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Of 60 children, 30 are happy, 10 are sad, and 20 are neither
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Updated on: 27 Jul 2014, 17:34
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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
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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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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither
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27 Jul 2014, 17:41
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. Answer: D. Hope it's clear.
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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither
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27 Jul 2014, 23:07
Answer = 8 =D Refer matrix below Values in pink are calculated
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pink.png [ 4.23 KiB  Viewed 3990 times ]



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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither
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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
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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. 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
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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
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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. Answer: D
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Re: Of 60 children, 30 are happy, 10 are sad, and 20 are neither
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07 Dec 2019, 04:23
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