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

CAT Questions | Set theory | Min and Max % of people

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 7: 95% of the students in a class have taken Marketing, 80% have chosen Finance, 84% have chosen operations (ops), and 90% have chosen Human Resources (HR). What is the maximum and minimum percentage of people who have chosen all of the four?

  1. 80% and 56%
  2. 95% and 53%
  3. 80% and 49%
  4. 80% and 51%

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

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

Finding the maximum percentage is easy. If F ⊂ O ⊂ H ⊂ M , then the percentage of people who have taken all 4 should be 80% and this is the maximum value it can take.

For the value to be minimum, the numbers should be as far ‘apart´ as possible. Let us do this iteratively. First, let us take Marketing and Finance, and see if we can find the minimum percentage of students who should have taken both.

CAT Question - Set theory

When M and F, are as far ‘apart´ as possible, M ∩ F would be minimum. And the minimum value would be 80% + 95% – 100% = 75%.
Now, let us start with this M ∪ F and add Ops to the mix.

CAT Question - Set theory

Now, the minimum value of M ∩ F ∩ O would be when these are as far ‘apart’ as possible. And the minimum value would be 75% + 84% – 100% = 59%.
Adding HR also to the mix, we get -

CAT Question - Set theory

The minimum possible value of M ∩ F ∩ O ∩ H = 59% + 90% – 100% = 49%.
As a formula, the minimum value is 100% – (100% – 95%) – (100% – 80%) – (100% – 84%) – (100% – 90%).
= 100% – 5% – 20% – 16% – 10% = 100% – 51% = 49%.

Again, do not go with just the formula. See the trial and error iteration. The trial and error iteration is far more useful than knowing the formula for a template.

The question is "What is the maximum and minimum percentage of people who have chosen all of the four?"

Hence, the answer is "80% and 49%".

Choice C is the correct answer.



CAT Online Coaching | CAT Arithmetic Videos On YouTube


Other useful sources for Arithmetic Questions | Set Theory Sample Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com