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 16: In a survey conducted to know people’s preference for android phones and I phones, 80 person preferred android phones while 60 person preferred I phones. There were 20 who liked both and may prefer any. If there was no one who didn’t prefer at least one of the phones,then on how many people was the survey conducted?

1. 120
2. 40
3. 80
4. 60

Explanatory Answer

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

Diagrammatic Approach -

It is quite clear from the diagram that the number of people at the party were 60 + 20 + 40 = 120
Mathematical approach :
Let n(A) be the no. of persons that prefers android phones , the no of persons that prefers IOS be n(B) and n(A∩B) be the persons who liked both may prefer both.
Thus using the formula n(AUB) = n(A) + n(B) – n(A∩B)
n(AUB) = 80 + 60 – 20 = 120

The question is "How many people was the survey conducted?"

Hence, the answer is "120".

Choice A is the correct answer.