Determine on which day in January 2001 Shaurabh purchased the watch. Statement…

2025

Determine on which day in January 2001 Shaurabh purchased the watch.

Statement I: The purchase was certainly before 11 January 2001 but not before 8 January 2001.

Statement II: The purchase was certainly after 9 January 2001 but not later than 12 January 2001.

  1. A.

    The statement I alone is sufficient in answering the problem question

  2. B.

    Statement II alone is sufficient in answering the problem question

  3. C.

    Both statements put together are sufficient in answering the problem question

  4. D.

    Both the statements even put together are not sufficient in answering the problem question

Show answer & explanation

Correct answer: C

Concept

In a data-sufficiency question, a statement (alone or in combination) is sufficient only if it narrows the possibilities down to exactly one value. If more than one value remains consistent with the given condition(s), that condition is insufficient, however precise it may sound.

Application

  1. Statement I: "before 11 January" means the date is at most 10 January, and "not before 8 January" means it is at least 8 January. So Statement I allows three possible days: 8, 9, or 10 January -- more than one value survives, so Statement I alone is NOT sufficient.

  2. Statement II: "after 9 January" means the date is at least 10 January, and "not later than 12 January" means it is at most 12 January. So Statement II allows three possible days: 10, 11, or 12 January -- again more than one value survives, so Statement II alone is NOT sufficient.

  3. Combine both windows: the days allowed by Statement I are {8, 9, 10} and the days allowed by Statement II are {10, 11, 12}. Their intersection contains exactly one day. Using both statements together therefore narrows the answer down to that single unique day.

Cross-check

Cross-check: test the shared day against each statement independently -- it is before 11 January and not before 8 January (Statement I holds), and it is after 9 January and not later than 12 January (Statement II holds); no other day in either three-day window satisfies both conditions at once, confirming the intersection is unique.

Result

Result: Statement I alone leaves three possibilities and Statement II alone leaves three possibilities, but the two statements together pin down exactly one day. Hence both statements put together are sufficient, while neither is sufficient alone.

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