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

The question is from CAT Set theory. It is about union and intersection. Our task is to find out the union when there is no intersection. 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 10: Sonu started a new business with accounts in two different banks (i.e. Axis and SBI).He deposited the earnings of each day in either of the two banks. However he does not deposit his earnings in both the banks simultaneously on any given day. However somehow he could not carry the business for long and had to shut it down. Find the total no of days Sonu carried on the business if…
1) He did not deposited in axis bank on 20 days and in SBI on 24 days.
2) He deposited on either axis bank or SBI on 28 days.

1. 36
2. 18
3. 13
4. 24

Explanatory Answer

Method of solving this CAT Question from Set theory: It is just about solving simple equations!

Let the total No. of days Sonu deposited the earnings in Axis bank be ‘n(a)’ and
that in SBI be ‘n(b)’
Now,
Total no of days he carried on the business = n(a) + n(b) – n(a∩b) + Neither (Days he didn’t earned)
Since on any given day he does not deposit in both the bank accounts
n(a∩b) = 0
Hence,
Total no of days he carried on the business = n(a) + n(b) + Neither (Days he didn’t earned)
Now,
A/Q
Total – n(a) = 20……………………………(1)
Total – n(b) = 24……………………………(2)
n(a) + n(b) = 28………………………………(3)

Solving the 3 equations we get,
n(a) = 16
n(b) = 12
Total = 36
Hence the total number of days he carried on the business = 36

The question is "Find the total no of days Sonu carried on the business if…"

Hence, the answer is "36".

Choice A is the correct answer.