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

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Intern
Joined: 17 Jun 2014
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Of 60 children, 30 are happy, 10 are sad, and 20 are neither  [#permalink]

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Updated on: 27 Jul 2014, 17:34
9
00:00

Difficulty:

15% (low)

Question Stats:

86% (02:09) correct 14% (02:38) wrong based on 178 sessions

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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

Originally posted by langtuprovn2007 on 27 Jul 2014, 17:30.
Last edited by Bunuel on 27 Jul 2014, 17:34, edited 1 time in total.
Edited the question and added the OA.
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Posts: 60694
Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither  [#permalink]

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27 Jul 2014, 17:41
1
3
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 [ 5.53 KiB | Viewed 4085 times ]
Numbers in black are given and in red are calculated.

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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27 Jul 2014, 23:07

Refer matrix below

Values in pink are calculated
Attachments

pink.png [ 4.23 KiB | Viewed 3990 times ]

Manager
Joined: 25 May 2014
Posts: 66
GMAT 1: 650 Q40 V40
Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither  [#permalink]

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02 Mar 2015, 19:40
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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02 Mar 2015, 20:21
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.

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.

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

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02 Mar 2015, 20:27
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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21 Jan 2018, 20:01
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.

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

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07 Dec 2019, 04:23
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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither   [#permalink] 07 Dec 2019, 04:23
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