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 to solve this one. 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 20: In a survey it was found that 10% people don’t use Facebook, Twitter or Whatsapp.8% uses all the three. There are 15% who use Facebook and Twitter only, 20% who use Twitter and Whatsapp only and 20% who use Facebook and Whatsapp only. Number of people that use only Facebook, only Twitter and only Whatsapp are equal. If the survey was conducted on 1000 people, answer the following:

1. How many people use Whatsapp only?
   
   1. 20
   2. 9
   3. 15
   4. 90
2. What is the ratio of number of people that uses Whatsapp only to the people using either Whats app or Facebook or both?
   
   1. \\frac{1}{6}\\)
   2. \\frac{25}{75}\\)
   3. \\frac{1}{3}\\)
   4. \\frac{1}{9}\\)

Explanatory Answer

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

Let the no. of people that use only Facebook = only Twitter = only Whatsapp = x
Let’s construct of venn diagram:

From the figure we can see that x + x + x + 8 + 20 + 20 + 15 + 10 = 100
=> 3x = 100 – 73
=> x = \\frac{27}{3}\\) = 9
1. Thus the of no people who use Whatsapp only = 9% or 9 x 1000/100 = 90
2. % of people that use Whatsapp only = 9
% of people that use either Whatsapp or Facebook or both = 20 + 20 + 8 + 9 + 9 +15 = 81
Thus the ratio = \\frac{9}{81}\\) = \\frac{1}{9}\\)

The question is "How many people use Whatsapp only?"

The question is "What is the ratio of number of people that uses Whatsapp only to the people using either Whats app or Facebook or both?"

Hence, the answer is "90 and \\frac{1}{9}\\)" respectively.