Of 60 students in a class anyone who has chosen to study maths elects to do physics as well But no o...........

Quantitative Aptitude ( CCS) Set theory

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?

40, 0

28, 0

38, 2

44, 0

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Explanation:

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.
Hence, the answer is "44 and 0".