NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 15:26 It is currently 26 Apr 2024, 15:26
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

A circle of radius 4 cm is carved with a sharp knife into

User avatar
B
kevincan
GMAT Instructor
Joined: 04 Jul 2006
Posts: 960
Own Kudos [?]: 693 [0]
Given Kudos: 6
Location: Madrid
 Q51  V50
Send PM
A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   Updated on: 16 Jul 2006, 13:03
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Hide Show timer Statistics
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!

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.
User avatar
Raghavender
Manager
Manager
Joined: 11 Jan 2006
Posts: 125
Own Kudos [?]: 110 [0]
Given Kudos: 18
Location: Arkansas, US
 Q49  V40
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   15 Jul 2006, 10:00
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
VP
VP
Joined: 20 Nov 2005
Posts: 1490
Own Kudos [?]: 1133 [0]
Given Kudos: 0
Concentration: Strategy, Entrepreneurship
Schools:Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
 Q50  V34
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   15 Jul 2006, 16:39
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
B
kevincan
GMAT Instructor
Joined: 04 Jul 2006
Posts: 960
Own Kudos [?]: 693 [0]
Given Kudos: 6
Location: Madrid
 Q51  V50
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 00:15
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
Manager
Manager
Joined: 11 Jan 2006
Posts: 125
Own Kudos [?]: 110 [0]
Given Kudos: 18
Location: Arkansas, US
 Q49  V40
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 02:56
ps_dahiya wrote:
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.



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
Manager
Manager
Joined: 11 Jan 2006
Posts: 125
Own Kudos [?]: 110 [0]
Given Kudos: 18
Location: Arkansas, US
 Q49  V40
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 07:10
kevincan wrote:
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...
User avatar
B
kevincan
GMAT Instructor
Joined: 04 Jul 2006
Posts: 960
Own Kudos [?]: 693 [0]
Given Kudos: 6
Location: Madrid
 Q51  V50
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 07:15
Raghavender wrote:
kevincan wrote:
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
User avatar
Raghavender
Manager
Manager
Joined: 11 Jan 2006
Posts: 125
Own Kudos [?]: 110 [0]
Given Kudos: 18
Location: Arkansas, US
 Q49  V40
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 07:28
kevincan wrote:
Raghavender wrote:
kevincan wrote:
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


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
B
kevincan
GMAT Instructor
Joined: 04 Jul 2006
Posts: 960
Own Kudos [?]: 693 [0]
Given Kudos: 6
Location: Madrid
 Q51  V50
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 10:32
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
Manager
Manager
Joined: 09 Aug 2005
Posts: 134
Own Kudos [?]: 17 [0]
Given Kudos: 0
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 12:38
kevincan wrote:
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
User avatar
Raghavender
Manager
Manager
Joined: 11 Jan 2006
Posts: 125
Own Kudos [?]: 110 [0]
Given Kudos: 18
Location: Arkansas, US
 Q49  V40
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 21:39
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
Manager
Manager
Joined: 09 Apr 2006
Posts: 114
Own Kudos [?]: 4 [0]
Given Kudos: 0
Location: Somewhere in Wisconsin!
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 22:00
old_dream_1976 wrote:
kevincan wrote:
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


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
SVP
SVP
Joined: 07 Jul 2004
Posts: 2004
Own Kudos [?]: 1900 [0]
Given Kudos: 0
Location: Singapore
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   16 Jul 2006, 22:11
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
Manager
Manager
Joined: 11 Jan 2006
Posts: 125
Own Kudos [?]: 110 [0]
Given Kudos: 18
Location: Arkansas, US
 Q49  V40
GPA: 3.3
WE 1: 2.5 yrs in manufacturing
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   17 Jul 2006, 19:43
yup yup..ywilfred, now understood the solution..thanx
User avatar
MA
Director
Director
Joined: 25 Nov 2004
Posts: 707
Own Kudos [?]: 449 [0]
Given Kudos: 0
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   17 Jul 2006, 21:30
ywilfred wrote:
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 wrote:
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%
User avatar
ywilfred
SVP
SVP
Joined: 07 Jul 2004
Posts: 2004
Own Kudos [?]: 1900 [0]
Given Kudos: 0
Location: Singapore
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   17 Jul 2006, 21:53
MA wrote:
ywilfred wrote:
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 wrote:
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...
User avatar
MA
Director
Director
Joined: 25 Nov 2004
Posts: 707
Own Kudos [?]: 449 [0]
Given Kudos: 0
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   17 Jul 2006, 21:56
ywilfred wrote:
MA wrote:
ywilfred wrote:
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 wrote:
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...


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
B
kevincan
GMAT Instructor
Joined: 04 Jul 2006
Posts: 960
Own Kudos [?]: 693 [0]
Given Kudos: 6
Location: Madrid
 Q51  V50
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   17 Jul 2006, 23:52
No, the question is fine. What makes you say the percentage will be so low?
User avatar
MA
Director
Director
Joined: 25 Nov 2004
Posts: 707
Own Kudos [?]: 449 [0]
Given Kudos: 0
Send PM
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink] New post   18 Jul 2006, 06:33
kevincan wrote:
No, the question is fine. What makes you say the percentage will be so low?


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!
GMAT Club Bot
gmatclubot
Re: A circle of radius 4 cm is carved with a sharp knife into [#permalink]
18 Jul 2006, 06:33
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 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