Colour

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Feb 10, 2010 10:40 am

Four circles having radius 1 cm, 2 cm, 3 cm and 4 cm intersect each other to create maximum possible number of bounded regions. What is the minimum possible number of different colours required to fill in the bounded regions so that no two adjacent regions are filled with the same colour?

A) 5
B) 4
C) 3
D) 6
E) 7

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Source: Beat The GMAT — Problem Solving | Wed Feb 10, 2010 10:40 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Wed Feb 10, 2010 9:45 pm

shashank.ism wrote:Four circles having radius 1 cm, 2 cm, 3 cm and 4 cm intersect each other to create maximum possible number of bounded regions. What is the minimum possible number of different colours required to fill in the bounded regions so that no two adjacent regions are filled with the same colour?

A) 5
B) 4
C) 3
D) 6
E) 7

For maximum possible bounded regions,there will always be a 2-set intersection.Let the circles be A,B,C,D.
1st circle-color 1
2nd circle-color 2
3rd circle-color 1
4th circle-color 2
intersections of 2 sets will be of the 3rd color.[spoiler]
Hence,C.[/spoiler]

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