If February 1, 1996 is Wednesday, what day is March 3, 1996 ?

Question

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Correct — D, Saturday. Two facts decide it, and the second is the one the question is really testing. First, 1996 is a leap year: it is divisible by 4 and is not a century year, so February 1996 has 29 days, not 28. Second, count the gap. From 1 February to 3 March is 28 remaining days of February after the 1st, plus 3 days of March — that is 31 days in all. Divide by 7 and the remainder, the 'odd days', is 3, because 31 = 4 × 7 + 3. Three days after Wednesday is Saturday. The same result can be reached without any arithmetic by walking the Wednesdays down the month: if 1 February is a Wednesday then so are 8, 15, 22 and 29 February. The 29th being a Wednesday makes 1 March a Thursday, 2 March a Friday and 3 March a Saturday. Notice how the leap day does its work in that walk — because February has a 29th, the month ends on the same weekday it began, and March 1 lands one day later in the week rather than on the same day. In a common year February has exactly 28 days, four whole weeks and no remainder, so 1 March would fall on the same weekday as 1 February; the whole answer swings on that one extra day. Work the question this way, from the leap-year status outwards, and the arithmetic becomes a formality rather than the difficulty.

Why the other options are wrong — (a) This is what a real 1996 calendar gives — 1 February 1996 was in fact a Thursday and 3 March 1996 was a Sunday. The stem, however, states its own premise, 'If February 1, 1996 is Wednesday', and a reasoning question must be answered from its premise, not from the historical calendar. A candidate who half-remembers the real dates, or who consults them afterwards, will convince himself this is right.  (b) The classic leap-year error. Treat February 1996 as having 28 days and the gap becomes 30 days, giving 30 mod 7 = 2 odd days, and Wednesday plus 2 is Friday. Everyone who forgets that 1996 is divisible by 4 lands exactly here, which is why this is the most heavily set distractor of the three.  (c) Corresponds to 5 odd days from Wednesday and to no defensible count of the interval — it is the filler option, present to fill the fourth slot rather than to catch a specific mistake. If your working produces Monday, you have miscounted the days in the gap rather than made a leap-year error.

Concept: Day-of-the-week problems are solved by the odd-days method. An 'odd day' is the remainder when a stretch of days is divided by 7 — the number of days by which a weekday advances across that stretch. An ordinary year of 365 days carries 1 odd day (365 = 52 × 7 + 1), so a date moves forward one weekday each year; a leap year of 366 days carries 2. Month lengths behave the same way: a 31-day month contributes 3 odd days, a 30-day month contributes 2, February contributes 0 in a common year and 1 in a leap year. Because February alone is 0 in an ordinary year, dates in early March fall on the same weekday as the matching date in February — until a leap year breaks the pattern. The leap-year rule itself is precise: a year is a leap year if divisible by 4, except that a century year must also be divisible by 400. So 1996, 2004 and 2024 are leap years, 2000 is a leap year, and 1700, 1800, 1900 and 2100 are not. That exception is what keeps the Gregorian calendar aligned to the tropical year of about 365.2422 days, and it is a frequent source of exam questions in its own right.

State PCS 2024 Q78 — Science & Technology PYQ with Answer

State PCS 2024 Q78 — Science & Technology PYQ with Answer