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A firm decides to inspect 48 of its distribution centers.They have a

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A firm decides to inspect 48 of its distribution centers.They have a [#permalink]

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New post 30 Jul 2017, 08:36
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A firm decides to inspect 48 of its distribution centers.They have a staff of 23 employees available for the inspection.If each person will inspect at least 1 center and at most 4 centers, what is the maximum and the minimum number of people who will inspect 4 centers, if all the 48 centers will be inspected?

A. (8,2)
B. (8,0)
C. (9,0)
D. (9,2)
E. (9,1)
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jul 2017, 20:19, edited 5 times in total.
Renamed the topic.

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Re: A firm decides to inspect 48 of its distribution centers.They have a [#permalink]

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New post 30 Jul 2017, 11:16
DH99 wrote:
A firm decides to inspect 48 of its distribution centers.They have a staff of 23 employees available for the inspection.If each person will inspect at least 1 center and at most 4 centers, what is the maximum and the minimum number of people who will inspect 4 centers, if all the 48 centers will be inspected?

A. (8,2)
B. (8,0)
C. (9,0)
D. (9,2)
E. (9,1)


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Re: A firm decides to inspect 48 of its distribution centers.They have a [#permalink]

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New post 30 Jul 2017, 12:08
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DH99 wrote:
A firm decides to inspect 48 of its distribution centers.They have a staff of 23 employees available for the inspection.If each person will inspect at least 1 center and at most 4 centers, what is the maximum and the minimum number of people who will inspect 4 centers, if all the 48 centers will be inspected?

A. (8,2)
B. (8,0)
C. (9,0)
D. (9,2)
E. (9,1)


Lets start with the easier calculation to find min employees.
-If each employees goes to one one center..we cover 23 center
- for each employee to 2 center ... we cover 46 center
- with employee to 3 shop...>48 center
so min is 0 employee can go to 4 center

This leaves with option B and C
- Lets pick 9,0. if we have 9 people going to 4 center we have covered 9*4=36 shops.
employee left are 23-9=14 and center left are 48-36=12.

Hence not a options as 14-12=2 will still be left to visit any center

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Re: A firm decides to inspect 48 of its distribution centers.They have a [#permalink]

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New post 01 Aug 2017, 00:21
DH99 wrote:
A firm decides to inspect 48 of its distribution centers.They have a staff of 23 employees available for the inspection.If each person will inspect at least 1 center and at most 4 centers, what is the maximum and the minimum number of people who will inspect 4 centers, if all the 48 centers will be inspected?

A. (8,2)
B. (8,0)
C. (9,0)
D. (9,2)
E. (9,1)


For maximum number of people, 48-23= 25
After each person inspects one center 25 centers will be left. In order to inspect 4 centers some people has to inspect 3 more centers. We know 3*8= 24. So, out of 23 people 8 will inspect 4 centers, 1 will inspect 2 centers (remaining one after 24 out of 25 centers are inspected) and remaining people will inspect 1 center each.
Maximum: 8

For minimum number of people, 23*2= 46
If each person inspects 2 centers, a total of 46 centers' inspection is done. We are left with 2 centers which we can divide among any 2 persons. Thus, 2 of the 23 people will inspect 3 centers and rest will inspect 2 centers. So, there is a possibility where none of the 23 people investigates 4 centers.
Minimum: 0

Answer: B. (8,0)
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Re: A firm decides to inspect 48 of its distribution centers.They have a   [#permalink] 01 Aug 2017, 00:21
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A firm decides to inspect 48 of its distribution centers.They have a

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