Calendars — On which day of the week is Arti's birthday? Statements: I. Arti's birthday is after Wednesday but before Sunday. II. Arti's birthday is after Friday but before Tuesday.
Verbal Reasoning
Data Sufficiency
Difficulty: Medium
Choose an option
Answer
Correct Answer: Both Statements I and II together are sufficient, but neither alone is sufficient.
Explanation
Introduction / Context:We must uniquely identify a weekday using two range constraints.
Given Data / Assumptions:
- Week sequence: Mon, Tue, Wed, Thu, Fri, Sat, Sun.
- I: Day ∈ {Thu, Fri, Sat}.
- II: Day ∈ {Sat, Sun, Mon}.
Concept / Approach:Intersect the candidate sets from both statements.
Step-by-Step Solution:
From I, candidates are Thu/Fri/Sat.From II, candidates are Sat/Sun/Mon.Intersection = {Sat}. Hence, the birthday must be on Saturday.Verification / Alternative check:No other day satisfies both inequalities simultaneously; the intersection is a singleton.
Why Other Options Are Wrong:
- I alone: three possibilities remain.
- II alone: three possibilities remain.
- Either alone sufficient: false.
- Both together not sufficient: false.
Common Pitfalls:Misreading boundaries ('after' excludes the day mentioned; 'before' excludes the endpoint).
Final Answer:Both together are sufficient (Saturday).