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The question is from CAT Set theory. It is about Venn Diagrams. Our task is to draw the venn diagram without any mistakes. CAT exam is known to test on basics rather than high funda ideas. CAT also tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 3: Of 60 students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, 16 do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. What are the maximum and minimum number of people who could have done Chemistry only?

1. 40, 0
2. 28, 0
3. 38, 2
4. 44, 0

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Method of solving this CAT Question from Set theory: What are the maximum and minimum number of people who could have done Chemistry only?

Let us outline the diagram. Anyone who does Maths does Physics also.

Maths is a subset of Physics. Now, let us build on this.

No one does maths and chemistry, 16 do physics and chemistry.

Number outside is 0 as all the students do at least one of the three subjects

a + b + c +16 = 60, or a + b + c = 44

The number of people who do exactly one of the three is more than the number who do more than one of the three. => a + b > c + 16
So, we have a + b + c = 44 and a + b > c + 16
We need to find the maximum and minimum possible values of b.
Let us start with the minimum. Let b = 0, a + c = 44. a > c + 16. We could have
a = 40, c = 4. So, b can be 0.
Now, thinking about the maximum value. b = 44, a = c = 0 also works.

So, minimum value = 0, maximum value = 44.

The question is "What are the maximum and minimum number of people who could have done Chemistry only?"

Hence, the answer is "44 and 0".

Choice D is the correct answer.

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