Each of the questions given below consists of a statement and/or a question…

2024

Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question.

Read both the statements and Give answer

What day is 14th of a month?

I. 2nd last day of the month is Tuesday

II. 3rd Saturday of the month is seventeenth

  1. A.

    the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.

  2. B.

    if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.

  3. C.

    if the data in each Statement I and Statement II alone is sufficient to answer the question.

  4. D.

    if the data even in both Statements I and II together are not sufficient to answer the question.

Show answer & explanation

Correct answer: B

Concept: A statement is sufficient only if the information it gives fixes a single, unambiguous value for whatever is asked -- here, the day of the week for the 14th. Day-of-week problems reduce to modulo-7 arithmetic: moving n days forward or backward from a known weekday shifts that weekday by n mod 7 places, and this shift holds however many days the month itself has.

Checking Statement I:

  1. Statement I says the 2nd-last day of the month is Tuesday. But the date-number of the '2nd-last day' depends on how many days the month has (28, 29, 30, or 31), which is unknown.

  2. If the month has 31 days, the 2nd-last day is the 30th, so the 30th is Tuesday; counting back 16 days to the 14th (16 mod 7 = 2) makes the 14th a Sunday.

  3. If the month has 30 days, the 2nd-last day is the 29th, so the 29th is Tuesday; counting back 15 days (15 mod 7 = 1) makes the 14th a Monday.

  4. If the month has 29 days, the 2nd-last day is the 28th, so the 28th is Tuesday; counting back 14 days (14 mod 7 = 0) makes the 14th a Tuesday itself.

  5. If the month has 28 days, the 2nd-last day is the 27th, so the 27th is Tuesday; counting back 13 days (13 mod 7 = 6) makes the 14th a Wednesday.

  6. Since the day changes with the (unknown) month length, Statement I alone does not fix one unique day for the 14th.

Checking Statement II:

  1. Statement II says the 3rd Saturday of the month is the 17th, i.e. Saturdays fall on 3, 10, 17, 24 (and possibly 31) -- fixed regardless of month length.

  2. The 14th is exactly 3 days before the 17th.

  3. Shifting Saturday back by 3 (mod 7) gives Wednesday, so the 14th is Wednesday -- a result independent of the month's length.

  4. So Statement II alone fixes the 14th's day uniquely.

Cross-check: counting forward instead confirms it -- from the 14th (Wednesday) to the 17th is 3 days forward (Wed to Thu to Fri to Sat), landing on Saturday, matching Statement II. So the 14th is indeed Wednesday.

Conclusion: Statement II alone is sufficient to answer the question, while Statement I alone is not sufficient.

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