Question on set

[Malabika Guha Mustafi]

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?  

 Hint{ People may not take maths and chemistry as a combination exclusively but may opt for three subjects}

[Sreenath V]

Chemistry only Students (Maximum Case)

Maths & Physics = 0

Physics & Chemistry = 16

Chemistry only is 60-16=44

Chemistry only Students (Minimum Case)

Maths & Physics = 13

Physics & Chemistry = 16

Chemistry Only Students = 31

[Malabika Guha Mustafi]

Maximum= 44

Minimum =0

[Anand Iyer]

Malabika,

I'm not sure if the hint is valid.  I think we'll get the right answers as you indicated last, without using the hint.  That is, no one does math and chemistry; and there are no students that do all 3 together.

[Anand Iyer]

yes, right.  Good problem...

On Sun, Nov 8, 2020 at 11:34 AM Malabika Guha Mustafi <malabi...@gmail.com> wrote:

See , the both way it is right, The trick is the maths student is actually subset of physics students.

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Cheers,

Anand

[Malabika Guha Mustafi]

See , the both way it is right, The trick is the maths student is actually subset of physics students.

[Malabika Guha Mustafi]

@ Anand, thank you.