# Set Theory, Calendars, Clocks and Binomial Theorem

You are here: Home  CAT Questionbank   CAT Quant  Set Theory  Question 16

## Sets and Unions

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

Choice A. 120

## Detailed Solution

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

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!