In a certain city each of 15 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)	Options:
A) 3	B) 4	C) 6	D) 5	E) 7
D.5:   if we have 5 colors we can choose pairs in 5C2 ways = 10 and single color flags are 5. Therefore total number of flags = 15.   ANS 5.
<result>D</result>
In a certain city each of 15 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)