Data sufficiency - total attendees using set theory
Question
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?
Options
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
The Question can be answered by using either Statement alone.
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
The Question cannot be answered even by using both the Statements together.
Explanation
First, analyze the tea and coffee users using set theory : Total(Tea \cup Coffee) = 75 + 60 - 15 = 120 persons .
The prompt states: "No one taking milk takes tea". This means the Milk group is completely disjoint from the Tea group, but it could overlap with the Coffee group (specifically the Coffee-only region, since the intersection of Tea and Coffee is barred)[cite: 4027, 4028]. Let's check the statements:
Statement 1: 50 persons took milk. We do not know how many of these 50 overlap with Coffee-only users, so we cannot find the unique total population. Insufficient .
Statement 2: Total attendance = 5 × (Milk only). Let total attendance T = 120 + (Milk only). Substitute this into the equation: 120 + (Milk only) = 5 × (Milk only) \implies 120 = 4 × (Milk only) \implies (Milk only) = 30. Therefore, T = 120 + 30 = 150. Statement 2 alone is completely sufficient.
Answer: (a).
Question details
Year
2023
Paper
CSAT
Question
Q58
Section
Data Interpretation & Sufficiency
Sub-topic
Data Sufficiency
Type
Data sufficiency
Difficulty
Medium
Source hint
Data sufficiency
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