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Jack has 24 clients and he wants to use color coding to identify each

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Joined: 26 Dec 2018
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Location: India
Jack has 24 clients and he wants to use color coding to identify each  [#permalink]

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31 Dec 2018, 04:23
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75% (hard)

Question Stats:

53% (02:08) correct 47% (01:53) wrong based on 76 sessions

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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

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Joined: 09 Mar 2018
Posts: 1004
Location: India
Re: Jack has 24 clients and he wants to use color coding to identify each  [#permalink]

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31 Dec 2018, 04:42
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UB001 wrote:
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

In this question, we can use Combination and the answer options as minimum number of colors

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

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Jack has 24 clients and he wants to use color coding to identify each  [#permalink]

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31 Dec 2018, 06:38
UB001 wrote:
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

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.

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Re: Jack has 24 clients and he wants to use color coding to identify each  [#permalink]

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31 Dec 2018, 09:08
1
UB001 wrote:
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

using answer options we can solve

single color : 4
Double color : 4c2= 6
Three colors : 4c3= 4
total 4+6+4 = 14
but we need is 24 color for 24 clients

option B ; 5
single color : 5
double color : 5c2: 10
triple color : 5c3: 10

5+10+10 = 25; sufficient

IMO B
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Joined: 02 Aug 2009
Posts: 7757
Re: Jack has 24 clients and he wants to use color coding to identify each  [#permalink]

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12 Jan 2019, 01:42
UB001 wrote:
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

Copy of https://gmatclub.com/forum/john-has-12-clients-and-he-wants-to-use-color-coding-to-iden-107307.html
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Re: Jack has 24 clients and he wants to use color coding to identify each   [#permalink] 12 Jan 2019, 01:42
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