Question

On a particular day, who came earlier, Anita or Vani?
Statement 1: Anita came not later than 2 PM on that day
Statement 2: Vani came not earlier than 1 PM on that day

• A. statement (1) alone is sufficient to answer the question
• B. statement (2) alone is sufficient to answer the question
• C. both the statements together are needed to answer the question
• D. statement (1) alone or statement (2) alone is sufficient to answer the question
• E. neither statement (1) nor statement (2) suffices to answer the question

Answer 1

Answer: (E)

The correct answer is option (E):

neither statement (1) nor statement (2) suffices to answer the question

Let's analyze the given statements and determine if we can definitively say who came earlier.

Statement 1 tells us: Anita came not later than 2 PM. This means Anita could have arrived at 2 PM, or any time earlier than that. It gives us an upper bound on Anita's arrival time.

Statement 2 tells us: Vani came not earlier than 1 PM. This means Vani could have arrived at 1 PM, or any time later than that. It gives us a lower bound on Vani's arrival time.

Now, consider the possibilities:

* Scenario 1: Anita arrives at 1:30 PM, and Vani arrives at 2:30 PM. In this case, Anita came earlier.
* Scenario 2: Anita arrives at 2 PM, and Vani arrives at 1 PM. In this case, Vani came earlier.
* Scenario 3: Anita arrives at 1:00 PM and Vani arrives at 1:00 PM. In this case, Anita came and Vani came at the same time.

Since we can create scenarios where either Anita or Vani came earlier, or the arrival times are equal, neither statement alone, nor both statements combined provide enough information to definitively say who arrived earlier. Therefore, the answer is "neither statement (1) nor statement (2) suffices to answer the question".