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Of 60 children, 30 are happy, 10 are sad, and 20 are neither

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Of 60 children, 30 are happy, 10 are sad, and 20 are neither [#permalink]

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New post 27 Jul 2014, 16:30
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Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 20 boys and 40 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jul 2014, 16:34, edited 1 time in total.
Edited the question and added the OA.
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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither [#permalink]

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New post 27 Jul 2014, 16:41
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langtuprovn2007 wrote:
Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 20 boys and 40 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10


Check the table below:
Attachment:
Untitled.png
Untitled.png [ 5.53 KiB | Viewed 2906 times ]
Numbers in black are given and in red are calculated.

Answer: D.

Hope it's clear.
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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither [#permalink]

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New post 27 Jul 2014, 22:07
Answer = 8 =D

Refer matrix below

Values in pink are calculated
Attachments

pink.png
pink.png [ 4.23 KiB | Viewed 2815 times ]


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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither [#permalink]

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New post 02 Mar 2015, 18:40
Is it possible to solve this question via a venn diagram approach? I'd greatly appreciate a solution that uses venn diagrams.
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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither [#permalink]

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New post 02 Mar 2015, 19:21
GhostA wrote:
Is it possible to solve this question via a venn diagram approach? I'd greatly appreciate a solution that uses venn diagrams.


Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.

Table method is shown above; here is how you will use logic:

There are 6 happy boys.
There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.

We have 6 happy boys and 6 sad boys. Total we have 20 boys. So 20 - 6 - 6 = 8 boys must be neither happy nor sad.

Answer (D)
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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither [#permalink]

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New post 02 Mar 2015, 19:27
Thanks Karishma. That's what I guessed. I usually prefer venn diagrams and just wanted to explore if there are any options besides the table. Thanks again!
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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither [#permalink]

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New post 21 Jan 2018, 19:01
langtuprovn2007 wrote:
Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 20 boys and 40 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10


Since there are 6 happy boys, there must be 24 happy girls.

Since there are 4 sad girls, there must be 6 sad boys.

Since there are a total of 20 boys, then there must be 20 - 6 - 6 = 8 boys who are neither sad nor happy.

Answer: D
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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither   [#permalink] 21 Jan 2018, 19:01
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