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 ?

Correct Answer: (A) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.

Let $T, C, M$ represent sets of persons drinking tea, coffee, and milk. Given $|T| = 75$, $|C| = 60$, and $|T$$\cap$ C| = 15, the number of persons drinking tea or coffee is $|T$$\cup$ C| = 75 + 60 - 15 = 120. Since no one taking milk takes tea ($T$$\cap$ M = $\emptyset$), total attendees $N = |T$$\cup$ C| + m_0 = 120 + m_0, where $m_0$ is the number of persons taking milk only. Statement 1 gives total milk drinkers $|M| = 50$, but does not reveal how many took coffee ($M$$\cap$ C), leaving $m_0$ unknown. Statement 2 gives $N = 5m_0$, so $5m_0 = 120 + m_0$$\implies$ 4m_0 = 120 $\implies$ m_0 = 30, uniquely determining $N = 150$. Thus, Statement 2 alone is sufficient while Statement 1 alone is not.