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?
Answer & explanation
Answer: (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
People taking tea or coffee number 75 + 60 − 15 = 120; everyone else took milk only. Statement 2 gives 120 + m = 5m, so m = 30 and 150 attended. Statement 1 does not say how many of the 50 milk drinkers also took coffee, so it cannot fix the total.
- Persons taking tea or coffee = 75 + 60 − 15 = 120.
- Everyone else takes milk only (milk drinkers never take tea). Let m = number taking milk only; total = 120 + m.
- Statement 1: 50 took milk, but some of them may also have taken coffee, so m is not fixed — not sufficient.
- Statement 2: 120 + m = 5m gives m = 30, so total = 150 — sufficient.
- So one Statement alone answers the Question and the other does not.
Remember · In set-based sufficiency, write the total as 'known union + unknown only-group' and see which statement pins down that group.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·