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

The question is from CAT Set theory. It is about union of sets. We need to determine a particular value from three sets. 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 21: In class of 280 students, each student needs to choose between the three extra subject (i.e IT, Hindi and Sanskrit) offered along with the course. The students that choose each of these subjects are 160, 130, 110. The number of students who choose more than one of the three is 40% more than the number of students who choose all the three subjects If there are no students who choose none of the 3 subjects, how many students study all the three subjects?

1. 40
2. 50
3. 80
4. 100

Explanatory Answer

Method of solving this CAT Question from Set theory:

In this question there are 260 students who are counted 160 + 130 + 110 = 400 times
This means there is an extra count of 400 – 280 = 120 students

Now, let the no. of students who choose all the three Subject be ‘n’
Then as per the question, the no. of students who choose more than 1 subject = 1.4 n
Thus, the no of students who study exactly 2 subjects = 1.4 n – n = 0.4 n

Extra count can occur from exactly 2 areas i.e from the ‘exactly two areas’ or ‘all three area’. We also know that a student placed in in all the three area will be counted 3 times, thus the extra count being 2 while in the case of exactly two students extra count is 1.

Thus the extra count from n students choose 3 subjects would be = 2 * n = 2n
And that of 0.4 student choose exactly 2 subjects = 1 * 0.4 n = 0.4n
Hence extra count = 120 = 2n + 0.4n
=> 120 = 2.4 n
=> \\frac{120}{2.4}\\) = n
=> 50 = n
Hence the no of students who choose all the three subjects = 50

The question is "How many students study all the three subjects?"

Hence, the answer is "50".

Choice B is the correct answer.