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There are 6 stores in town that had a total of 20 visitors

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There are 6 stores in town that had a total of 20 visitors [#permalink]

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There are 6 stores in town that had a total of 20 visitors on a particular day. However, only 10 people went shopping that day; some people visited more than one store. If 6 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?

A. 6
B. 8
C. 5
D. 9
E. 2
[Reveal] Spoiler: OA
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Re: Overlapping sets [#permalink]

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New post 09 Sep 2011, 05:04
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Since 6 people visited two stores each, 12 visitors (6+6) can be deducted from the total 20 visitors.
We now have 8 visitors to be filled in by the remaining 4 people whilst trying to maximize the visits a person could have made. (Note that we cannot consider the 6 people now, as they have visited exactly 2 stores)
The remaining four people (10-6) will be distributed such that the three people visit one store each i.e 1+1+1 and the fourth person visits 5 stores thereby maximizing the number of visits he has.
This can be understood easily by using slots as shown below:
6 slots for six stores: _ _ _ _ _ _
6 people visit exactly 2 stores: 6 6 _ _ _ _
This means, we have considered 12 of 20 visitors. Remaining - 8 visitors
3 people visit exactly 1 of the remaining 3 stores: 6 6 1 1 1 _
Thus we now have considered 15 visitors (6+6+1+1+1)
The 4th person now visits 5 stores: 6 7 2 2 2 1

So the answer is 5
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Re: Overlapping sets [#permalink]

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If 6 people visited exactly two stores each, number of visits so covered = 12

This leaves 8 visits to be accounted for among 4 people.
To find the largest number of stores anyone could have visited, assume that 3 of these 4 people visited just one store.

Therefore the last person would visit 8 - 3 = 5 stores

Option (C)
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Re: Overlapping sets [#permalink]

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New post 17 Sep 2011, 04:25
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since 6 people have visited 2 stores,the total of visiting of this ppl is 6*2=12
20-12=8 (the rest of visits) 10ppl-6 ppl=4 ppl

since at least 1 store is visited by each of ppl, and since to maximize one option we need to minimize the other ones , then 1+1+1 +x=8
x=5
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Re: There are 6 stores in town that had a total of 20 visitors [#permalink]

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New post 23 Nov 2014, 21:35
1 Person ---> 1 store = 1 visit. (as the question says that some people visited more than 1 store, meaning that there was at least 1 person who visited 1 store)
6 People ---> 2 store = 12 visit.
Remaining 3 People, to maximize the number of store visited by an individual, we minimize the store visited by other 2.
So,
2 people ---> 1 store = 2 visit.
Total visit remaining = 20 -1-12-2 = 5 visit. (which is done by the last person). Hope it helps.
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Re: There are 6 stores in town that had a total of 20 visitors [#permalink]

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ruturaj wrote:
There are 6 stores in town that had a total of 20 visitors on a particular day. However, only 10 people went shopping that day; some people visited more than one store. If 6 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?

A. 6
B. 8
C. 5
D. 9
E. 2


Given:
Total visits = 20
Total people = 10

6 people visited 2 stores.
Hence total visits accounter for = 6*2 = 12

Now, we are left with 8 visits and 4 people.
To maximize the visits by one person, we need to minimize by others.

So, 3 persons visit 1 store each
Left visits = 5, Left persons = 1
Hence the maximum number of visits = 5

Option C
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Re: There are 6 stores in town that had a total of 20 visitors [#permalink]

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New post 03 Oct 2016, 10:36
Though i understand and agree with the reasoning above, please can anyone let me know where did i go wrong with the below approach:

10 people went shopping, out of which 6 visited two stores each. Therefore, the number of visits=10+6=16. Since the total number of visits are 20, 4 additional visits are to be undertaken. Also, since each one has already visited minimum one store and because the number of visits has to be maximised, if one of the six guys who has already visited two stores each visits the remaining four stores, he would have visited 6 stores?

Thanks.
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Re: There are 6 stores in town that had a total of 20 visitors [#permalink]

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New post 04 Oct 2016, 09:32
WilDThiNg wrote:
Though i understand and agree with the reasoning above, please can anyone let me know where did i go wrong with the below approach:

10 people went shopping, out of which 6 visited two stores each. Therefore, the number of visits=10+6=16. Since the total number of visits are 20, 4 additional visits are to be undertaken. Also, since each one has already visited minimum one store and because the number of visits has to be maximised, if one of the six guys who has already visited two stores each visits the remaining four stores, he would have visited 6 stores?

Thanks.


The error is highlighted above. We are given that those 6 people visit EXACTLY two stores, so for the remaining stores, we need to choose a person other than these 6.
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Re: There are 6 stores in town that had a total of 20 visitors [#permalink]

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New post 26 Dec 2016, 04:36
ruturaj wrote:
There are 6 stores in town that had a total of 20 visitors on a particular day. However, only 10 people went shopping that day; some people visited more than one store. If 6 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?

A. 6
B. 8
C. 5
D. 9
E. 2



total visits = 20 , number of people = 10 let the people be. restriction criteria is 6 visitors has exactly 2 visits and each individual visited at least 1

people .......A:B:C:D:E:F:G:H:I:J
Visits 2:2:2:2:2:2:1:1:1:1
thus we have 4 visits left after satisfying the restrictive criteria above and only visitors G,H,I,J can make those extra visit because A,B,C,D,E,,F are restricted to 2 each.

thus any of visitors G.H.I.J can make the remaining 4 visits to total 5 visits

C
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Re: There are 6 stores in town that had a total of 20 visitors [#permalink]

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New post 29 Jun 2017, 22:13
ruturaj wrote:
There are 6 stores in town that had a total of 20 visitors on a particular day. However, only 10 people went shopping that day; some people visited more than one store. If 6 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?

A. 6
B. 8
C. 5
D. 9
E. 2


1. There are 20 visits by 10 people.
2. 6 people made exactly 2 visits i.,e a total of 12 visits
3. There are 4 people who made the remaining 8 visits.
4. Since we want to find the maximum possible visits by one person, we minimize the visits of the other 3 which has to be 3 visits , of 1 each
5. So the maximum number of visits possible is 8-3=5
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Re: There are 6 stores in town that had a total of 20 visitors [#permalink]

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New post 12 Apr 2018, 16:25
ruturaj wrote:
There are 6 stores in town that had a total of 20 visitors on a particular day. However, only 10 people went shopping that day; some people visited more than one store. If 6 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?

A. 6
B. 8
C. 5
D. 9
E. 2


We must recognize that when the problem says there are 20 visitors, it doesn’t mean there are 20 people (since it later says there are only 10 people). It really means, if a person visited one store, then he or she is considered as one visitor. However, if that person visited two stores, then he or she is considered as two visitors since each of the two stores he or she visited will consider him or her as one visitor. Similarly, if he or she visited three stores, then he or she is considered as three visitors and so on.

Since 6 people visited exactly two stores each, then they are considered to be 12 visitors. Thus we have 20 - 12 = 8 visitors left for the remaining 10 - 6 = 4 people. In order to maximize the number of stores visited for one person, we must minimize the number of stores visited for the other 3 individuals. Thus, if those 3 people each visited exactly 1 store, then they are considered to be 3 visitors. Thus, we have 8 - 3 = 5 visitors left for the last person, which means he or she must have visited 5 stores.

Answer: C
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Re: There are 6 stores in town that had a total of 20 visitors   [#permalink] 12 Apr 2018, 16:25
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