NEW HERE? LEARN MORE
closeclose
Last visit was: 09 May 2024, 04:33 It is currently 09 May 2024, 04:33
Decision Tracker
My Rewards
New posts
New comers' posts

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

If a circle is inscribed in a square as shown above, is the area of th

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93119
Own Kudos [?]: 622366 [0]
Given Kudos: 81810
Send PM
CAT Tests Forum Quiz Mode
If a circle is inscribed in a square as shown above, is the area of th [#permalink] New post   13 Sep 2018, 02:23
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

54% (02:07) correct 46% (01:35) wrong based on 52 sessions
Hide Show timer Statistics

If a circle is inscribed in a square as shown above, is the area of the circle greater than 16π?

(1) The area of the square is greater than16.
(2) Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.


Show Spoiler
Attachment:
image014.gif
image014.gif [ 782 Bytes | Viewed 1230 times ]
ShowHide Answer
Official Answer
B
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5974
Own Kudos [?]: 13457 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge Forum Quiz Mode
If a circle is inscribed in a square as shown above, is the area of th [#permalink] New post   13 Sep 2018, 03:50
Expert Reply
Bunuel wrote:

If a circle is inscribed in a square as shown above, is the area of the circle greater than 16π?

(1) The area of the square is greater than16.
(2) Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.


Show Spoiler
Attachment:
image014.gif


Question: Is area of circle > 16π?
Question: Is Radius of circle > 4?
Question: Is Side of the square > 8?

Statement 1: The area of the square is greater than16.
i.e. side of square > 4
but it may or may not be greater than 8 hence
NOT SUFFICIENT

Statement 2: Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.
i.e. \((1/4[(2r)^2 - πr^2] = 9 - (9/4)π\)
i.e. r = 3
i.e. r is NOT greater than 4 hence

SUFFICIENT

Answer: option B
avatar
B
rajamech
Intern
Intern
Joined: 06 Feb 2017
Posts: 31
Own Kudos [?]: 25 [0]
Given Kudos: 5
Location: India
Schools: HBS '22 HEC '22
GMAT 1: 570 Q39 V28
GMAT 2: 620 Q49 V26
GPA: 4
Send PM
Re: If a circle is inscribed in a square as shown above, is the area of th [#permalink] New post   13 Sep 2018, 03:55
Answer is B
By the first statement, we can say that the area of circle will be minimum 4*Pie i.e., approx 12 but it can also be greater than 16. Hence Insufficient.
By the second statement, we will get a specific value of radius. Hence sufficient.
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8024
Own Kudos [?]: 4118 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User
Re: If a circle is inscribed in a square as shown above, is the area of th [#permalink] New post   13 Sep 2018, 03:58
GMATinsight:

Statement 2: Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.
i.e. (1/4[(2r)2−πr2]=9−(9/4)π(1/4[(2r)2−πr2]=9−(9/4)π
i.e. r = 3
i.e. r is NOT greater than 4 hence

Hello, could you please explain statement 2:
LHS of i.e. (1/4[(2r)2−πr2]=9−(9/4)π

How did you arrive at it?
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5974
Own Kudos [?]: 13457 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge Forum Quiz Mode
Re: If a circle is inscribed in a square as shown above, is the area of th [#permalink] New post   13 Sep 2018, 04:09
1
Kudos
Expert Reply
archish3113 wrote:
GMATinsight:

Statement 2: Each of the four shaded regions between the square and the circle has an area equal to 9 – 9/4*π.
i.e. (1/4[(2r)2−πr2]=9−(9/4)π(1/4[(2r)2−πr2]=9−(9/4)π
i.e. r = 3
i.e. r is NOT greater than 4 hence

Hello, could you please explain statement 2:
LHS of i.e. (1/4[(2r)2−πr2]=9−(9/4)π

How did you arrive at it?


archish3113

One shaded portion at one of the corners = (1/4)*(Area of Square - Area of Circle) = \((1/4)*[(2r)^2−πr^2]=9−(9/4)π\)

Side of the square = 2r i.e. area of square = \((2r)^2\)

I hope this helps!!!

P.S. The Circle is inscribed in square i.e. Circle is tightly packed and touching all sides of teh square
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8024
Own Kudos [?]: 4118 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User
Re: If a circle is inscribed in a square as shown above, is the area of th [#permalink] New post   13 Sep 2018, 04:19
GMATinsight : understood where I was going wrong, thanks ...
GMAT Club Bot
gmatclubot
Re: If a circle is inscribed in a square as shown above, is the area of th [#permalink]
13 Sep 2018, 04:19
Moderator:
Bunuel
Math Expert
93119 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions