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UB001
Joined: 26 Dec 2018
Last visit: 10 Apr 2022
Posts: 106
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Location: India
Schools: Mannheim"20 Smurfit "20 NUS '21 NTU '20
31 Dec 2018, 04:23
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
64% (02:14) correct
36%
(02:15)
wrong
based on 176
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Jack has 24 clients and he wants to use color coding to identify each client. If a single color or two different colors or three 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 combination of two or three does not produce different codes.
A. 4
B. 5
C. 6
D. 12
E. 24
A. 4
B. 5
C. 6
D. 12
E. 24
KanishkM
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
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Schools: DeGroote'21 Desautels '21 NUS '21
31 Dec 2018, 04:42
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UB001
In this question, we can use Combination and the answer options as minimum number of colors
When you start with A=4
No of ways you can select 1 color out of 4 will be = 4
No of ways you can select 2 color out of 4 will be = 4C2 = 6
No of ways you can select 3 color out of 4 will be = 4
Giving total as 14 which is less than 24(Total number of clients)
Now you can take the number of colors = 5
No of ways you can select 1 color out of 5 will be = 5
No of ways you can select 2 color out of 5 will be = 5C2 = 10
No of ways you can select 3 color out of 5 will be = 5C3 = 10
Giving total as 25 which is more than 24(Total number of clients)
Thereby satisfying our condition and giving the answer as B
Correct Answer B.
31 Dec 2018, 06:38
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UB001
Using options would be a good way to go here.
12 and 24 are far too many. With 12 colours, you have distinct 12 colours fro 12 clients. Then combination of 2 colours with 12C2 gives another 66 distinct combinations and so on. So the answer must be one of 4/5/6.
Let's try 5 so we will know whether to go up or down (to 4 or 6)
With 5 colours, we can make 5 distinct single colour codes.
We can make 5C2 = 10 distinct double colour codes.
And we can make 5C3 = 10 distinct triple colour codes.
This gives us a total of 5+10+10 = 25 distinct colour codes. This is just enough to over 24 clients.
If we have any fewer colours, we will not be able to make 24 codes.
Answer (B)
