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# Challenge If each of the 20 bolts of fabric on a shelf is

Author Message
Intern
Joined: 30 Mar 2006
Posts: 26
Location: New Jersey
Challenge If each of the 20 bolts of fabric on a shelf is  [#permalink]

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05 May 2006, 11:10
5. Challenge

If each of the 20 bolts of fabric on a shelf is either 100 percent cotton, 100 percent wool, or a mixture of cotton and wool, how many bolts are cotton and wool mixtures?

(1) Of the 20 bolts, 18 contian some wool and 14 contain some cotton

(2) Of the 20 bolts, 6 are 100% wool.

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Andre Crompton
andre.crompton@cit.com

Intern
Joined: 30 Mar 2006
Posts: 26
Location: New Jersey

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05 May 2006, 11:23
5. Challenge

If each of the 20 bolts of fabric on a shelf is either 100 percent cotton, 100 percent wool, or a mixture of cotton and wool, how many bolts are cotton and wool mixtures?

(1) Of the 20 bolts, 18 contian some wool and 14 contain some cotton

(2) Of the 20 bolts, 6 are 100% wool.

Figured it out the answer is "a"

x=cotton
y= wool
z= mix

x+y+z= 20
y+z= 18
x+z= 14

you can solve the first equation x=2 then subsitute into the 3rd equation.
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Andre Crompton
andre.crompton@cit.com

VP
Joined: 29 Dec 2005
Posts: 1288

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13 May 2006, 20:08
andrecrompton wrote:
Quote:
If each of the 20 bolts of fabric on a shelf is either 100 percent cotton, 100 percent wool, or a mixture of cotton and wool, how many bolts are cotton and wool mixtures?
(1) Of the 20 bolts, 18 contian some wool and 14 contain some cotton
(2) Of the 20 bolts, 6 are 100% wool.

Figured it out the answer is "a"
x=cotton
y= wool
z= mix
x+y+z= 20
y+z= 18
x+z= 14
you can solve the first equation x=2 then subsitute into the 3rd equation.

i think the information given 1 is not clear however the question is clear.
first if 18 contain some some wool means the same 18 also contain rest cotton. the applies with 14. ok, agreed that 14 are included in 18 but what about the 6's. what are they? r they all wool or cotton? they all cannot be wool cuz it says they contain some wool and some doesnot implies all. so this is so convulated statement.

suppose if 18 contains some wool, that means the same 18 must contain rest cotton. then rest 2 could all wool or cotton or 1 cotton and 1 wool..........

imo, not a good question...
guys, lets have more discussions.
Senior Manager
Joined: 08 Jun 2004
Posts: 473
Location: Europe

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13 May 2006, 21:02
As I understand this question - word 'some' means eather part or whole of bolt consists of wool or cotton.
Could we apply Venn diagram to his one?
From 1) 20=18+14-both, both=12
So A is sufficient.
Intern
Joined: 10 Jan 2006
Posts: 25

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13 May 2006, 21:07
Professor wrote:
andrecrompton wrote:
Quote:
If each of the 20 bolts of fabric on a shelf is either 100 percent cotton, 100 percent wool, or a mixture of cotton and wool, how many bolts are cotton and wool mixtures?
(1) Of the 20 bolts, 18 contian some wool and 14 contain some cotton
(2) Of the 20 bolts, 6 are 100% wool.

Figured it out the answer is "a"
x=cotton
y= wool
z= mix
x+y+z= 20
y+z= 18
x+z= 14
you can solve the first equation x=2 then subsitute into the 3rd equation.

i think the information given 1 is not clear however the question is clear.
first if 18 contain some some wool means the same 18 also contain rest cotton. the applies with 14. ok, agreed that 14 are included in 18 but what about the 6's. what are they? r they all wool or cotton? they all cannot be wool cuz it says they contain some wool and some doesnot implies all. so this is so convulated statement.

suppose if 18 contains some wool, that means the same 18 must contain rest cotton. then rest 2 could all wool or cotton or 1 cotton and 1 wool..........

imo, not a good question...
guys, lets have more discussions.

I think 18 contains some wool implies each of the 18 bolts contains some wool. Might be all wool or some wool. Thats the only thing that makes sense but not correctly worded.

Given that its quite simple.

using set theory A + B - AB = U

i.e 18 + 14 - AB = 20

Therefore 32-AB = 20 i.e AB = 12.
Director
Joined: 16 Aug 2005
Posts: 915
Location: France

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14 May 2006, 03:14
1

From (1), if 18 contain some wool then 2 are only cotton. Then if 14 contain some cotton then 6 are only wool. From here we know 12 are a mixture of cotton and wool.

(2) Insufficient
Director
Joined: 16 Aug 2005
Posts: 915
Location: France

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14 May 2006, 03:15
Yurik79 wrote:
I ll go with E

Also, what is OA?
VP
Joined: 29 Dec 2005
Posts: 1288

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14 May 2006, 05:35
gmatmba wrote:

From (1), if 18 contain some wool then 2 are only cotton. Then if 14 contain some cotton then 6 are only wool. From here we know 12 are a mixture of cotton and wool.

(2) Insufficient

if 18 contain some wool, the same 18 also contain some cotton. then how 12 or 14 can contain some cotton??????
Senior Manager
Joined: 08 Jun 2004
Posts: 473
Location: Europe

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14 May 2006, 11:29
Professor wrote:
gmatmba wrote:

From (1), if 18 contain some wool then 2 are only cotton. Then if 14 contain some cotton then 6 are only wool. From here we know 12 are a mixture of cotton and wool.

(2) Insufficient

if 18 contain some wool, the same 18 also contain some cotton. then how 12 or 14 can contain some cotton??????

Prof, question is unclear, in my opinion word 'some' means either part or whole of bolt consists of wool or cotton - either it wool/cotton or 100% wool or 100% cotton. Look up at my answer.
Director
Joined: 16 Aug 2005
Posts: 915
Location: France

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14 May 2006, 12:26
Prof, this is basically a venn diagram type question, like M8 said here some means "either part or whole". I think the OA should confirm whether I am right or wrong...

do we have an OA?
Manager
Joined: 05 Jan 2006
Posts: 66

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16 May 2006, 10:51
gmatmba-
i solved this using the venn diagram method and got A also.

II: Is insufficient because you don't know how many bolts are 100% cotton.
Intern
Joined: 15 May 2006
Posts: 3

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18 May 2006, 06:51
gmatmba wrote:

From (1), if 18 contain some wool then 2 are only cotton. Then if 14 contain some cotton then 6 are only wool. From here we know 12 are a mixture of cotton and wool.

(2) Insufficient

Its not clear, the question is badly worded. Ofcourse its not hard to figure out the answer is A but still the question can be better worded.
CEO
Joined: 20 Nov 2005
Posts: 2781
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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18 May 2006, 08:17
A

Seems simple.

Mixture = x

100% wool + x = 18 = y
100% connton + x = 14 = z

Total = y+z -x = 18+14-x = 20

So x = 12
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Manager
Joined: 28 Mar 2006
Posts: 145

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18 May 2006, 08:26
Agree with M8.....Nice explanation

M8 wrote:
As I understand this question - word 'some' means eather part or whole of bolt consists of wool or cotton.
Could we apply Venn diagram to his one?
From 1) 20=18+14-both, both=12
So A is sufficient.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Non-Human User
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Posts: 9128
Re: Challenge If each of the 20 bolts of fabric on a shelf is  [#permalink]

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11 Aug 2018, 03:56
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