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An artist is planning on mixing together any number of diffe

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Senior Manager
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An artist is planning on mixing together any number of diffe [#permalink] New post 05 Oct 2017, 20:40
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12% (00:00) correct 87% (01:27) wrong based on 8 sessions
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

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[Reveal] Spoiler: OA
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Re: An artist is planning on mixing together any number of diffe [#permalink] New post 05 Oct 2017, 22:15
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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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Re: An artist is planning on mixing together any number of diffe [#permalink] New post 03 Nov 2018, 07:02
For 8 colors, no. of mixtures the artist makes must be 8C2+8C3+8C4+8C5+8C6+.... which is (2^8 - 8C0 - 8C1)
For 9 colors, the number is 2^9 - 9C0 - 9C1 which is > 500.
Hence, the number of colors on palette is EIGHT!
Re: An artist is planning on mixing together any number of diffe   [#permalink] 03 Nov 2018, 07:02
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