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In a certain laboratory, chemicals are identified by a color-coding sy
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12 Dec 2018, 03:24
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58% (01:41) correct 42% (01:48) wrong based on 113 sessions
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In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?
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05 Jun 2019, 05:14
Bunuel wrote:
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?
A. 5 B. 6 C. 7 D. 20 E. 40
Shouldn't the approach to solve this question be the following:
Let the number of colours be 'n', and we have n + n(n-1)/2 >= 20
We get 2n + n^2 - n = 40, simplifying further we get n^2 + n = 40
Now, putting in the values (since we only require the minimum no. of colors), we see that n cannot be equal to 5 and 6 is the first (and the minimum) value that satisfies the equation.
In a certain laboratory, chemicals are identified by a color-coding sy
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12 Dec 2018, 03:33
Bunuel wrote:
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?
A. 5 B. 6 C. 7 D. 20 E. 40
6c1 +6c2 : 21
IMO 6 should be correct.. IMO b
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Re: In a certain laboratory, chemicals are identified by a color-coding sy
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12 Dec 2018, 10:07
Let say there are 2 colors : A & B. All possible combination would be A , B , AB. If there are 3 : A, B & C. Combinations would be A , B , C , AB, AC , BC.
In a certain laboratory, chemicals are identified by a color-coding sy
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04 Jan 2019, 03:19
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?
CONSIDER ANSWER CHOICES
5 colours
A,B,C,D,E AB, AC, AD, AE BC, BD, BE CD, CE DE falls short of 20.
6 colours
all the above + a new colour F F, FA, FB, FC,FD, FE totals 21.
Re: In a certain laboratory, chemicals are identified by a color-coding sy
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06 Jun 2019, 18:01
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Bunuel wrote:
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?
A. 5 B. 6 C. 7 D. 20 E. 40
Let’s analyze the answer choices.
If there are 5 different colors, the number of codes that can be formed is 5C1 + 5C2 = 5 + 10 = 15, which is not sufficient for the 20 different chemicals.
If there are 6 different colors, the number of codes that can be formed is 6C1 + 6C2 = 6 + 15 = 21, which IS sufficient for the 20 different chemicals. Therefore, we need at least 6 different colors.
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58% (01:41) correct 
