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# If 119 of the 200 children in a school like juice with their breakfast

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
If 119 of the 200 children in a school like juice with their breakfast  [#permalink]

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06 Dec 2016, 09:36
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Difficulty:

5% (low)

Question Stats:

90% (01:21) correct 10% (02:37) wrong based on 90 sessions

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If 119 of the 200 children in a school like juice with their breakfast, 113 like milk and 51 like to have both, how many like neither juice nor milk?

A. 83
B. 70
C. 51
D. 32
E. 19

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Re: If 119 of the 200 children in a school like juice with their breakfast  [#permalink]

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06 Dec 2016, 10:43
Bunuel wrote:
If 119 of the 200 children in a school like juice with their breakfast, 113 like milk and 51 like to have both, how many like neither juice nor milk?

A. 83
B. 70
C. 51
D. 32
E. 19

$$n (J) = 119$$

$$n (M) = 113$$

$$n ( M ∩ J ) = 51$$

$$n ( M ∪ J ) = n (J) + n (M) - n ( M ∩ J )$$

$$n ( M ∪ J ) = 119 + 113 - 51$$

$$n ( M ∪ J ) = 181$$

$$n ( M ∪ J )' = Σ - n ( M ∪ J )$$

$$n ( M ∪ J )' = 200 - 181$$

So, $$n ( M ∪ J )' = 19$$

Hence, Answer will be (E) 19

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Re: If 119 of the 200 children in a school like juice with their breakfast  [#permalink]

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08 Dec 2016, 10:24
Option E)

Total no. of students = 200

No. of students who like Juice = 119
No. of students who like Milk = 113
No. of students who like Both = 51

Total no. of students = No. of students who like only Juice + No. of students who like only Milk + No. of students who like Both + No. of students who like Neither
200 = (119 - 51) + (113 - 51) + 51 + No. of students who like Neither

No. of students who like Neither = 200 - 68 - 62 - 51 = 19
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Re: If 119 of the 200 children in a school like juice with their breakfast  [#permalink]

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08 Dec 2016, 10:55
1
I really like to emphasize on using the Manahattan Prep method for these kind of problems. See the image for the method and answer.

The given values are in green and the calculated values are in blue.

Please give Kudos+1 if you like the procedure.
Attachments

Untitled.png [ 50.42 KiB | Viewed 1088 times ]

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Re: If 119 of the 200 children in a school like juice with their breakfast  [#permalink]

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26 Feb 2018, 11:16
Bunuel wrote:
If 119 of the 200 children in a school like juice with their breakfast, 113 like milk and 51 like to have both, how many like neither juice nor milk?

A. 83
B. 70
C. 51
D. 32
E. 19

We can create the equation:

Total students = like milk + like juice - like both + like neither

200 = 113 + 119 - 51 + n

200 = 181 + n

19 = n

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Re: If 119 of the 200 children in a school like juice with their breakfast   [#permalink] 26 Feb 2018, 11:16
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