When is Anjali graduating? Statements: I. The date is before 4th and after 1st…
2023
When is Anjali graduating? Statements: I. The date is before 4th and after 1st Jan. II. The date is after 2nd and before 5th Jan.
- A.
Statement I alone is sufficient.
- B.
Statement II alone is sufficient.
- C.
Both statements put together are sufficient.
- D.
Both statements put together are not sufficient.
Attempted by 8 students.
Show answer & explanation
Correct answer: C
Concept
This is a Data Sufficiency problem. A single statement is SUFFICIENT only if it narrows the answer down to exactly ONE value. If a statement leaves two or more possibilities, it is insufficient on its own. When neither statement alone pins down a unique value, you test whether COMBINING them does. Translate each "before/after" condition into the exact set of allowed dates, then check the size of each set (and of their overlap).
Application
Read each clue as a strict inequality on the day of January, then list the integer days it permits:
Statement I: "before 4th and after 1st" means the day d satisfies 1 < d < 4, so d can be the 2nd or the 3rd. That is two possibilities, so Statement I alone does not fix a single date.
Statement II: "after 2nd and before 5th" means 2 < d < 5, so d can be the 3rd or the 4th. Again two possibilities, so Statement II alone does not fix a single date.
Both together: the day must lie in BOTH sets {2nd, 3rd} and {3rd, 4th}. The only day common to both is the 3rd, so combining the two clues leaves exactly one date: 3rd January.
Each statement alone gives two candidates, but their overlap is a single day, so only the two clues used together determine the graduation date.
Cross-check
Verify the lone survivor against both clues: is the 3rd "before 4th and after 1st"? Yes. Is it "after 2nd and before 5th"? Yes. And no other day satisfies both at once (the 2nd fails clue II, the 4th fails clue I), confirming the answer is unique only when both statements are used.