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 two 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 23: In a survey it was found that, the number of people that like only Pepsi, only Coke, both Coke and Pepsi and neither of them are 2n, 3n, \\frac{69}{n}\\), \\frac{69}{3n}\\) respectively. What is the no of people who drink coke?

1. 72
2. 49
3. Both a and b
4. cannot be determined

Explanatory Answer

Method of solving this CAT Question from Set theory: A small finding and an additon will take you through!

Since the no. of people cannot be in fraction in any situation. We can deduce that the values of n and 3n need to be factors of 69.
Thus the value of n can only be either 1 or 23.
So the no of people who drink coke is equal to 3n + \\frac{69}{n}\\) = 72 for both 1 and 23.

The question is "In a survey it was found that, the number of people that like only Pepsi, only Coke, both Coke and Pepsi and neither of them are 2n, 3n, \\frac{69}{n}\\), \\frac{69}{3n}\\) respectively."

Hence, the answer is "72".

Choice A is the correct answer.