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# A box contains either blue or red flags. The total number of flags in

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Manager
Joined: 03 Aug 2010
Posts: 98
GMAT Date: 08-08-2011
A box contains either blue or red flags. The total number of flags in  [#permalink]

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28 Mar 2011, 19:19
3
00:00

Difficulty:

15% (low)

Question Stats:

82% (00:59) correct 18% (00:33) wrong based on 56 sessions

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A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?

A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined
Director
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Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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28 Mar 2011, 19:33
1
60+55=115% hence the overlap is 115-100=15% answer C

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Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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28 Mar 2011, 20:08
Yalephd wrote:
A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?

A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined

Is is just me or is this question flawed?

Why do think that this question is flawed?

Let there be 100 children
Number of children with Blue Flag $$= n(B) = 60$$
Number of children with Red Flag $$= n(R) = 55$$
Number of children with either Red or Blue Flag $$= n(R \cup B) = 100$$
Number of children with both Red & Blue Flag $$= n(R \cap B) = ?$$

$$n(R \cup B) = n(B) + n(R) - n(R \cap B)$$

$$n(R \cap B) = n(B) + n(R) - n(R \cup B)$$

$$n(R \cap B) = 60 + 55 - 100 = 15$$

Ans: "C"
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GMAT Date: 08-08-2011
Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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29 Mar 2011, 04:24
I didn't read the question correctly. At first I didn't think that there had to be any overlap, but now that I see that 60% + 55% is greater than 100%, and there has to be overlap. I was thinking of 60 and 55 as real numbers and not as percents. This is now a very easy question in hingsight.
Thanks, fluke and gmat1220

fluke wrote:
Yalephd wrote:
A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?

A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined

Is is just me or is this question flawed?

Why do think that this question is flawed?

Let there be 100 children
Number of children with Blue Flag $$= n(B) = 60$$
Number of children with Red Flag $$= n(R) = 55$$
Number of children with either Red or Blue Flag $$= n(R \cup B) = 100$$
Number of children with both Red & Blue Flag $$= n(R \cap B) = ?$$

$$n(R \cup B) = n(B) + n(R) - n(R \cap B)$$

$$n(R \cap B) = n(B) + n(R) - n(R \cup B)$$

$$n(R \cap B) = 60 + 55 - 100 = 15$$

Ans: "C"
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A box contains either blue or red flags. The total number of flags in  [#permalink]

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29 Mar 2011, 17:42
Yalephd wrote:
A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?

A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined

Is is just me or is this question flawed?

When I read this question, I double checked to ensure that it actually is as simple as it seemed. It wasn't a probability question at all (even though, when I started reading it, it looked like a probability question) It was straight forward overlapping sets. The 'number of flags is an even number' is just there to distract you. If each child picked 2 flags and the box got emptied, the number of flag has to be an even number!
This does happen quite often in GMAT. The basic concepts remain the same but the presentation changes a little pumping the level of the question up by 50-100 points.
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Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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30 Mar 2011, 12:23
Yalephd wrote:
Karishma, that's what threw me off, too. I was confused between approaching this as probability question versus as an overlapping sets problem. Thanks for posting Brian's post. Brian is awesome. I also just took a course with David Newland.

Yes, it does start off as a prob question would but it changes tracks mid way. Anyway, all for the better since it turns out to be on sets which are generally straight forward (GMAT context)
I have heard some very good things about David though I haven't got a chance to meet him yet. I have met Brian a couple of times (He is a Michigan guy too!) and he is hilarious. It was fun talking to him and he loves telling these stories, all of them with a lesson for GMAT! I am sure his classes are fun too.
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Manager
Joined: 20 Nov 2010
Posts: 157
A box contains either blue or red flags. The total number of flags in  [#permalink]

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20 Aug 2011, 02:13
A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?

A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined
_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MGMAT 6 650 (51,31) on 31/8/11
MGMAT 1 670 (48,33) on 04/9/11
MGMAT 2 670 (47,34) on 07/9/11
MGMAT 3 680 (47,35) on 18/9/11
GMAT Prep1 680 ( 50, 31) on 10/11/11

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Intern
Joined: 26 Jul 2011
Posts: 22
Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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20 Aug 2011, 02:31
The ans is C = 15%

Solution: let the total number of flags be 100(even number)

let the total number of 'blue' flags alone be 'a'
let the total number of 'red' flags alone be 'b'
let the total number of 'both' flags be 'c'

We have given,
total number of blue flags = 60% = 60 = a+c
total number of red flags=55%=55=b+c
total number of flags = a+b+c=100 (since all the flage have been utlized)

So, substituting for c in the third equation, we have,
60-c+c+55-c=100
c=15

Option C.

If the above solution looks a bit confusing, try to interpret using Venn diagram. The picture will be more clear.
Manager
Joined: 19 Jul 2011
Posts: 91
Concentration: Finance, Economics
Schools: Duke '15
GPA: 3.9
Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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20 Aug 2011, 02:33
60 + 55 = 115 -100 = 15

C
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Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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20 Aug 2011, 02:40
+1 for C.

I have a question though. How does below statement affect the solution?
catfreak wrote:
The total number of flags in the box is an even number.

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Manager
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Concentration: Finance, Economics
Schools: Duke '15
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Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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20 Aug 2011, 02:48
It has no effect, it is simply there to complicate the answer adding another layer to the problem and thus increasing the difficulty.
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Manager
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Posts: 157
Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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20 Aug 2011, 06:44
I posted this problem because i have a doubt.
Since its not mentioned in the problem that every children got two flags each instead its mentioned that all the flags are used in the process so how can we calculate the %age of children who got flags of both colors.
What i want to say is that there might be children who didn't get any flags and we don't know their number.
_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MGMAT 6 650 (51,31) on 31/8/11
MGMAT 1 670 (48,33) on 04/9/11
MGMAT 2 670 (47,34) on 07/9/11
MGMAT 3 680 (47,35) on 18/9/11
GMAT Prep1 680 ( 50, 31) on 10/11/11

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Manager
Joined: 20 Nov 2010
Posts: 157
Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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Updated on: 20 Aug 2011, 06:49
This has an effect on the solution as each of the children is supposed to pick two flags and every children will have two flags in case the number of flags are even.
In other words, it is to ensure that there is no child with just one flag.

+1 for C.

I have a question though. How does below statement affect the solution?
catfreak wrote:
The total number of flags in the box is an even number.

_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MGMAT 6 650 (51,31) on 31/8/11
MGMAT 1 670 (48,33) on 04/9/11
MGMAT 2 670 (47,34) on 07/9/11
MGMAT 3 680 (47,35) on 18/9/11
GMAT Prep1 680 ( 50, 31) on 10/11/11

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Originally posted by catfreak on 20 Aug 2011, 06:46.
Last edited by catfreak on 20 Aug 2011, 06:49, edited 1 time in total.
Manager
Joined: 20 Nov 2010
Posts: 157
Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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20 Aug 2011, 06:48
Its total number of children with blue flags and not total number of flags.
You might want to reread the question.

vishal4584 wrote:
The ans is C = 15%

Solution: let the total number of flags be 100(even number)

let the total number of 'blue' flags alone be 'a'
let the total number of 'red' flags alone be 'b'
let the total number of 'both' flags be 'c'

We have given,
total number of blue flags = 60% = 60 = a+c
total number of red flags=55%=55=b+c
total number of flags = a+b+c=100 (since all the flage have been utlized)

So, substituting for c in the third equation, we have,
60-c+c+55-c=100
c=15

Option C.

If the above solution looks a bit confusing, try to interpret using Venn diagram. The picture will be more clear.

_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MGMAT 6 650 (51,31) on 31/8/11
MGMAT 1 670 (48,33) on 04/9/11
MGMAT 2 670 (47,34) on 07/9/11
MGMAT 3 680 (47,35) on 18/9/11
GMAT Prep1 680 ( 50, 31) on 10/11/11

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Director
Joined: 01 Feb 2011
Posts: 664
Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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20 Aug 2011, 11:23
= 60+55-100

= 15%

Director
Joined: 27 May 2012
Posts: 604
Re: A box contains either blue or red flags. The total number of flags in  [#permalink]

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13 Sep 2018, 05:45
Yalephd wrote:
A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors?

A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined

Dear Moderator,
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Re: A box contains either blue or red flags. The total number of flags in &nbs [#permalink] 13 Sep 2018, 05:45
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