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Gmat club PS.

by bblast » Tue May 24, 2011 9:59 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.

24
12
7
6
5

OA-e
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by djiddish98 » Tue May 24, 2011 10:11 am
We'll want to setup an equation where x + xC2 > 12

We can easily eliminate 24 and 12, since we don't need an individual color for each client if we can make pairs.

Start with the lowest amount

5 + 5C2 = 5 + 5!/(3!*2!) -> 5 + 5*4/2 -> 5 + 5*2 = 15. Since 15 > 12, we have enough colors with 5 colors to have 12 unique codes.
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by rohu27 » Tue May 24, 2011 5:16 pm
i thnk this is best solved using the answer choices.
start from the least value first. 5-> we can paint 5 indentities first. nxt it would 5c2 (as 12 is same as 21- we dnt want duplicate combos). so total 5+10=15
pick e
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