Last visit was: 21 Apr 2026, 09:15 It is currently 21 Apr 2026, 09:15
Home
Messages
Tests
Schools
Events
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
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 21 Apr 2026
Posts: 1,582
Own Kudos:
1,976
Given Kudos: 152
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,582
Kudos: 1,976
A circle of radius 4 cm is carved with a sharp knife into Updated on: 16 Jul 2006, 13:03
Originally posted by kevincan on 15 Jul 2006, 08:00.
Last edited by kevincan on 16 Jul 2006, 13:03, edited 3 times in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

History

Date
Time
Result
Not Attempted Yet
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the carved path of the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%



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 Problem Solving (PS) 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!
User avatar
Raghavender
User avatar
Joined: 11 Jan 2006
Last visit: 05 Nov 2013
Posts: 125
Own Kudos:
127
Given Kudos: 18
Location: Arkansas, US
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Posts: 125
Kudos: 127
A circle of radius 4 cm is carved with a sharp knife into 15 Jul 2006, 10:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hey...How can a square have a diameter of 100 cm..., DId i read it wrong...or I guess it;s a typo..

Cud u please clarify tht..
User avatar
ps_dahiya
User avatar
Joined: 20 Nov 2005
Last visit: 15 Oct 2019
Posts: 1,486
Own Kudos:
1,238
Concentration: Strategy, Entrepreneurship
Schools:Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Posts: 1,486
Kudos: 1,238
A circle of radius 4 cm is carved with a sharp knife into 15 Jul 2006, 16:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I am getting 43.5%, when we assume that the edge of circle and edge of square are atleast 4cm apart.

But if circle is carved on edge then the black painted area will be less and if carved on a corner then black painted area will be even least.

I think this is an ambiguous question.
User avatar
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 21 Apr 2026
Posts: 1,582
Own Kudos:
1,976
Given Kudos: 152
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,582
Kudos: 1,976
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 00:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Good work- the question has been corrected- the original version I came up with had concentric circles and thus avoided this possibility. Thanks!
User avatar
Raghavender
User avatar
Joined: 11 Jan 2006
Last visit: 05 Nov 2013
Posts: 125
Own Kudos:
127
Given Kudos: 18
Location: Arkansas, US
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Posts: 125
Kudos: 127
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 02:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ps_dahiya
I am getting 43.5%, when we assume that the edge of circle and edge of square are atleast 4cm apart.

But if circle is carved on edge then the black painted area will be less and if carved on a corner then black painted area will be even least.

I think this is an ambiguous question.
Show more



Hey Dahiya, wen it says, the painted area has to 2 b 2 cms from both edge of circle n edge of board, u have to subtract the area of a circle of radius 6 cms (2+ 4 cms radius) from the area of a square with side 21cms(25 cms is the boards side, cut 2 cms frm each side), the remainin part is the painted area..

Hope the explanation makes sense..plz..point out any loopholes
User avatar
Raghavender
User avatar
Joined: 11 Jan 2006
Last visit: 05 Nov 2013
Posts: 125
Own Kudos:
127
Given Kudos: 18
Location: Arkansas, US
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Posts: 125
Kudos: 127
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 07:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevincan
Not all the circle is painted black!
Show more


In my explanation, I subtract the area of the ciricle with radius 6, so im not paintin any part of the circle..does it make sense...
User avatar
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 21 Apr 2026
Posts: 1,582
Own Kudos:
1,976
Given Kudos: 152
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,582
Kudos: 1,976
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 07:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Raghavender
kevincan
Not all the circle is painted black!

In my explanation, I subtract the area of the ciricle with radius 6, so im not paintin any part of the circle..does it make sense...
Show more


But some of the circle is painted back
User avatar
Raghavender
User avatar
Joined: 11 Jan 2006
Last visit: 05 Nov 2013
Posts: 125
Own Kudos:
127
Given Kudos: 18
Location: Arkansas, US
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Posts: 125
Kudos: 127
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 07:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevincan
Raghavender
kevincan
Not all the circle is painted black!

In my explanation, I subtract the area of the ciricle with radius 6, so im not paintin any part of the circle..does it make sense...

But some of the circle is painted back
Show more


Hey mayb I missd something, but I cant c anywhere, where he implies that the circle is painted black...cud u plzz...help me out...

I read it like this...there is a square board, in which a circle is cut out. then in the remainin part of the board,(square with a hole) he paints some part...
User avatar
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 21 Apr 2026
Posts: 1,582
Own Kudos:
1,976
Given Kudos: 152
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,582
Kudos: 1,976
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 10:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The portion of the board that is within 2 cm of either the edge of the board or the circle is painted black
User avatar
old_dream_1976
User avatar
Joined: 09 Aug 2005
Last visit: 30 Nov 2006
Posts: 133
Own Kudos:
17
Posts: 133
Kudos: 17
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 12:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%
Show more



(20pi +184)/(625-16pi)

but the problem is how to approximate to arrive at the answer. % are too close .......

in the exam i would pick 43.5 and move on
User avatar
Raghavender
User avatar
Joined: 11 Jan 2006
Last visit: 05 Nov 2013
Posts: 125
Own Kudos:
127
Given Kudos: 18
Location: Arkansas, US
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Posts: 125
Kudos: 127
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 21:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hey old dream,

cud u plzz give ur explanation for ur sol:(20pi +184)/(625-16pi)
I did not get it clearly
User avatar
Zooroopa
User avatar
Joined: 09 Apr 2006
Last visit: 07 Sep 2008
Posts: 114
Own Kudos:
4
Location: Somewhere in Wisconsin!
Posts: 114
Kudos: 4
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 22:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
old_dream_1976
kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%


(20pi +184)/(625-16pi)

but the problem is how to approximate to arrive at the answer. % are too close .......

in the exam i would pick 43.5 and move on
Show more


When they say entire board, should we consider the original board i.e. area = 625 sq cm? So should we subtract 16Π from the denominator?
User avatar
ywilfred
User avatar
Joined: 07 Jul 2004
Last visit: 06 Mar 2012
Posts: 1,987
Own Kudos:
2,051
Location: Singapore
Posts: 1,987
Kudos: 2,051
A circle of radius 4 cm is carved with a sharp knife into 16 Jul 2006, 22:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Length of each side of the square = 100/4 = 25cm

The sum of the difference between the square of sides 25cm and 21 cm, and the difference between a circle of 12cm diameter and 8cm diameter will be the total area painted.

Painted area
= (25^2 - 21^2) + [(pi*6^2) - (pi*4^2)]
= 184 + 20pi

Percentage = (184 + 20pi)/25^2 * 100 = 39.5%
User avatar
Raghavender
User avatar
Joined: 11 Jan 2006
Last visit: 05 Nov 2013
Posts: 125
Own Kudos:
127
Given Kudos: 18
Location: Arkansas, US
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Posts: 125
Kudos: 127
A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 19:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
yup yup..ywilfred, now understood the solution..thanx
User avatar
MA
User avatar
Joined: 25 Nov 2004
Last visit: 09 Aug 2011
Posts: 695
Own Kudos:
533
Posts: 695
Kudos: 533
A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 21:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ywilfred
Length of each side of the square = 100/4 = 25cm

The sum of the difference between the square of sides 25cm and 21 cm, and the difference between a circle of 12cm diameter and 8cm diameter will be the total area painted.

Painted area
= (25^2 - 21^2) + [(pi*6^2) - (pi*4^2)]
= 184 + 20pi

Percentage = (184 + 20pi)/25^2 * 100 = 39.5%
Show more

ywilfred,

the question says "within" 2 cm of the carved path of the circle but you assumed outside the edge of the carved path.

shouldn't the Percentage be = (25^2 - 21^2) + [(pi*4^2) - (pi*2^2)] =
(184 + 12pi)/25^2 * 100

kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the carved path of the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%
Show more
User avatar
ywilfred
User avatar
Joined: 07 Jul 2004
Last visit: 06 Mar 2012
Posts: 1,987
Own Kudos:
2,051
Location: Singapore
Posts: 1,987
Kudos: 2,051
A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 21:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MA
ywilfred
Length of each side of the square = 100/4 = 25cm

The sum of the difference between the square of sides 25cm and 21 cm, and the difference between a circle of 12cm diameter and 8cm diameter will be the total area painted.

Painted area
= (25^2 - 21^2) + [(pi*6^2) - (pi*4^2)]
= 184 + 20pi

Percentage = (184 + 20pi)/25^2 * 100 = 39.5%

ywilfred,

the question says "within" 2 cm of the carved path of the circle but you assumed outside the edge of the carved path.

shouldn't the Percentage be = (25^2 - 21^2) + [(pi*4^2) - (pi*2^2)] =
(184 + 12pi)/25^2 * 100

kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the carved path of the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%
Show more


Hmm.... good point.. I took the meaning 'within 2cm' to be anywhere 2cm outside of the circle or inside the board.... but I think you can take it the other way round and say 2cm inside the circle and inside the board...
User avatar
MA
User avatar
Joined: 25 Nov 2004
Last visit: 09 Aug 2011
Posts: 695
Own Kudos:
533
Posts: 695
Kudos: 533
A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 21:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ywilfred
MA
ywilfred
Length of each side of the square = 100/4 = 25cm

The sum of the difference between the square of sides 25cm and 21 cm, and the difference between a circle of 12cm diameter and 8cm diameter will be the total area painted.

Painted area
= (25^2 - 21^2) + [(pi*6^2) - (pi*4^2)]
= 184 + 20pi

Percentage = (184 + 20pi)/25^2 * 100 = 39.5%

ywilfred,

the question says "within" 2 cm of the carved path of the circle but you assumed outside the edge of the carved path.

shouldn't the Percentage be = (25^2 - 21^2) + [(pi*4^2) - (pi*2^2)] =
(184 + 12pi)/25^2 * 100

kevincan
A circle of radius 4 cm is carved with a sharp knife into the middle of a square board that has a perimeter of 100cm. The portion of the board that is within 2 cm of either the edge of the board or the carved path of the circle is painted black. What percent of the entire board is painted black?

(A) 39.5% (B) 41.5% (C) 43.5% (D) 45.5% (E) 47.5%

Hmm.... good point.. I took the meaning 'within 2cm' to be anywhere 2cm outside of the circle or inside the board.... but I think you can take it the other way round and say 2cm inside the circle and inside the board...
Show more


seems the question is not properly structured. if we take the values as per the information provided, the prob will be below 39.5% (however i have not calculated anything), which is not the AC.

hope kevin will take care of it.
User avatar
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 21 Apr 2026
Posts: 1,582
Own Kudos:
1,976
Given Kudos: 152
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GRE 1: Q170 V170
Posts: 1,582
Kudos: 1,976
A circle of radius 4 cm is carved with a sharp knife into 17 Jul 2006, 23:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
No, the question is fine. What makes you say the percentage will be so low?
User avatar
MA
User avatar
Joined: 25 Nov 2004
Last visit: 09 Aug 2011
Posts: 695
Own Kudos:
533
Posts: 695
Kudos: 533
A circle of radius 4 cm is carved with a sharp knife into 18 Jul 2006, 06:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevincan
No, the question is fine. What makes you say the percentage will be so low?
Show more


if Painted area is 184 + 20pi, p = 39.5%.
if Painted area is 184 + 12pi, p = 35.47

imo, it should be 2nd one and in that case you need to update the ACs.



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 Problem Solving (PS) 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!
Moderator:
Bunuel
Math Expert
109729 posts