Practice GMAT Problem Solving 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
1. In this problem, let A be the event that a child picks up a blue flag, B be the event that a child picks up a red flag. Then, A∪B is the event that the child picks up either a blue or a red flag, and A∩B is the event that the child picks up both a blue and a red flag.
2. From the problem statement we know:
I. P(AUB) = 100% (Since there are even number of flags and all the flags in the box are taken by the children)
II. P(A) = 60%
III.P(B) = 55%
IV. P(A∩B)=?
3. We are trying to find the percentage of children who have flags of both the colors. Substituting the values from (3.) into the equation given in (1.) we get:
4. P(A∪B) = P(A) + P(B) - P(A∩B)
100% = 60% + 55% - P(A∩B)
P(A∩B) = (60% +55%)-100%
P(A∩B) =115%-100%
P(A∩B) =15%
Therefore the percentage of children who got both a red flag and a blue flag is 15%. Thus, C is the correct answer choice.