Question

In a class of 175 students, the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 60; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered mathematics alone?
A.35
B.48
C.60
D.22

Answer 1

Hint: Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.

Complete step by step solution:
In this question, we are given data showing the number of students opting for different subjects. We are given that 100 students opted Mathematics; 60 opted Physics; 40 opted Chemistry; 30 opted Mathematics and Physics; 28 opted Mathematics and Chemistry; 23 opted Physics and Chemistry; and 18 opted Mathematics, Physics and Chemistry. And we have to find the number of students who opted only mathematics. So, to find it we will use the given data to formulate an equation.
We have to find the number of students who have offered only mathematics. We know that –
n(Only Mathematics) = n(Mathematics) – [ n(Mathematics and Physics) + n(Mathematics and Chemistry)- n(Mathematics, Chemistry and Physics)]
We know that –
n(Mathematics) = 100
n(Mathematics, Chemistry and Physics) = 18
n(Mathematics and Physics) = 30
n(Mathematics and Chemistry) = 28
So, we get –
$
  n(Only\,Mathematics) = 100 - (30 + 28 - 18) \\
   \Rightarrow n(Only\,Mathematics) = 100 - 40 \\
   \Rightarrow n(Only\,Mathematics) = 60 \;
 $
So the number of students who offered only mathematics is 60.
Hence option (C) is the correct answer.
So, the correct answer is “Option C”.

Note: We know the total number of students who have opted mathematics, so it includes the students who have opted only mathematics, mathematics and physics, mathematics and chemistry and all of them. The number of students who have opted mathematics and physics; and mathematics and chemistry, also includes the students who have opted all three subjects. So, we subtract the number of students opting all the subjects and the sum of the number of students opting mathematics and chemistry, and mathematics and physics; and then subtract the whole expression from the total number of students opting mathematics to get the number of students who have opted only mathematics.