous: Sort by

Circles X and Y are concentric. If the radius of circle X is three

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne