CAT 2020 Exam Shift 2 Solved Paper

Question : 59 of 76

Marks: +1, -0

Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18 , choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25 . The smallest possible number of students who could choose chemistry as one of their subjects is

Validate

Solution:

Let

a, b, c

represent number of students who opted for two subjects - Maths and Chemistry, Maths and Physics and Physics and Chemistry respectively.
Given,

a+b=23-18=5

and

b+c=25-18=7

Since

a, b

and

c

cannot be negative the least value for any of the three is 5 .
We get

a+c+18=(23+25-18)-2 b

Minimum value of number of students who chose chemistry

=23+25-18-10=20

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