# Set Theory, Calendars, Clocks and Binomial Theorem

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## Sets and Unions

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, 69/n, 69/3n respectively.
1. 72
2. 49
3. Both a and b
4. cannot be determined

Choice A. 72

## Detailed Solution

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 + 69/n = 72 for both 1 and 23.Therefore,

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