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color combinations

by tonebeeze » Sun May 08, 2011 12:08 pm
John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes.

a. 24
b. 12
c. 7
d. 6
e. 5

OA = E
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by GMATGuruNY » Sun May 08, 2011 12:53 pm
tonebeeze wrote:John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes.

a. 24
b. 12
c. 7
d. 6
e. 5

OA = E
We can plug in the answers, which represent the minimum number of colors needed.
We should start with the smallest answer choice.

Answer choice E: 5 colors.
One color per client = 5 client codes.
Two colors per client = 5C2 = 10 client codes.
Total client codes = 5+10 = 15.
Since there are only 12 clients, 15 client codes is sufficient, and no more colors are needed.

The correct answer is E.
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