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There are 68 children in the cafeteria of a school and all of the chil

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There are 68 children in the cafeteria of a school and all of the chil [#permalink]

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New post 31 Mar 2017, 02:54
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Question Stats:

50% (02:07) correct 50% (01:47) wrong based on 82 sessions

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There are 68 children in the cafeteria of a school and all of the children have something for lunch. Thirty-four of the children brought lunches from home, 23 of the children bought a drink from the cafeteria beverage machine, and 32 of the children bought fruit in the cafeteria. If 18 children did at least 2 of these things, how many children did exactly two of these things?

A. 3
B. 6
C. 9
D. 13
E. 15
[Reveal] Spoiler: OA

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Re: There are 68 children in the cafeteria of a school and all of the chil [#permalink]

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New post 01 Apr 2017, 08:07
There are 68 children in the cafeteria of a school and all of the children have something for lunch. Thirty-four of the children brought lunches from home, 23 of the children bought a drink from the cafeteria beverage machine, and 32 of the children bought fruit in the cafeteria. If 18 children did at least 2 of these things, how many children did exactly two of these things?

A. 3
B. 6
C. 9
D. 13
E. 15

34 - Home lunch
34 - No home lunch

Scenario 1:
Out of 34 without Home lunch, lets say 32 with fruit from cafeteria & remaining 2 out of 23 drink from cafeteria. Therefore, 34 home lunch includes 21 with drink from cafeteria. Therefore, atleast 2 will be 34-21=13.

Scenario 2:
Out of 34 without Home lunch, lets say 23 with drink from cafeteria & remaining 11 out of 32 fruit from cafeteria. Therefore, 34 home lunch includes 21 with fruit from cafeteria. Therefore, atleast 2 will be 34-21=13.

Hence, answer is 13 (D).
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Re: There are 68 children in the cafeteria of a school and all of the chil [#permalink]

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New post 13 Apr 2017, 10:04
I m confused. Can somebody explain this using Venn diagram?
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Re: There are 68 children in the cafeteria of a school and all of the chil [#permalink]

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New post 13 Apr 2017, 10:40
As per the question stem total number of children having only one type of meal and having at least two meals would be equal to 50 and 18 respectively. Now, 50 =(34+23+32)-2(at least two)- all three and that implies all three = 3. Subsequently, only two = 18-3 =15 (AT LEAST TWO = ONLY 2 + ALL 3)
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Re: There are 68 children in the cafeteria of a school and all of the chil [#permalink]

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New post 13 Apr 2017, 10:45
34+23+32=89
89-68=21
21-18=3
So there are 3 children doing all 3 things
Leaves us with 21-(3×2)=15 children doing exactly 2 things

E

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Re: There are 68 children in the cafeteria of a school and all of the chil [#permalink]

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New post 13 Apr 2017, 21:08
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Re: There are 68 children in the cafeteria of a school and all of the chil [#permalink]

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New post 13 Apr 2017, 21:09
@parulM Please check The Venn Diagram ...According to me E will be the answer


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Re: There are 68 children in the cafeteria of a school and all of the chil   [#permalink] 13 Apr 2017, 21:09
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There are 68 children in the cafeteria of a school and all of the chil

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