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

###### CAT Questions | Set theory | Union and Intersection
CAT Questions

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 2020. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 15: 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 only, 26 who took both Math and Science only, 28 who took Science and English only 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.
What percent of students did not take Science?

1. Less than 55%
2. approx. 59%
3. 72%
4. 79%

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##### 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 "What percent of students took English and Math but not Science?" ##### Hence, the answer is "approx. 59%". Choice B is the correct answer. ###### 🐤 Early Bird Offer! 4,000 off on CAT '22 Online courses. Valid until 25th July ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Coaching | CAT Arithmetic Videos On YouTube #### Other useful sources for Arithmetic Questions | Set Theory Sample Questions ##### 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
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