Last visit was: 24 Jul 2024, 11:30 It is currently 24 Jul 2024, 11:30
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
SORT BY:
Date
Tags:
Difficulty: Sub 505 Level,   Geometry,                           
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94607
Own Kudos [?]: 643594 [36]
Given Kudos: 86737
Send PM
Most Helpful Reply
Retired Moderator
Joined: 08 Dec 2013
Status:Greatness begins beyond your comfort zone
Posts: 2091
Own Kudos [?]: 8992 [10]
Given Kudos: 171
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
Send PM
Manager
Manager
Joined: 04 May 2014
Status:One Last Shot !!!
Posts: 195
Own Kudos [?]: 627 [6]
Given Kudos: 141
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32
GMAT 2: 680 Q47 V35
Send PM
General Discussion
Current Student
Joined: 13 Apr 2015
Posts: 1426
Own Kudos [?]: 4603 [0]
Given Kudos: 1228
Location: India
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Area of circumscribed circle = (pi/2)*Area of square
Area of square = (2/pi)*Area of circumscribed circle.
So St1 is sufficient.

St2: 2*pi*r = 16*pi --> r = 8... Area of circle can be found out.
St2: Sufficient.

Answer: D
User avatar
Intern
Intern
Joined: 29 Aug 2013
Posts: 24
Own Kudos [?]: 3 [0]
Given Kudos: 51
GMAT 1: 560 Q41 V25
WE:Consulting (Consulting)
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Once you find the diameter [d = 16] of circle, you can find the side [s] of a square using the relation:

d = s * sq.root(2)

s = 16/sq.root(2)
avatar
Manager
Manager
Joined: 02 Jul 2015
Posts: 90
Own Kudos [?]: 46 [0]
Given Kudos: 59
Schools: ISB '18
GMAT 1: 680 Q49 V33
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Answer is D as the diameter of circle is the diagonal of the square.
User avatar
Intern
Intern
Joined: 14 Mar 2015
Posts: 27
Own Kudos [?]: 29 [0]
Given Kudos: 11
Schools: ISB '18
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.



Since, square ABCD is inscribed in the circle, the only way that is possible is when the diagonal of the square is equal to the diameter of the circle.
AB\(\sqrt{2}\) = diameter of circle = 2r

1) Area of O is 64π, i.e. \(πr^2\) = 64π.
From this we can find the radius of the circle, thus determine the diameter and thereby we can deduce the area of the square ABCD.

2) Circumference of O is 16π, i.e. 2πr = 16π.
From this we deduce radius, r and finally the area of square ABCD.
avatar
Manager
Manager
Joined: 02 Jun 2015
Posts: 58
Own Kudos [?]: 41 [1]
Given Kudos: 27
Location: United States
Concentration: Strategy, Human Resources
WE:Engineering (Manufacturing)
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
1
Kudos
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.



Using Formula :-

Area of a circumscribed circle = 1.57 * Area of the square

St 1 - Sufficient
St 2 - Sufficient as C of cricle we can apply the above formula easily by calculating the area of circle

Answer D
User avatar
Retired Moderator
Joined: 29 Apr 2015
Posts: 717
Own Kudos [?]: 4237 [1]
Given Kudos: 302
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE:Asset Management (Investment Banking)
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
1
Bookmarks
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.


Draw the circle and inscribe a square to see that: The radius of the circle is half of the square's diagonal and hence all you need to to know is the radius from the circle in order to calculate the area of the square.

Area of a square can be calculated as \(\frac{D^2}{2}\)

Statement 1: From this we can calculate the radius since r^2π=64π, therefore r = 8
Statement 2: From this we can too, calculate the radius 2rπ = 16π, therefore 2r=16, r = 8

From both statements we can calculate the diagonal = 16 (=2*r) and hence the area of the square.

Answer D.
Intern
Intern
Joined: 10 Aug 2015
Posts: 20
Own Kudos [?]: 56 [0]
Given Kudos: 232
Location: India
GMAT 1: 700 Q48 V38
GPA: 3.5
WE:Consulting (Computer Software)
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.


There is nothing to solve here.
We know ABCD is inscribed so its vertices are on the circle and the diagonal is the diameter of the circle.
Once we know the diameter of circle we can find the area = D1*D2/2. here diagonal 1=diagonal 2 because both are diameter of circle and diagonal of a square.
1. we can find the diameter from area.
2. we can find the diameter from circumference.

So Answer is D
Senior Manager
Senior Manager
Joined: 04 Jun 2016
Posts: 482
Own Kudos [?]: 2366 [0]
Given Kudos: 36
GMAT 1: 750 Q49 V43
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.


The area of any square is also given by the formula \(\frac{diagonal^2}{2}\)
In a square inscribed inside a circle the diagonal becomes equal to the diameter
SO if we can figure out the radius we can double it to find the diameter and hence the diagonal of the square and finally the area

Option 1 ) gives us the area ; radius can be calculated easily ; SUFFICIENT
Option 2) gives us the circumference ; again radius be calculated easily; SUFFICIENT

ANSWER IS D
Senior Manager
Senior Manager
Joined: 04 Jun 2016
Posts: 482
Own Kudos [?]: 2366 [0]
Given Kudos: 36
GMAT 1: 750 Q49 V43
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.


The area of any square is also given by the formula \(\frac{(diagonal^2)}{2}\)
In a square inscribed inside a circle, the diagonal of square is equal to the diameter of the circle
SO if we can figure out the radius we can double it to find the diameter and using diameter we can figure the area of Square by using \(\frac{(diagonal^2)}{2}\)

Option 1 ) gives us the area ; radius can be calculated easily ; SUFFICIENT
Option 2) gives us the circumference ; again radius be calculated easily; SUFFICIENT

ANSWER IS D
Mannheim Thread Master
Joined: 10 Feb 2017
Status:It's now or never
Posts: 129
Own Kudos [?]: 63 [0]
Given Kudos: 51
Location: India
GMAT 1: 650 Q40 V39
GPA: 3
WE:Consulting (Consulting)
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Thank you for the explanation. It helps.

I also wanted to know if Square inside a circle with corners touching the circle can also be an equilateral triangle?
Intern
Intern
Joined: 26 Mar 2018
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 10
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.



Bunuel, why should we assume the corners of the square touch the circle? It just says the square is inscribed, nothing about how the inscription is made. Maybe I'm just overthinking the wording, but it really bothers me it doesn't specifically say "Sqaure ABCD inscribed in circle O with corners of sqaure touching the outside of the circle.
Math Expert
Joined: 02 Sep 2009
Posts: 94607
Own Kudos [?]: 643594 [0]
Given Kudos: 86737
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Expert Reply
ahawkins wrote:
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.



Bunuel, why should we assume the corners of the square touch the circle? It just says the square is inscribed, nothing about how the inscription is made. Maybe I'm just overthinking the wording, but it really bothers me it doesn't specifically say "Sqaure ABCD inscribed in circle O with corners of sqaure touching the outside of the circle.


In geometry "inscribed" means drawing one shape inside another so that it just touches. It does not mean just inside.
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6031
Own Kudos [?]: 13825 [2]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
2
Kudos
Expert Reply
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.


Wanna make solving the Official Questions interesting???


Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course


Answer: Option D

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub :)
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19191
Own Kudos [?]: 22715 [2]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
1
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:
Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.
(2) The circumference of circle O is 16π.


Kudos for a correct solution.

Solution:

Question Stem Analysis:

We need to determine the area of square region ABCD, which is inscribed in circle O. Recall that the diameter of a circle is the diagonal of its inscribed square. Therefore, if we can determine the radius (and hence the diameter) of the circle, then we can determine the diagonal (and hence the side and area) of the inscribed square.

Statement One Alone:

Since we are given the area of the circle, we can determine its radius, and hence we can determine the area of the inscribed square. Statement one alone is sufficient.

Statement Two Alone:

Since we are given the circumference of the circle, we can determine its radius, and hence we can determine the area of the inscribed square. Statement two alone is sufficient.

Answer: D
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 1749 [1]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
1
Kudos
Expert Reply
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34067
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
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: Square ABCD is inscribed in circle O. What is the area of square regio [#permalink]
Moderator:
Math Expert
94607 posts