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.

Question

Accepted Answer

The correct answer is option A. 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.

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