QUESTION

CSAT

Easy

Maths

Prelims 2023

In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.

Question: how many persons attended the party? Statement-1: 50 persons took milk. Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.

Which one of the following is correct in respect of the above Question and the Statements?

Select an option to attempt

Explanation

In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. We can represent this information via a Venn diagram for better visualization.

Venn Diagram

Venn Diagram

You may notice that the circles representing Tea and Milk are not overlapping. That’s because no one taking milk takes tea.

Venn Diagram

Venn Diagram

We can further deduce the following information from the Venn diagram given above.

So, the total number of persons that attended the party = 75+45+y=120+y75 + 45 + y = 120 + y

Now, let’s consider the given statements. Statement 1: 50 persons took milk.

So, x+y=50x + y = 50. But using this we cannot find out the total number of persons that attended the party, as we cannot find the value of yy. So, Statement 1 alone is not sufficient.

Statement 2: Number of persons who attended the party is five times the number of persons who took milk only. So, 120+y=5y120 + y = 5y Or 4y=1204y = 120 Or y=30y = 30

So, the total number of persons that attended the party = 120+y=120+30=150120 + y = 120 + 30 = 150 So, Statement 2 alone is sufficient.

Hence, option (A) is correct.

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