color combinations

[tonebeeze]

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

[GMATGuruNY]

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.