Bunuel wrote:
An artist is planning on mixing together any number of different colors from her palette. A mixture results as long as the artist combines at least two colors. If the number of possible mixtures is less than 500, what is the greatest number of colors the artist could have in her palette?
(A) 8
(B) 9
(C) 11
(D) 12
(E) 13
Kudos for correct solution.
Since we have to mix at least 2 colors to form a mixture so we can write as -
1 color = 2 mixture
2 color = 2 * 2 =4 mixture
3 color = 2 * 2 * 2 = 8 mixture
4 color = 2 * 2 * 2 * 2 = 16 mixture
5 color = 2 * 2 * 2 * 2 * 2 = 32 mixture
6 color = 2 * 2 * 2 * 2 * 2 * 2 = 64 mixture
7 color = 2 * 2 * 2 * 2 * 2 * 2 * 2 = 128 mixture
8 color = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 256 mixture
9 color = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 512 mixture
so there are 8 colors, because if we use 9 then total becomes > 500
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