BPSC 70th CCE Prelims General Studies · Question 78 of 143

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.

• (a)Sunday — 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)Friday — 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)Monday — 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.

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.

Approach every question of this type in three steps and it becomes mechanical. Step one: is the year a leap year? Step two: how many days lie between the two dates? Step three: take the remainder on division by 7 and count forward from the given weekday. Here that is yes, 31, remainder 3, Wednesday plus 3 equals Saturday. The single most common failure is skipping step one, and BPSC has set the distractors to catch precisely that — Friday is exactly two days after Wednesday, the answer for a 28-day February. Two habits protect you. Count the gap as 'days remaining in the first month plus days into the second month', never by subtracting date numbers, which quietly assumes equal month lengths. And answer from the premise the stem supplies: this question invents a Wednesday for a date that was actually a Thursday, which is entirely legitimate in a reasoning item and is why the historically correct Sunday appears among the options as a trap for the over-informed.

• Leap-year rule: divisible by 4, except century years, which must also be divisible by 400 — so 1996 and 2000 are leap years but 1900 and 2100 are not
• Odd days: an ordinary year carries 1, a leap year 2; a 31-day month carries 3, a 30-day month 2, February 0 in a common year and 1 in a leap year
• Here the interval 1 February to 3 March 1996 is 28 + 3 = 31 days, and 31 mod 7 = 3, so the weekday advances by three from Wednesday to Saturday
• Because 1996 is a leap year, 1 March falls one weekday later than 1 February; in a common year the two dates share a weekday
• In the real calendar 1 February 1996 was a Thursday and 3 March 1996 a Sunday — the stem's premise is hypothetical, and answering from the real calendar produces option (a)

• Forgetting that 1996 is a leap year and treating February as 28 days, which gives Friday
• Answering from the real 1996 calendar instead of the stem's stated premise, which gives Sunday
• Computing the gap by subtracting date numbers (3 minus 1) instead of counting days remaining in February plus days into March

BPSC keeps a small block of pure reasoning inside the General Studies paper, and the calendar item is almost always framed as 'if date X is weekday Y, what is date Z' with the interval crossing a month boundary — the leap year is the hidden variable in nearly every one of them. UPSC moved this kind of arithmetic out of the General Studies paper into the CSAT paper after 2011, and in General Studies now asks about calendars as systems instead — the Saka era, the Hijri calendar, the Gregorian reform — so the same word points at two different skills depending on the paper.

• practice — not a real PYQ

  If 1 March 2024 is a Friday, what day is 1 April 2024 ?

  • (a)Sunday
  • (b)Monday
  • (c)Tuesday
  • (d)Wednesday

  Answer(b) Monday — March has 31 days, so 31 mod 7 = 3 odd days, and Friday plus 3 is Monday. Note that the leap day of 2024 falls before 1 March and so does not affect this interval.

• practice — not a real PYQ

  Which of the following years is NOT a leap year ?

  • (a)1600
  • (b)1900
  • (c)2000
  • (d)2400

  Answer(b) 1900 — a century year is a leap year only if it is divisible by 400. 1600, 2000 and 2400 all pass that test; 1900 does not.