Last visit was: 15 Dec 2024, 04:25 It is currently 15 Dec 2024, 04:25
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
RMD007
User avatar
Joined: 03 Jul 2016
Last visit: 08 Jun 2019
Posts: 237
Own Kudos:
170
 []
Given Kudos: 80
Status:Countdown Begins...
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE:Information Technology (Consulting)
Products:
My Reviews
Schools: IIMB
GMAT 1: 580 Q48 V22
Posts: 237
Kudos: 170
 []
A Circle, with its radius an integer, is inscribed in a square. 17 Jul 2017, 11:54
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

39% (01:37) correct 61% (01:55) wrong based on 56 sessions

History

Date
Time
Result
Not Attempted Yet
A Circle, with its radius an integer, is inscribed in a square. What is the probability that a point randomly chosen inside the square will lie outside the circle?

1. Side of the square is a prime number.

2. Another square inscribed in the circle has side \(\sqrt{2}\)

Source : Self-made. :)



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
ShowHide Answer
Official Answer
D
User avatar
darn
User avatar
Joined: 12 Sep 2016
Last visit: 06 Jan 2020
Posts: 58
Own Kudos:
21
 []
Given Kudos: 794
Location: India
Schools: Kellogg '20 Schulich Sept 18 Intake (I)
GMAT 1: 700 Q50 V34
GPA: 3.15
Products:
My Reviews
Schools: Kellogg '20 Schulich Sept 18 Intake (I)
GMAT 1: 700 Q50 V34
Posts: 58
Kudos: 21
 []
A Circle, with its radius an integer, is inscribed in a square. 18 Jul 2017, 00:59
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How is statement A sufficient?
User avatar
RMD007
User avatar
Joined: 03 Jul 2016
Last visit: 08 Jun 2019
Posts: 237
Own Kudos:
170
 []
Given Kudos: 80
Status:Countdown Begins...
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE:Information Technology (Consulting)
Products:
My Reviews
Schools: IIMB
GMAT 1: 580 Q48 V22
Posts: 237
Kudos: 170
 []
A Circle, with its radius an integer, is inscribed in a square. 18 Jul 2017, 02:00
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
darn
How is statement A sufficient?

Question says circle's radius is an integer. Now the side of square is 2*radius. So the side is an even number.

If, the side is a prime number, then the side must be 2. Because 2 is the only even prime number and hence radius must be 1.

Hope this helps..
avatar
Meechampolee
avatar
Joined: 02 May 2016
Last visit: 16 Feb 2020
Posts: 17
Own Kudos:
8
Given Kudos: 20
Location: Nigeria
Concentration: Strategy, Entrepreneurship
Schools: HBS '19 Boston U '19 (WL) Rotman '20 (A) ISB '19 (A$) HHL Leipzig"20 (A$)
GMAT 1: 590 Q43 V28
GPA: 3.52
WE:Operations (Retail Banking)
Schools: HBS '19 Boston U '19 (WL) Rotman '20 (A) ISB '19 (A$) HHL Leipzig"20 (A$)
GMAT 1: 590 Q43 V28
Posts: 17
Kudos: 8
A Circle, with its radius an integer, is inscribed in a square. 19 Jul 2017, 09:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel please help with a detailed explanation.

Regards
avatar
mcm2112
avatar
Joined: 18 Aug 2015
Last visit: 05 Nov 2018
Posts: 16
Own Kudos:
3
Given Kudos: 9
Location: United States
GPA: 3.38
Posts: 16
Kudos: 3
A Circle, with its radius an integer, is inscribed in a square. 19 Jul 2017, 11:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I am a bit confused why you would need a statement to figure this out at all.

If the circle is in the square, then we have the area of the square and the triangle.

Circle = x2
Triangle = π(1/2)x2

Let's say x=2 Ac=4 At=3.14

Probability =.86/2

Does that seam right?
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 13 Dec 2024
Posts: 4,126
Own Kudos:
9,925
Given Kudos: 97
 Q51  V47
Expert reply
Posts: 4,126
Kudos: 9,925
A Circle, with its radius an integer, is inscribed in a square. 19 Jul 2017, 12:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
RMD007
A Circle, with its radius an integer, is inscribed in a square. What is the probability that a point randomly chosen inside the square will lie outside the circle?

1. Side of the square is a prime number.

2. Another square inscribed in the circle has side \(\sqrt{2}\)

You don't need any statements to answer the question. The area of the circle is π r^2, and the area of the square is (2r)^2 = 4r^2, since the diameter of the circle is equal in length to a side of the square, if the circle is inscribed in the square. To find the probability a point chosen randomly from within the square is inside the circle, we just work out what fraction of square the circle takes up - we divide the area of the circle by the area of the square. So a random point in the square is also in the circle with probability π*r^2 / 4*r^2 = π/4, and the probability that point is not in the circle is thus 1 - (π/4). The length of the radius doesn't matter.

edit - had included another comment, but misread statement 2 :)
User avatar
rekhabishop
User avatar
Joined: 22 Sep 2016
Last visit: 18 May 2018
Posts: 132
Own Kudos:
70
Given Kudos: 42
Location: India
Schools: Degroote McMaster"19 (A$) HBS '20 (D) Stanford '20 (D) Wharton '20 (D) Booth '20 (D) Kellogg '20 Haas '20
GMAT 1: 710 Q50 V35
GPA: 4
Schools: Degroote McMaster"19 (A$) HBS '20 (D) Stanford '20 (D) Wharton '20 (D) Booth '20 (D) Kellogg '20 Haas '20
GMAT 1: 710 Q50 V35
Posts: 132
Kudos: 70
A Circle, with its radius an integer, is inscribed in a square. 02 Aug 2017, 02:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
RMD007
A Circle, with its radius an integer, is inscribed in a square. What is the probability that a point randomly chosen inside the square will lie outside the circle?

1. Side of the square is a prime number.

2. Another square inscribed in the circle has side \(\sqrt{2}\)

Source : Self-made. :)

If a circle is inscribed in a square, is it mandatory for the circle to touch the sides of the square? Shouldn't this be mentioned?

This way, the answer should be E.
avatar
vineet6316
avatar
Joined: 15 Oct 2016
Last visit: 01 Sep 2022
Posts: 20
Own Kudos:
29
Given Kudos: 9
Posts: 20
Kudos: 29
A Circle, with its radius an integer, is inscribed in a square. 02 Aug 2017, 04:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
RMD007
A Circle, with its radius an integer, is inscribed in a square. What is the probability that a point randomly chosen inside the square will lie outside the circle?

1. Side of the square is a prime number.

2. Another square inscribed in the circle has side \(\sqrt{2}\)

Source : Self-made. :)

The original problem statement is good enough to answer this question. We do not need the 2 statements at all, because in such a symmetric arrangement all the peripherial lengths will be proportionate to each other.

The required probability = 1 - Probability that the point will lie both inside the square and the circle = 1 - pi*r^2/(2r)^2= 1 - pi/4 = 0.215
User avatar
sahilvijay
User avatar
Joined: 29 Jun 2017
Last visit: 16 Apr 2021
Posts: 305
Own Kudos:
847
Given Kudos: 76
GPA: 4
WE:Engineering (Transportation)
Products:
My Reviews
Posts: 305
Kudos: 847
A Circle, with its radius an integer, is inscribed in a square. 07 Sep 2017, 02:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1) Side of square is prime
Clearly side = a ( prime ) which is = 2r as circle is inscribed

P( reqd) = {a^2 - (πa^2)/4 }/a^2
=> (4-π)/4
Definite Ans A/D

2) A square is again inscribed in circle of side √2
=> radius =√(2+2) = 2
and side =4
again P reqd = ( 4x4- π4 )/16
p(reqd) = (4-π)/4
So D is the Answer

Bunuel
HOWEVER QUES SHOULD CLEARLY SPECIFY THAT WE HAVE TO TAKE A POINT INSIDE OF FIRST SQUARE AND OUTSIDE OF CIRCLE.
THIS COULD BE MISUNDERSTOOD AS A POINT MAY BE TAKEN INSIDE OF THE INNER SQUARE THEN ANS WOULD HAVE BEEN DIFFERENT.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderators:
Bunuel
Math Expert
97881 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3116 posts
GMATBusters
GMAT Tutor
1930 posts