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

Question

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?

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

gmat1220 · Answer

60+55=115% hence the overlap is 115-100=15% answer C

Posted from my mobile device

fluke · Answer

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"

Yalephd · Answer

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

KarishmaB · Answer

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.

KarishmaB · Answer

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.

catfreak · Answer

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?

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

vishal4584 · Answer

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.

nammers · Answer

Question is about overlapping sets
60 + 55 = 115 -100 = 15

C

jamifahad · Answer

+1 for C.

I have a question though. How does below statement affect the solution?

nammers · Answer

It has no effect, it is simply there to complicate the answer adding another layer to the problem and thus increasing the difficulty.

catfreak · Answer

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.

catfreak · Answer

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.

catfreak · Answer

Its total number of children with blue flags and not total number of flags. 
You might want to reread the question.

Spidy001 · Answer

= 60+55-100

= 15%

Answer is C.

stne · Answer

Dear Moderator, 
Please untag probability. Thank you.

bumpbot · Answer

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

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