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

Question

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

Bunuel · Accepted Answer

Check the table below: Untitled.png Numbers in black are given and in red are calculated. Answer: D. Hope it's clear.

PareshGmat · Answer

Answer = 8 =D

Refer matrix below

Values in pink are calculated

GhostA · Answer

Is it possible to solve this question via a venn diagram approach? I'd greatly appreciate a solution that uses venn diagrams.

KarishmaB · Answer

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)

GhostA · Answer

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!

ScottTargetTestPrep · Answer

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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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

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