CAT Quantitative Aptitude Questions | CAT Set theory Questions - Union and Intersection

The question is from CAT Set theory. It is about venn diagrams. We just need to draw the 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 2023. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 14: In a class of 345 students, the students who took English, Math and Science are equal in number. There are 30 students who took both English and Math, 26 who took both Math and Science, 28 who took Science and English and 14 who took all the 3 subjects.There are 43 students who didn’t take any of the subjects. Answer the following question according to the data given above.
How many students have taken only one subject?

1. 286
2. 124
3. 246
4. 108

Explanatory Answer

Method of solving this CAT Question from Set theory: If you get the Venn Diagram right, you are halfway through !!

Let total no of students who took English be x
Then students who took math, science will also be x
Now let’s draw the Venn diagram

E U M U S = 345 – 43 (Neither of the subjects)
E U M U S = E + M + S – E ∩ M - E ∩ S - S ∩ M + E ∩ M ∩ S
=> 302 = 3x - 84 + 14
=> 302 + 84 – 14 = 3x
=> x = \\frac{372}{3}\\) = 124
Thus the total no of students who took English as a subject = 124
Consequently the Venn diagram becomes

Again,
The students who has taken only one subject = E U M U S - E ∩ M - E ∩ S - S ∩ M - E ∩ M ∩ S
= 302 - 16 - 14 - 14 - 12 = 246
The students who took English and Math but not science = only E + Only M + E ∩ M
= 80 + 82 + 16 = 178
Percent of students who took English and Math but not science = \\frac{178}{302}\\) * 100 = approx. 59 %

The question is "How many students have taken only one subject?"

Hence, the answer is "246".

Choice C is the correct answer.