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.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
2. B. The Question can be answered by using either Statement alone.
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. D. The Question cannot be answered even by using both the Statements together.

Answer: A

Explanation

Let T be tea, C be coffee, M be milk. Given: |T|=75, |C|=60, |T∩C|=15. No one taking milk takes tea, so |M∩T|=0. Each person takes at least one drink.
Number of people taking only tea = 75 – 15 = 60.
Number of people taking only coffee = 60 – 15 = 45.
Number of people taking tea or coffee (or both) = 60 + 45 + 15 = 120.
Since |M∩T|=0, people taking milk either took only milk (M_only) or milk and coffee (M∩C). Total persons = 120 + M_only.
Statement 1: 50 persons took milk. This means M_only + M∩C = 50. We don’t know M_only or M∩C individually, so we cannot find the total persons. Not sufficient.
Statement 2: Total persons = 5 × (M_only). We know Total persons = 120 + M_only. So, 120 + M_only = 5 × M_only => 120 = 4 × M_only => M_only = 30. Then, Total persons = 120 + 30 = 150. This statement alone is sufficient.
Therefore, the question can be answered by using Statement 2 alone, but not Statement 1 alone.