Vincen wrote: ↑

Thu Mar 18, 2021 11:19 am

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

Answer: E

Source: GMAT Club Tests

We need to be able to create AT LEAST 12 codes (to represent the 12 clients).

Let's test the options, starting with the smallest value....answer choice E

So, can we get 12 or more color codes with 5 colors?
Let's see . . .
1-color codes = 5 (since there are 5 colors)
2-color codes = We need to choose 2 colors from 5. This can be accomplished in 5C2 ways (using combinations). 5C2 = 10

So, using 5 colors, the total number of color codes we can create = 5 + 10 = 15
Perfect!

The answer is 5 (E)